---
title: "NCERT Solutions for Class 6 Maths Chapter 7 Fractions (2026-27)"
url: https://www.swavid.com/maths/class/6/chapter/fractions/ncert-solutions
dateModified: 2026-10-07T14:55:07+00:00
---

# NCERT Solutions for Class 6 Maths Chapter 7 Fractions (2026-27)

This chapter's questions cover foundational concepts of fractions including equal shares, fractional units, number line representation, mixed fractions, equivalent fractions, comparing fractions, addition and subtraction of fractions, and historical context.

Free PDF (31 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-6/swavid-ncert-solutions-class-6-maths-chapter-7-fractions-e718fb7729.pdf

## Figure it Out (Page 152)

### Question 1

*1 mark · Fill in the blank*

Three guavas together weigh $1\text{ kg}$. If they are roughly of the same size, each guava will roughly weigh ____ $\text{kg}$.

**Solution**

1. Divide the total weight of $1\text{ kg}$ equally among the 3 guavas to get $\frac{1}{3}\text{ kg}$.

**Answer:** $\frac{1}{3}$

> Common mistake: Writing 3 instead of $\frac{1}{3}$.

### Question 2

*1 mark · Fill in the blank*

A wholesale merchant packed $1\text{ kg}$ of rice in four packets of equal weight. The weight of each packet is ___ $\text{kg}$.

**Solution**

1. Divide the total weight of $1\text{ kg}$ equally into 4 packets to get $\frac{1}{4}\text{ kg}$.

**Answer:** $\frac{1}{4}$

> Common mistake: Writing 4 instead of $\frac{1}{4}$.

### Question 3

*1 mark · Fill in the blank*

Four friends ordered $3$ glasses of sugarcane juice and shared it equally among themselves. Each one drank ____ glass of sugarcane juice.

**Solution**

1. Divide the 3 glasses of sugarcane juice equally among 4 friends to get $\frac{3}{4}$ glass.

**Answer:** $\frac{3}{4}$

> Common mistake: Reversing the numerator and denominator to write $\frac{4}{3}$.

### Question 4

*1 mark · Fill in the blank*

The big fish weighs $\frac{1}{2}\text{ kg}$. The small one weighs $\frac{1}{4}\text{ kg}$. Together they weigh ____ $\text{kg}$.

**Solution**

1. Add the weight of the big fish and the small fish by finding a common denominator: $\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

**Answer:** $\frac{3}{4}$

> Common mistake: Adding numerators and denominators directly to get $\frac{2}{6}$.

### Question 5

*3 marks · Short answer*

Arrange these fraction words in order of size from the smallest to the biggest in the empty box below:
One and a half, three quarters, one and a quarter, half, quarter, two and a half.

**Solution**

1. Translate each fraction word into numerical form: quarter = $\frac{1}{4}$, half = $\frac{1}{2}$, three quarters = $\frac{3}{4}$, one and a quarter = $1\frac{1}{4}$, one and a half = $1\frac{1}{2}$, two and a half = $2\frac{1}{2}$.
2. Compare the whole number parts and fractional parts: $\frac{1}{4} < \frac{1}{2} < \frac{3}{4} < 1\frac{1}{4} < 1\frac{1}{2} < 2\frac{1}{2}$.
3. Arrange the fraction words from smallest to biggest as: Quarter, half, three quarters, one and a quarter, one and a half, two and a half.

**Answer:** Quarter, half, three quarters, one and a quarter, one and a half, two and a half

> Common mistake: Confusing 'one and a quarter' ($1\frac{1}{4}$) with 'three quarters' ($\frac{3}{4}$) or misordering proper fractions and mixed numbers.

## Figure it Out (Page 155)

### Question 1

*3 marks · Short answer*

The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece?
(a) to (h)

**Part a (0.375 marks)**

1. Observe the whole chikki divided into 12 equal parts.
2. Each piece represents one part out of 12 equal parts.

Answer a: $\frac{1}{12}$

**Part b (0.375 marks)**

1. Observe the whole chikki divided into 4 equal parts.
2. Each piece represents one part out of 4 equal parts.

Answer b: $\frac{1}{4}$

**Part c (0.375 marks)**

1. Observe the whole chikki divided into 8 equal parts.
2. Each piece represents one part out of 8 equal parts.

Answer c: $\frac{1}{8}$

**Part d (0.375 marks)**

1. Observe the whole chikki divided into 6 equal parts.
2. Each piece represents one part out of 6 equal parts.

Answer d: $\frac{1}{6}$

**Part e (0.375 marks)**

1. Observe the whole chikki divided into 8 equal parts.
2. Each piece represents one part out of 8 equal parts.

Answer e: $\frac{1}{8}$

**Part f (0.375 marks)**

1. Observe the whole chikki divided into 6 equal parts.
2. Each piece represents one part out of 6 equal parts.

Answer f: $\frac{1}{6}$

**Part g (0.375 marks)**

1. Observe the whole chikki divided into 24 equal parts.
2. Each piece represents one part out of 24 equal parts.

Answer g: $\frac{1}{24}$

**Part h (0.375 marks)**

1. Observe the whole chikki divided into 24 equal parts.
2. Each piece represents one part out of 24 equal parts.

Answer h: $\frac{1}{24}$

**Answer:** The fractional values of the chikki pieces are (a) $\frac{1}{12}$, (b) $\frac{1}{4}$, (c) $\frac{1}{8}$, (d) $\frac{1}{6}$, (e) $\frac{1}{8}$, (f) $\frac{1}{6}$, (g) $\frac{1}{24}$, (h) $\frac{1}{24}$.

> Common mistake: Counting only the shaded part incorrectly without checking the total number of equal parts the whole chikki is divided into.

## Figure it Out (Page 158)

### Question 1

*3 marks · Short answer*

Continue this table of $\frac{1}{2}$ for 2 more steps.

**Solution**

1. The pattern adds successive halves to represent multiples of $\frac{1}{2}$.
2. Step 6: $\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 6 \text{ times } \frac{1}{2}$
3. Step 7: $\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 7 \text{ times } \frac{1}{2}$

**Answer:** $$\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 6 \text{ times } \frac{1}{2}$$\n$$\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 7 \text{ times } \frac{1}{2}$$

> Common mistake: Counting the number of terms incorrectly.

### Question 2

*3 marks · Short answer*

Can you create a similar table for $\frac{1}{4}$?

**Solution**

1. For $\frac{1}{4}$, 1-time quarter is $\frac{1}{4}$.
2. 2 times quarter is $\frac{1}{4} + \frac{1}{4} = \frac{2}{4}$.
3. 3 times quarter is $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4}$, and 4 times quarter is $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{4}{4}$.

**Answer:** A table showing 1 to 4 times $\frac{1}{4}$ as sums of unit fractions.

> Common mistake: Writing multiplication instead of repeated addition as shown in the textbook table.

### Question 3

*Activity*

Make $\frac{1}{3}$ using a paper strip. Can you use this to also make $\frac{1}{6}$?

**Solution**

1. Step 1: Fold a paper strip into 3 equal parts to make $\frac{1}{3}$.
2. Step 2: Fold each of those three parts into two equal parts to divide the whole strip into 6 equal parts, thereby making $\frac{1}{6}$.

**Answer:** Yes, by folding each third into two equal parts.

### Question 4

*3 marks · Short answer*

Draw a picture and write an addition statement as above to show:
a. $5\text{ times } \frac{1}{4} \text{ of a roti}$
b. $9\text{ times } \frac{1}{4} \text{ of a roti}$

**Part a (1.5 marks)**

1. Draw 5 quarters of a roti (equivalent to 1 full roti and 1 quarter roti).
2. Write the addition statement: $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{5}{4} = 1 \frac{1}{4}$.

Answer a: $$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{5}{4} = 1 \frac{1}{4}$$

**Part b (1.5 marks)**

1. Draw 9 quarters of a roti (equivalent to 2 full rotis and 1 quarter roti).
2. Write the addition statement: $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{9}{4} = 2 \frac{1}{4}$.

Answer b: $$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{9}{4} = 2 \frac{1}{4}$$

**Answer:** Represented both fractions as sums of unit fractions with corresponding pictures showing rotis.

> Common mistake: Forgetting to write the addition statement with repeated unit fractions or miscounting the number of terms.

### Question 5

*3 marks · Short answer*

Match each fractional unit with the correct picture:

**Solution**

1. Step 1: Count the total number of equal parts in each circle to find the denominator.
2. Step 2: Match $\frac{1}{3}$ with the circle divided into 3 parts, $\frac{1}{5}$ into 5 parts, $\frac{1}{6}$ into 6 parts, and $\frac{1}{8}$ into 8 parts.

**Answer:** $\frac{1}{3} \rightarrow \text{3-part circle}, \frac{1}{5} \rightarrow \text{5-part circle}, \frac{1}{6} \rightarrow \text{6-part circle}, \frac{1}{8} \rightarrow \text{8-part circle}$

> Common mistake: Confusing the number of shaded parts with the fractional unit value.

## Figure it Out (Page 160)

### Question 1

*3 marks · Short answer*

On a number line, draw lines of lengths $\frac{1}{10}$, $\frac{3}{10}$, and $\frac{4}{5}$.

**Solution**

1. Draw a straight line with arrows on both ends and mark 0 and 1 at a suitable distance.
2. Divide the unit length between 0 and 1 into 10 equal parts so that each small division represents $\frac{1}{10}$.
3. Mark $\frac{1}{10}$ at the first division, $\frac{3}{10}$ at the third division, and $\frac{4}{5}$ (which is equivalent to $\frac{8}{10}$) at the eighth division from 0.

**Answer:** Fractions $\frac{1}{10}$, $\frac{3}{10}$, and $\frac{4}{5}$ marked on the number line.

> Common mistake: Marking $\frac{4}{5}$ incorrectly by dividing the unit into only 5 parts when $\frac{1}{10}$ is also required, instead of using a common denominator of 10.

### Question 2

*3 marks · Short answer*

Write five more fractions of your choice and mark them on the number line.

**Solution**

1. Choose any five fractions, such as $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, $\frac{1}{5}$, and $\frac{3}{5}$.
2. Draw a number line and mark the whole numbers 0 and 1.
3. Divide the unit length into required equal parts and place points corresponding to each chosen fraction.

**Answer:** Five fractions chosen and marked on the number line.

> Common mistake: Incorrectly spacing the subdivisions on the number line.

### Question 3

*3 marks · Short answer*

How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.

**Solution**

1. Observe that between any two fractions, we can always find another fraction (for example, by taking their average or by finding equivalent fractions with larger denominators).
2. As we can continue this process without end, we can write fractions with denominators like 10, 100, 1000, and so on.
3. Therefore, an uncountable number of fractions lie between 0 and 1.

**Answer:** Uncountable number of fractions

> Common mistake: Stating that only a finite number of fractions exist between 0 and 1.

### Question 4

*3 marks · Short answer*

What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is $\frac{1}{2}$. So the blue line is $\frac{1}{2}$ units long. Write the fraction that gives the length of the black line in the box.

**Solution**

1. Note that the distance between 0 and 1 is divided into two equal parts, each of length $\frac{1}{2}$.
2. The black line extends from 0 past 1, covering three equal parts of length $\frac{1}{2}$ up to the mark after 1.
3. The total length of the black line is therefore $3 \times \frac{1}{2} = \frac{3}{2}$ units.

**Answer:** $\frac{3}{2}$

> Common mistake: Counting only the fractional part beyond 1 instead of measuring total length from 0.

### Question 5

*3 marks · Short answer*

Write the fraction that gives the lengths of the black lines in the respective boxes.

**Solution**

1. Identify that the unit length between 0 and 1 is divided into 5 equal parts, so each small division is $\frac{1}{5}$.
2. Count the number of $\frac{1}{5}$ units from 0 to the end of each black line.
3. The respective lengths correspond to 6 parts ($\frac{6}{5}$), 7 parts ($\frac{7}{5}$), 8 parts ($\frac{8}{5}$), and 9 parts ($\frac{9}{5}$).

**Answer:** $\frac{6}{5}$, $\frac{7}{5}$, $\frac{8}{5}$, $\frac{9}{5}$

> Common mistake: Starting the count from 1 instead of 0 when reading fractions greater than one.

## Figure it Out (Page 162)

### Question 1

*2 marks · Very short answer*

How many whole units are there in $\frac{7}{2}$?

**Solution**

1. $\frac{7}{2} = 3 + \frac{1}{2}$
2. Therefore, there are 3 whole units in $\frac{7}{2}$.

**Answer:** 3 whole units

> Common mistake: Writing the numerator instead of finding the whole part.

### Question 2

*2 marks · Very short answer*

How many whole units are there in $\frac{4}{3}$ and in $\frac{7}{3}$?

**Solution**

1. $\frac{4}{3} = 1 + \frac{1}{3}$, so there is 1 whole unit in $\frac{4}{3}$.
2. $\frac{7}{3} = 2 + \frac{1}{3}$, so there are 2 whole units in $\frac{7}{3}$.

**Answer:** 1 whole unit in $\frac{4}{3}$ and 2 whole units in $\frac{7}{3}$

> Common mistake: Confusing the remainder with the whole number part.

## Figure it Out (Page 162)

### Question 1

*2 marks · Very short answer*

Figure out the number of whole units in each of the following fractions:
a. $\frac{8}{3}$
b. $\frac{11}{5}$
c. $\frac{9}{4}$

**Part a**

1. Divide the numerator by the denominator: $8 \div 3 = 2$ with a remainder of $2$, so there are $2$ whole units.

Answer a: 2

**Part b**

1. Divide the numerator by the denominator: $11 \div 5 = 2$ with a remainder of $1$, so there are $2$ whole units.

Answer b: 2

**Part c**

1. Divide the numerator by the denominator: $9 \div 4 = 2$ with a remainder of $1$, so there are $2$ whole units.

Answer c: 2

**Answer:** a. 2, b. 2, c. 2

> Common mistake: Confusing the remainder with the number of whole units.

### Question 2

*3 marks · Short answer*

Can all fractions greater than 1 be written as such mixed numbers?

**Solution**

1. A fraction greater than 1 has a numerator larger than its denominator.
2. When we divide the numerator by the denominator, we get a whole number quotient and a remainder.
3. If the remainder is zero, the fraction is a whole number (such as $\frac{8}{4} = 2$), which represents a whole number part with a zero fractional part, so it can be considered as a mixed number or whole number.

**Answer:** Yes, all fractions greater than 1 can be written as mixed numbers or whole numbers.

> Common mistake: Thinking that fractions whose numerator is a multiple of the denominator cannot be written as mixed fractions.

### Question 3

*3 marks · Short answer*

Write the following fractions as mixed fractions (e.g., $\frac{9}{2} = 4\frac{1}{2}$):
a. $\frac{9}{2}$
b. $\frac{9}{5}$
c. $\frac{21}{19}$
d. $\frac{47}{9}$
e. $\frac{12}{11}$
f. $\frac{19}{6}$

**Part a (0.5 marks)**

1. Divide $9$ by $2$, giving a quotient of $4$ and a remainder of $1$.
2. Write the mixed fraction as $4\frac{1}{2}$.

Answer a: $4\frac{1}{2}$

**Part b (0.5 marks)**

1. Divide $9$ by $5$, giving a quotient of $1$ and a remainder of $4$.
2. Write the mixed fraction as $1\frac{4}{5}$.

Answer b: $1\frac{4}{5}$

**Part c (0.5 marks)**

1. Divide $21$ by $19$, giving a quotient of $1$ and a remainder of $2$.
2. Write the mixed fraction as $1\frac{2}{19}$.

Answer c: $1\frac{2}{19}$

**Part d (0.5 marks)**

1. Divide $47$ by $9$, giving a quotient of $5$ and a remainder of $2$.
2. Write the mixed fraction as $5\frac{2}{9}$.

Answer d: $5\frac{2}{9}$

**Part e (0.5 marks)**

1. Divide $12$ by $11$, giving a quotient of $1$ and a remainder of $1$.
2. Write the mixed fraction as $1\frac{1}{11}$.

Answer e: $1\frac{1}{11}$

**Part f (0.5 marks)**

1. Divide $19$ by $6$, giving a quotient of $3$ and a remainder of $1$.
2. Write the mixed fraction as $3\frac{1}{6}$.

Answer f: $3\frac{1}{6}$

**Answer:** a. $4\frac{1}{2}$, b. $1\frac{4}{5}$, c. $1\frac{2}{19}$, d. $5\frac{2}{9}$, e. $1\frac{1}{11}$, f. $3\frac{1}{6}$

> Common mistake: Writing the remainder in the denominator instead of the numerator of the fractional part.

## Figure it Out (Page 163)

### Question 1

*3 marks · Short answer*

Write the following mixed numbers as fractions:
a. $3\frac{1}{4}$
b. $7\frac{2}{3}$
c. $9\frac{4}{9}$
d. $3\frac{1}{6}$
e. $2\frac{3}{11}$
f. $3\frac{9}{10}$

**Part a (0.5 marks)**

1. $3\frac{1}{4} = 3 + \frac{1}{4} = 1 + 1 + 1 + \frac{1}{4}$
2. $= \left(\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}\right) + \left(\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}\right) + \left(\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}\right) + \frac{1}{4}$
3. $= \frac{13}{4}$

Answer a: $\frac{13}{4}$

**Part b (0.5 marks)**

1. $7\frac{2}{3} = 7 + \frac{2}{3}$
2. $= \frac{7 \times 3}{3} + \frac{2}{3}$
3. $= \frac{21 + 2}{3} = \frac{23}{3}$

Answer b: $\frac{23}{3}$

**Part c (0.5 marks)**

1. $9\frac{4}{9} = 9 + \frac{4}{9}$
2. $= \frac{9 \times 9}{9} + \frac{4}{9}$
3. $= \frac{81 + 4}{9} = \frac{85}{9}$

Answer c: $\frac{85}{9}$

**Part d (0.5 marks)**

1. $3\frac{1}{6} = 3 + \frac{1}{6}$
2. $= \frac{3 \times 6}{6} + \frac{1}{6}$
3. $= \frac{18 + 1}{6} = \frac{19}{6}$

Answer d: $\frac{19}{6}$

**Part e (0.5 marks)**

1. $2\frac{3}{11} = 2 + \frac{3}{11}$
2. $= \frac{2 \times 11}{11} + \frac{3}{11}$
3. $= \frac{22 + 3}{11} = \frac{25}{11}$

Answer e: $\frac{25}{11}$

**Part f (0.5 marks)**

1. $3\frac{9}{10} = 3 + \frac{9}{10}$
2. $= \frac{3 \times 10}{10} + \frac{9}{10}$
3. $= \frac{30 + 9}{10} = \frac{39}{10}$

Answer f: $\frac{39}{10}$

**Answer:** See sub-parts for answers.

> Common mistake: Multiplying the whole number by the denominator and forgetting to add the numerator.

## Answer the following questions after looking at the fraction wall (Page 164)

### Question 1

*2 marks · Very short answer*

Are the lengths $\frac{1}{2}$ and $\frac{3}{6}$ equal?

**Solution**

1. Observe the lengths of $\frac{1}{2}$ and $\frac{3}{6}$ on the fraction wall in the textbook (Fig. 7.6).
2. Both fractions occupy the exact same length on the fraction wall, so they are equal.

**Answer:** Yes, the lengths $\frac{1}{2}$ and $\frac{3}{6}$ are equal.

> Common mistake: Writing 'no' without checking the alignment of fraction strips on the fraction wall.

### Question 2

*3 marks · Short answer*

Are $\frac{2}{3}$ and $\frac{4}{6}$ equivalent fractions? Why?

**Solution**

1. Look at the fraction wall in the textbook (Fig. 7.6) to compare the lengths of $\frac{2}{3}$ and $\frac{4}{6}$.
2. The lengths represented by $\frac{2}{3}$ and $\frac{4}{6}$ are equal as they cover the exact same horizontal span.
3. Since they denote the same length expressed in terms of different fractional units, they are equivalent fractions.

**Answer:** Yes, $\frac{2}{3}$ and $\frac{4}{6}$ are equivalent fractions because they represent the same length.

> Common mistake: Forgetting to explain why they are equivalent fractions.

### Question 3

*2 marks · Very short answer*

How many pieces of length $\frac{1}{6}$ will make a length of $\frac{1}{2}$?

**Solution**

1. Refer to the fraction wall in the textbook (Fig. 7.6) and align pieces of length $\frac{1}{6}$ with the length $\frac{1}{2}$.
2. We can see that exactly 3 pieces of length $\frac{1}{6}$ make up the length of $\frac{1}{2}$.

**Answer:** 3 pieces of length $\frac{1}{6}$ will make a length of $\frac{1}{2}$.

> Common mistake: Counting 2 pieces or 6 pieces by misreading the fraction wall strips.

### Question 4

*2 marks · Very short answer*

How many pieces of length $\frac{1}{6}$ will make a length of $\frac{1}{3}$?

**Solution**

1. Refer to the fraction wall in the textbook (Fig. 7.6) and check how many $\frac{1}{6}$ pieces fit into the length of $\frac{1}{3}$.
2. We observe that 2 pieces of length $\frac{1}{6}$ make a length of $\frac{1}{3}$.

**Answer:** 2 pieces of length $\frac{1}{6}$ will make a length of $\frac{1}{3}$.

> Common mistake: Confusing the number of $\frac{1}{6}$ pieces for $\frac{1}{3}$ with those for $\frac{1}{2}$.

## Figure it Out (Page 165)

### Question 1

*3 marks · Short answer*

Are $\frac{3}{6}$, $\frac{4}{8}$, $\frac{5}{10}$ equivalent fractions? Why?

**Solution**

1. Observe the given fractions $\frac{3}{6}$, $\frac{4}{8}$, and $\frac{5}{10}$.
2. Look at the fraction wall given in the textbook.
3. Since all these fractions represent the same length or share on the fraction wall, they are equivalent fractions.

**Answer:** Yes, they are equivalent fractions because their lengths are equal on the fraction wall.

> Common mistake: Thinking fractions with different numerators and denominators cannot represent the same value.

### Question 2

*3 marks · Short answer*

Write two equivalent fractions for $\frac{2}{6}$.

**Solution**

1. Take the given fraction $\frac{2}{6}$.
2. Multiply or divide both the numerator and denominator by the same non-zero number to find an equivalent fraction, such as dividing by 2 to get $\frac{1}{3}$.
3. Multiply both the numerator and denominator by another number, such as 3, to get $\frac{6}{18}$, or use the fraction wall to find another equivalent fraction like $\frac{3}{9}$.

**Answer:** Two equivalent fractions for $\frac{2}{6}$ are $\frac{1}{3}$ and $\frac{3}{9}$.

> Common mistake: Multiplying only the numerator or only the denominator instead of both.

### Question 3

*3 marks · Short answer*

$\frac{4}{6} = \dots = \dots = \dots = \dots \dots\dots\dots\dots$ (Write as many as you can)

**Solution**

1. Take the given fraction $\frac{4}{6}$.
2. Divide both numerator and denominator by 2 to get $\frac{2}{3}$.
3. Multiply both numerator and denominator by 2, 3, 4, and so on to write more equivalent fractions such as $\frac{8}{12}$, $\frac{12}{18}$, and $\frac{16}{24}$.

**Answer:** $\frac{4}{6} = \frac{2}{3} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \dots$

> Common mistake: Adding the same number to numerator and denominator instead of multiplying or dividing both.

## Figure it Out (Page 166)

### Question 1

*3 marks · Short answer*

Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.

**Part i (1 mark)**

1. Three rotis divided equally among four children gives each child a share of $\frac{3}{4}$ roti.

Answer i: $\frac{3}{4}$ roti

**Part ii (2 marks)**

1. The division fact is $3 \div 4 = \frac{3}{4}$.
2. The addition fact is $3 = \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}$.
3. The multiplication fact is $3 = 4 \times \frac{3}{4}$.

Answer ii: Division fact: $3 \div 4 = \frac{3}{4}$, Addition fact: $3 = \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}$, Multiplication fact: $3 = 4 \times \frac{3}{4}$

**Answer:** Each child gets $\frac{3}{4}$ roti.

> Common mistake: Confusing the numerator and denominator in the fraction.

### Question 2

*3 marks · Short answer*

Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

**Solution**

1. Total number of rotis = 2, total number of children = 4, so each child gets $\frac{2}{4}$ or $\frac{1}{2}$ of a roti.
2. Division fact: $2 \div 4 = \frac{2}{4}$ (or $\frac{1}{2}$)
3. Addition fact: $2 = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$
4. Multiplication fact: $2 = 4 \times \frac{1}{2}$

**Answer:** Each child gets $\frac{1}{2}$ roti; Division fact: $2 \div 4 = \frac{1}{2}$, Addition fact: $2 = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$, Multiplication fact: $2 = 4 \times \frac{1}{2}$

> Common mistake: Writing the addition and multiplication facts with the total and share values reversed.

### Question 3

*2 marks · Very short answer*

Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

**Solution**

1. When 2 cakes are divided equally among 5 children, the share of each child is given by dividing 2 by 5.
2. Anil will get $\frac{2}{5}$ of a cake.

**Answer:** $\frac{2}{5}$ cake

> Common mistake: Writing the fraction as $\frac{5}{2}$ instead of $\frac{2}{5}$.

## Figure it Out (Page 168)

### Question 1

*3 marks · Short answer*

Find the missing numbers:
a. 5 glasses of juice shared equally among 4 friends is the same as ____ glasses of juice shared equally among 8 friends. So, $\frac{5}{4} = \frac{\dots}{8}$.
b. $4\text{ kg}$ of potatoes divided equally in 3 bags is the same as $12\text{ kgs}$ of potatoes divided equally in ___ bags. So, $\frac{4}{3} = \frac{12}{\dots}$.
c. 7 rotis divided among 5 children is the same as ____ rotis divided among _____ children. So, $\frac{7}{5} = \frac{\dots}{\dots}$.

**Part a (1 mark)**

1. We are given the relation $\frac{5}{4} = \frac{\square}{8}$.
2. The denominator 4 is multiplied by 2 to get 8.
3. To keep the fractions equivalent, multiply the numerator 5 by 2 to get $5 \times 2 = 10$.

Answer a: 10

**Part b (1 mark)**

1. We are given the relation $\frac{4}{3} = \frac{12}{\square}$.
2. The numerator 4 is multiplied by 3 to get 12.
3. To keep the fractions equivalent, multiply the denominator 3 by 3 to get $3 \times 3 = 9$.

Answer b: 9

**Part c (1 mark)**

1. We are given the relation $\frac{7}{5} = \frac{\square}{\square}$.
2. We can find an equivalent fraction by multiplying both the numerator and the denominator by the same number, such as 2.
3. Multiplying both by 2 gives $\frac{7 \times 2}{5 \times 2} = \frac{14}{10}$.

Answer c: 14 and 10 (or any other equivalent fraction pair)

**Answer:** Completed statements with missing numbers: (a) 10, (b) 9, (c) 14 and 10

> Common mistake: Multiplying only the numerator or only the denominator instead of both by the same number.

## Figure it Out (Page 170)

### Question 1

*3 marks · Short answer*

Group 1 : 3 glasses of sugarcane juice divided equally among 4 children.
Group 2: 7 glasses of sugarcane juice divided equally among 10 children.

**Solution**

1. The share of each child in Group 1 is $\frac{3}{4}$ glasses of sugarcane juice.
2. The share of each child in Group 2 is $\frac{7}{10}$ glasses of sugarcane juice.
3. To compare $\frac{3}{4}$ and $\frac{7}{10}$, we find equivalent fractions with a common denominator, which is $4 \times 10 = 40$.
4. $\frac{3}{4} = \frac{3 \times 10}{4 \times 10} = \frac{30}{40}$ and $\frac{7}{10} = \frac{7 \times 4}{10 \times 4} = \frac{28}{40}$.
5. Since $\frac{30}{40} > \frac{28}{40}$, the children in Group 1 get a larger share.

**Answer:** Each child in Group 1 gets a larger share.

> Common mistake: Comparing the numerators or denominators directly without converting them to fractions with the same fractional unit.

### Question 2

*3 marks · Short answer*

Group 1 : 4 glasses of sugarcane juice divided equally among 7 children.
Group 2: 5 glasses of sugarcane juice divided equally among 7 children.

**Part (ii) (3 marks)**

1. Each child's share in Group 1 is $\frac{4}{7}$ glasses of juice.
2. Each child's share in Group 2 is $\frac{5}{7}$ glasses of juice.
3. Since the denominators (number of children) are the same, compare the numerators.
4. Since $5 > 4$, $\frac{5}{7} > \frac{4}{7}$.
5. Therefore, each child in Group 2 gets a larger share.

Answer (ii): Group 2

**Answer:** Group 2

> Common mistake: Thinking the group with fewer shared units gets more even when denominators are equal.

## Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. (Page 172)

### Question 1

*3 marks · Short answer*

Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
a. $\frac{7}{2}$ and $\frac{3}{5}$
b. $\frac{8}{3}$ and $\frac{5}{6}$
c. $\frac{3}{4}$ and $\frac{3}{5}$
d. $\frac{6}{7}$ and $\frac{8}{5}$
e. $\frac{9}{4}$ and $\frac{5}{2}$
f. $\frac{1}{10}$ and $\frac{2}{9}$
g. $\frac{8}{3}$ and $\frac{11}{4}$
h. $\frac{13}{6}$ and $\frac{1}{9}$

**Part (a) (1 mark)**

1. Given fractions are $\frac{7}{2}$ and $\frac{3}{5}$.
2. The common denominator is $2 \times 5 = 10$.
3. $\frac{7 \times 5}{2 \times 5} = \frac{35}{10}$ and $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$.

Answer (a): $\frac{35}{10}$ and $\frac{6}{10}$

**Part (b) (1 mark)**

1. Given fractions are $\frac{8}{3}$ and $\frac{5}{6}$.
2. The common denominator can be taken as 6.
3. $\frac{8 \times 2}{3 \times 2} = \frac{16}{6}$ and $\frac{5}{6}$ remains $\frac{5}{6}$.

Answer (b): $\frac{16}{6}$ and $\frac{5}{6}$

**Part (c) (1 mark)**

1. Given fractions are $\frac{3}{4}$ and $\frac{3}{5}$.
2. The common denominator is $4 \times 5 = 20$.
3. $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$ and $\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$.

Answer (c): $\frac{15}{20}$ and $\frac{12}{20}$

**Part (d) (1 mark)**

1. Given fractions are $\frac{6}{7}$ and $\frac{8}{5}$.
2. The common denominator is $7 \times 5 = 35$.
3. $\frac{6 \times 5}{7 \times 5} = \frac{30}{35}$ and $\frac{8 \times 7}{5 \times 7} = \frac{56}{35}$.

Answer (d): $\frac{30}{35}$ and $\frac{56}{35}$

**Part (e) (1 mark)**

1. Given fractions are $\frac{9}{4}$ and $\frac{5}{2}$.
2. The common denominator can be taken as 4.
3. $\frac{9}{4}$ remains $\frac{9}{4}$ and $\frac{5 \times 2}{2 \times 2} = \frac{10}{4}$.

Answer (e): $\frac{9}{4}$ and $\frac{10}{4}$

**Part (f) (1 mark)**

1. Given fractions are $\frac{1}{10}$ and $\frac{2}{9}$.
2. The common denominator is $10 \times 9 = 90$.
3. $\frac{1 \times 9}{10 \times 9} = \frac{9}{90}$ and $\frac{2 \times 10}{9 \times 10} = \frac{20}{90}$.

Answer (f): $\frac{9}{90}$ and $\frac{20}{90}$

**Part (g) (1 mark)**

1. Given fractions are $\frac{8}{3}$ and $\frac{11}{4}$.
2. The common denominator is $3 \times 4 = 12$.
3. $\frac{8 \times 4}{3 \times 4} = \frac{32}{12}$ and $\frac{11 \times 3}{4 \times 3} = \frac{33}{12}$.

Answer (g): $\frac{32}{12}$ and $\frac{33}{12}$

**Part (h) (1 mark)**

1. Given fractions are $\frac{13}{6}$ and $\frac{1}{9}$.
2. The common denominator can be taken as 18.
3. $\frac{13 \times 3}{6 \times 3} = \frac{39}{18}$ and $\frac{1 \times 2}{9 \times 2} = \frac{2}{18}$.

Answer (h): $\frac{39}{18}$ and $\frac{2}{18}$

**Answer:** Equivalent fractions obtained by using common denominators.

> Common mistake: Multiplying only the numerator or denominator instead of both by the same number when finding equivalent fractions.

## Figure it Out (Page 173)

### Question 1

*3 marks · Short answer*

Express the following fractions in lowest terms:
a. $\frac{17}{51}$
b. $\frac{64}{144}$
c. $\frac{126}{147}$
d. $\frac{525}{112}$

**Part a**

1. Find the common factor of $17$ and $51$, which is $17$.
2. Divide both the numerator and the denominator by $17$: $\frac{17 \div 17}{51 \div 17} = \frac{1}{3}$.
3. Hence, the fraction in lowest terms is $\frac{1}{3}$.

Answer a: $\frac{1}{3}$

**Part b**

1. Find the highest common factor of $64$ and $144$, which is $16$.
2. Divide both the numerator and the denominator by $16$: $\frac{64 \div 16}{144 \div 16} = \frac{4}{9}$.
3. Hence, the fraction in lowest terms is $\frac{4}{9}$.

Answer b: $\frac{4}{9}$

**Part c**

1. Find the highest common factor of $126$ and $147$, which is $21$.
2. Divide both the numerator and the denominator by $21$: $\frac{126 \div 21}{147 \div 21} = \frac{6}{7}$.
3. Hence, the fraction in lowest terms is $\frac{6}{7}$.

Answer c: $\frac{6}{7}$

**Part d**

1. Find the highest common factor of $525$ and $112$, which is $7$.
2. Divide both the numerator and the denominator by $7$: $\frac{525 \div 7}{112 \div 7} = \frac{75}{16}$.
3. Hence, the fraction in lowest terms is $\frac{75}{16}$.

Answer d: $\frac{75}{16}$

**Answer:** a. $\frac{1}{3}$, b. $\frac{4}{9}$, c. $\frac{6}{7}$, d. $\frac{75}{16}$

> Common mistake: Stopping before dividing completely by the highest common factor, leaving a common factor other than 1.

## Figure it Out (Page 174)

### Question 1

*3 marks · Short answer*

Compare the following fractions and justify your answers:
a. $\frac{8}{3}$, $\frac{5}{2}$
b. $\frac{4}{9}$, $\frac{3}{7}$
c. $\frac{7}{10}$, $\frac{9}{14}$
d. $\frac{12}{5}$, $\frac{8}{5}$
e. $\frac{9}{4}$, $\frac{5}{2}$

**Part a (0.6 marks)**

1. Find a common denominator for $\frac{8}{3}$ and $\frac{5}{2}$, which is $3 \times 2 = 6$.
2. Convert both fractions: $\frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6}$ and $\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}$.
3. Since $\frac{16}{6} > \frac{15}{6}$, we get $\frac{8}{3} > \frac{5}{2}$.

Answer a: \frac{8}{3} > \frac{5}{2}

**Part b (0.6 marks)**

1. Find a common denominator for $\frac{4}{9}$ and $\frac{3}{7}$, which is $9 \times 7 = 63$.
2. Convert both fractions: $\frac{4}{9} = \frac{4 \times 7}{9 \times 7} = \frac{28}{63}$ and $\frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63}$.
3. Since $\frac{28}{63} > \frac{27}{63}$, we get $\frac{4}{9} > \frac{3}{7}$.

Answer b: \frac{4}{9} > \frac{3}{7}

**Part c (0.6 marks)**

1. Find a common denominator for $\frac{7}{10}$ and $\frac{9}{14}$, using their lowest common multiple $70$.
2. Convert both fractions: $\frac{7}{10} = \frac{7 \times 7}{10 \times 7} = \frac{49}{70}$ and $\frac{9}{14} = \frac{9 \times 5}{14 \times 5} = \frac{45}{70}$.
3. Since $\frac{49}{70} > \frac{45}{70}$, we get $\frac{7}{10} > \frac{9}{14}$.

Answer c: \frac{7}{10} > \frac{9}{14}

**Part d (0.6 marks)**

1. Both fractions $\frac{12}{5}$ and $\frac{8}{5}$ already have the same denominator, which is $5$.
2. Compare their numerators: $12 > 8$.
3. Therefore, $\frac{12}{5} > \frac{8}{5}$.

Answer d: \frac{12}{5} > \frac{8}{5}

**Part e (0.6 marks)**

1. Find a common denominator for $\frac{9}{4}$ and $\frac{5}{2}$, which is $4$.
2. Convert the second fraction: $\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}$.
3. Compare with $\frac{9}{4}$: since $\frac{9}{4} < \frac{10}{4}$, we get $\frac{9}{4} < \frac{5}{2}$.

Answer e: \frac{9}{4} < \frac{5}{2}

**Answer:** Compared all pairs by finding equivalent fractions with a common denominator.

> Common mistake: Comparing numerators directly when denominators are different.

### Question 2

*3 marks · Short answer*

Write the following fractions in ascending order.
a. $\frac{7}{10}$, $\frac{11}{15}$, $\frac{2}{5}$
b. $\frac{19}{24}$, $\frac{5}{6}$, $\frac{7}{12}$

**Part a (1.5 marks)**

1. The denominators are $10$, $15$, and $5$. The smallest common multiple is $30$.
2. Convert each fraction to have $30$ as the denominator: $\frac{7}{10} = \frac{21}{30}$, $\frac{11}{15} = \frac{22}{30}$, and $\frac{2}{5} = \frac{12}{30}$.
3. Compare numerators: $12 < 21 < 22$, so $\frac{12}{30} < \frac{21}{30} < \frac{22}{30}$.
4. Write in ascending order: $\frac{2}{5} < \frac{7}{10} < \frac{11}{15}$.

Answer a: \frac{2}{5} < \frac{7}{10} < \frac{11}{15}

**Part b (1.5 marks)**

1. The denominators are $24$, $6$, and $12$. The smallest common multiple is $24$.
2. Convert each fraction to have $24$ as the denominator: $\frac{19}{24} = \frac{19}{24}$, $\frac{5}{6} = \frac{20}{24}$, and $\frac{7}{12} = \frac{14}{24}$.
3. Compare numerators: $14 < 19 < 20$, so $\frac{14}{24} < \frac{19}{24} < \frac{20}{24}$.
4. Write in ascending order: $\frac{7}{12} < \frac{19}{24} < \frac{5}{6}$.

Answer b: \frac{7}{12} < \frac{19}{24} < \frac{5}{6}

**Answer:** Arranged the given fractions in ascending order after finding a common denominator for each set.

> Common mistake: Not finding the lowest common multiple and ending up with cumbersome numbers.

### Question 3

*3 marks · Short answer*

Write the following fractions in descending order.
a. $\frac{25}{16}$, $\frac{7}{8}$, $\frac{13}{4}$, $\frac{17}{32}$
b. $\frac{3}{4}$, $\frac{12}{5}$, $\frac{7}{12}$, $\frac{5}{4}$

**Part a (1.5 marks)**

1. The denominators are $16$, $8$, $4$, and $32$. The smallest common multiple is $32$.
2. Convert each fraction: $\frac{25}{16} = \frac{50}{32}$, $\frac{7}{8} = \frac{28}{32}$, $\frac{13}{4} = \frac{104}{32}$, and $\frac{17}{32} = \frac{17}{32}$.
3. Compare numerators in descending order: $104 > 50 > 28 > 17$.
4. Write in descending order: $\frac{13}{4} > \frac{25}{16} > \frac{7}{8} > \frac{17}{32}$.

Answer a: \frac{13}{4} > \frac{25}{16} > \frac{7}{8} > \frac{17}{32}

**Part b (1.5 marks)**

1. The denominators are $4$, $5$, $12$, and $4$. The smallest common multiple is $60$.
2. Convert each fraction: $\frac{3}{4} = \frac{45}{60}$, $\frac{12}{5} = \frac{144}{60}$, $\frac{7}{12} = \frac{35}{60}$, and $\frac{5}{4} = \frac{75}{60}$.
3. Compare numerators in descending order: $144 > 75 > 45 > 35$.
4. Write in descending order: $\frac{12}{5} > \frac{5}{4} > \frac{3}{4} > \frac{7}{12}$.

Answer b: \frac{12}{5} > \frac{5}{4} > \frac{3}{4} > \frac{7}{12}

**Answer:** Arranged the given fractions in descending order after finding a common denominator for each set.

> Common mistake: Mixing up ascending and descending order.

## Figure it Out (Page 179)

### Question 1

*3 marks · Short answer*

Add the following fractions using Brahmagupta’s method:
a. $\frac{2}{7} + \frac{5}{7} + \frac{6}{7}$
b. $\frac{3}{4} + \frac{1}{3}$
c. $\frac{2}{3} + \frac{5}{6}$
d. $\frac{2}{3} + \frac{2}{7}$
e. $\frac{3}{4} + \frac{1}{3} + \frac{1}{5}$
f. $\frac{2}{3} + \frac{4}{5}$
g. $\frac{4}{5} + \frac{2}{3}$
h. $\frac{3}{5} + \frac{5}{8}$
i. $\frac{9}{2} + \frac{5}{4}$
j. $\frac{8}{3} + \frac{2}{7}$
k. $\frac{3}{4} + \frac{1}{3} + \frac{1}{5}$
l. $\frac{2}{3} + \frac{4}{5} + \frac{3}{7}$
m. $\frac{9}{2} + \frac{5}{4} + \frac{7}{6}$

**Part a**

1. $\frac{2}{7} + \frac{5}{7} + \frac{6}{7} = \frac{2+5+6}{7}$
2. $= \frac{13}{7}$

Answer a: $13/7$

**Part b**

1. Common denominator for $4$ and $3$ is $12$.
2. $\frac{3 \times 3}{4 \times 3} + \frac{1 \times 4}{3 \times 4} = \frac{9}{12} + \frac{4}{12}$
3. $= \frac{13}{12}$

Answer b: $13/12$

**Part c**

1. Common denominator for $3$ and $6$ is $6$.
2. $\frac{2 \times 2}{3 \times 2} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{9}{6}$
3. Simplify by dividing by $3$: $\frac{3}{2}$

Answer c: $3/2$

**Part d**

1. Common denominator for $3$ and $7$ is $21$.
2. $\frac{2 \times 7}{3 \times 7} + \frac{2 \times 3}{7 \times 3} = \frac{14}{21} + \frac{6}{21}$
3. $= \frac{20}{21}$

Answer d: $20/21$

**Part e**

1. Common denominator for $4$, $3$, and $5$ is $60$.
2. $\frac{45}{60} + \frac{20}{60} + \frac{12}{60}$
3. $= \frac{77}{60}$

Answer e: $77/60$

**Part f**

1. Common denominator for $3$ and $5$ is $15$.
2. $\frac{10}{15} + \frac{12}{15}$
3. $= \frac{22}{15}$

Answer f: $22/15$

**Part g**

1. Common denominator for $5$ and $3$ is $15$.
2. $\frac{12}{15} + \frac{10}{15}$
3. $= \frac{22}{15}$

Answer g: $22/15$

**Part h**

1. Common denominator for $5$ and $8$ is $40$.
2. $\frac{24}{40} + \frac{25}{40}$
3. $= \frac{49}{40}$

Answer h: $49/40$

**Part i**

1. Common denominator for $2$ and $4$ is $4$.
2. $\frac{18}{4} + \frac{5}{4}$
3. $= \frac{23}{4}$

Answer i: $23/4$

**Part j**

1. Common denominator for $3$ and $7$ is $21$.
2. $\frac{56}{21} + \frac{6}{21}$
3. $= \frac{62}{21}$

Answer j: $62/21$

**Part k**

1. Common denominator for $4$, $3$, and $5$ is $60$.
2. $\frac{45}{60} + \frac{20}{60} + \frac{12}{60}$
3. $= \frac{77}{60}$

Answer k: $77/60$

**Part l**

1. Common denominator for $3$, $5$, and $7$ is $105$.
2. $\frac{70}{105} + \frac{84}{105} + \frac{45}{105}$
3. $= \frac{199}{105}$

Answer l: $199/105$

**Part m**

1. Common denominator for $2$, $4$, and $6$ is $12$.
2. $\frac{54}{12} + \frac{15}{12} + \frac{14}{12}$
3. $\frac{83}{12}$

Answer m: $83/12$

**Answer:** See sub-parts for answers.

> Common mistake: Failing to find the correct common denominator before adding the numerators.

### Question 2

*3 marks · Short answer*

Rahim mixes $\frac{2}{3}$ litres of yellow paint with $\frac{3}{4}$ litres of blue paint to make green paint. What is the volume of green paint he has made?

**Solution**

1. Volume of yellow paint = $\frac{2}{3}$ litres and volume of blue paint = $\frac{3}{4}$ litres.
2. Total volume of green paint = $\frac{2}{3} + \frac{3}{4}$.
3. The least common multiple of the denominators 3 and 4 is 12.
4. Convert both fractions to have 12 as the denominator: $\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ and $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
5. Add the numerators while keeping the denominator same: $\frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}$ litres.

**Answer:** $1\frac{5}{12}$ litres

> Common mistake: Adding the numerators and denominators directly as $\frac{2+3}{3+4} = \frac{5}{7}$ instead of finding a common denominator.

### Question 3

*3 marks · Short answer*

Geeta bought $\frac{2}{5}$ meter of lace and Shamim bought $\frac{3}{4}$ meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?

**Solution**

1. Length of lace bought by Geeta = $\frac{2}{5}$ meter and length bought by Shamim = $\frac{3}{4}$ meter.
2. Total length of lace bought = $\frac{2}{5} + \frac{3}{4}$.
3. The least common multiple of 5 and 4 is 20.
4. Convert both fractions to have 20 as the denominator: $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ and $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$.
5. Add the fractions: $\frac{8}{20} + \frac{15}{20} = \frac{23}{20} = 1\frac{3}{20}$ meter.
6. Since the perimeter of the tablecloth is 1 meter and $1\frac{3}{20}$ meters is greater than 1 meter, the lace will be sufficient.

**Answer:** $1\frac{3}{20}$ m; Yes

> Common mistake: Failing to compare the total length with the 1 meter perimeter to answer whether it is sufficient.

## Figure it Out (Page 181)

### Question 1

*2 marks · Very short answer*

$\frac{5}{8} - \frac{3}{8}$

**Solution**

1. Subtract the numerators while keeping the same denominator.
2. $\frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4}$ in lowest terms.

**Answer:** $\frac{1}{4}$

> Common mistake: Subtracting the denominators along with the numerators.

### Question 2

*2 marks · Very short answer*

$\frac{7}{9} - \frac{5}{9}$

**Solution**

1. Subtract the numerators while keeping the same denominator.
2. $\frac{7 - 5}{9} = \frac{2}{9}$

**Answer:** $\frac{2}{9}$

> Common mistake: Subtracting the denominators.

### Question 3

*2 marks · Very short answer*

$\frac{10}{27} - \frac{1}{27}$

**Solution**

1. Subtract the numerator 1 from 10 while keeping the common denominator 27.
2. Simplify the fraction $\frac{9}{27}$ to its lowest terms by dividing the numerator and denominator by 9.

**Answer:** $\frac{1}{3}$

> Common mistake: Subtracting the denominators along with the numerators.

## Figure it Out (Page 182)

### Question 1

*3 marks · Short answer*

Carry out the following subtractions using Brahmagupta’s method:
a. $\frac{8}{15} - \frac{3}{15}$
b. $\frac{2}{5} - \frac{4}{15}$
c. $\frac{5}{6} - \frac{4}{9}$
d. $\frac{2}{3} - \frac{1}{2}$

**Part (a)**

1. The denominators are already the same, so subtract the numerators directly.
2. $\frac{8}{15} - \frac{3}{15} = \frac{8 - 3}{15} = \frac{5}{15}$
3. Express the result in lowest terms by dividing numerator and denominator by 5: $\frac{5 \div 5}{15 \div 5} = \frac{1}{3}$

Answer (a): $\frac{1}{3}$

**Part (b)**

1. Convert fractions to a common denominator, which is 15.
2. $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
3. Subtract the numerators: $\frac{6}{15} - \frac{4}{15} = \frac{6 - 4}{15} = \frac{2}{15}$

Answer (b): $\frac{2}{15}$

**Part (c)**

1. Find the lowest common multiple of the denominators 6 and 9, which is 18.
2. Convert each fraction: $\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ and $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}$
3. Subtract the numerators: $\frac{15}{18} - \frac{8}{18} = \frac{15 - 8}{18} = \frac{7}{18}$

Answer (c): $\frac{7}{18}$

**Part (d)**

1. Find the lowest common multiple of the denominators 3 and 2, which is 6.
2. Convert each fraction: $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$ and $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
3. Subtract the numerators: $\frac{4}{6} - \frac{3}{6} = \frac{4 - 3}{6} = \frac{1}{6}$

Answer (d): $\frac{1}{6}$

**Answer:** a. $\frac{1}{3}$, b. $\frac{2}{15}$, c. $\frac{7}{18}$, d. $\frac{1}{6}$

> Common mistake: Forgetting to convert fractions to a common denominator before subtracting.

### Question 2

*3 marks · Short answer*

Subtract as indicated:
a. $\frac{13}{4}$ from $\frac{10}{3}$
b. $\frac{18}{5}$ from $\frac{23}{3}$
c. $\frac{29}{7}$ from $\frac{45}{7}$

**Part (a) (1 mark)**

1. Subtract $\frac{13}{4}$ from $\frac{10}{3}$ means calculating $\frac{10}{3} - \frac{13}{4}$.
2. The common denominator for 3 and 4 is 12.
3. Convert fractions: $\frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12}$ and $\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}$
4. Subtract numerators: $\frac{40}{12} - \frac{39}{12} = \frac{1}{12}$

Answer (a): $\frac{1}{12}$

**Part (b) (1 mark)**

1. Subtract $\frac{18}{5}$ from $\frac{23}{3}$ means calculating $\frac{23}{3} - \frac{18}{5}$.
2. The common denominator for 3 and 5 is 15.
3. Convert fractions: $\frac{23}{3} = \frac{23 \times 5}{3 \times 5} = \frac{115}{15}$ and $\frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15}$
4. Subtract numerators: $\frac{115}{15} - \frac{54}{15} = \frac{61}{15}$

Answer (b): $\frac{61}{15}$

**Part (c) (1 mark)**

1. Subtract $\frac{29}{7}$ from $\frac{45}{7}$ means calculating $\frac{45}{7} - \frac{29}{7}$.
2. Since denominators are the same, subtract numerators directly: $\frac{45 - 29}{7} = \frac{16}{7}$

Answer (c): $\frac{16}{7}$

**Answer:** a. $\frac{1}{12}$, b. $\frac{61}{15}$, c. $\frac{16}{7}$

> Common mistake: Reversing the order of subtraction since the phrase says 'from'.

### Question 3

*3 marks · Short answer*

Solve the following problems:
a. Jaya’s school is $\frac{7}{10}\text{ km}$ from her home. She takes an auto for $\frac{1}{2}\text{ km}$ from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?
b. Jeevika takes $\frac{10}{3}$ minutes to take a complete round of the park and her friend Namit takes $\frac{13}{4}$ minutes to do the same. Who takes less time and by how much?

**Part (a) (1 mark)**

1. Total distance to school = $\frac{7}{10}\text{ km}$, distance by auto = $\frac{1}{2}\text{ km}$.
2. Remaining distance walked = $\frac{7}{10} - \frac{1}{2}$
3. Convert $\frac{1}{2}$ to have denominator 10: $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$
4. Subtract: $\frac{7}{10} - \frac{5}{10} = \frac{2}{10} = \frac{1}{5}\text{ km}$

Answer (a): $\frac{1}{5}\text{ km}$

**Part (b) (2 marks)**

1. Jeevika's time = $\frac{10}{3}\text{ minutes}$, Namit's time = $\frac{13}{4}\text{ minutes}$.
2. Find a common denominator for 3 and 4, which is 12.
3. Convert fractions: $\frac{10}{3} = \frac{40}{12}$ and $\frac{13}{4} = \frac{39}{12}$
4. Compare: $\frac{39}{12} < \frac{40}{12}$, so Namit takes less time.
5. Difference = $\frac{40}{12} - \frac{39}{12} = \frac{1}{12}\text{ minute}$

Answer (b): Namit takes less time than Jeevika by $\frac{1}{12}$ minutes

**Answer:** a. $\frac{1}{5}\text{ km}$, b. Namit takes less time than Jeevika by $\frac{1}{12}$ minutes

> Common mistake: Comparing unlike fractions directly without finding a common denominator in part (b).

## Puzzle! (Page 184)

### Question 1

*3 marks · Short answer*

Can you find three different fractional units that add up to 1?

**Solution**

1. We know that $\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1$.
2. To get different fractional units, we replace one $\frac{1}{3}$ with $\frac{1}{2}$ and adjust the remaining parts.
3. Thus, the three different fractional units that add up to $1$ are $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{6}$.

**Answer:** $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$

> Common mistake: Trying to use two different fractional units to add up to 1, which is impossible.

## Puzzle! (Page 185)

### Question 2

*3 marks · Long answer*

Can you find four different fractional units that add up to 1?

**Part (i)**

1. We are looking for four different unit fractions whose sum is $1$.
2. Using Egyptian fraction expansion or systematic search, one valid combination of four distinct unit fractions is $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{10}$, and $\frac{1}{15}$.
3. Let us check the sum: find the common denominator of $2$, $3$, $10$, and $15$, which is $30$.
4. Convert each fraction: $\frac{1}{2} = \frac{15}{30}$, $\frac{1}{3} = \frac{10}{30}$, $\frac{1}{10} = \frac{3}{30}$, and $\frac{1}{15} = \frac{2}{30}$.
5. Add the numerators: $\frac{15 + 10 + 3 + 2}{30} = \frac{30}{30} = 1$.
6. Thus, one solution is $\frac{1}{2} + \frac{1}{3} + \frac{1}{10} + \frac{1}{15} = 1$.

Answer (i): $\frac{1}{2} + \frac{1}{3} + \frac{1}{10} + \frac{1}{15} = 1$

**Answer:** One set of four different fractional units that add up to $1$ is $\frac{1}{2} + \frac{1}{3} + \frac{1}{10} + \frac{1}{15} = 1$. (Note: There are six possible solutions in total.)

> Common mistake: Listing fractions that are not all distinct or whose sum does not exactly equal 1.

## Frequently asked questions

### How many total questions are there in Class 6 Maths Chapter 7 Fractions based on the new NCERT book?

The chapter contains multiple sections of Figure it Out and puzzles across various pages, such as 5 questions on Page 152 and 3 questions on Page 174. You can find complete step-by-step solutions for all these questions in the free PDF available on this SwaVid page.

### Which important topics are covered in the exercises of this chapter?

The questions cover core concepts like addition and subtraction of fractions with different denominators, equivalent fractions using a fraction wall, marking fractions greater than one on a number line, and converting improper fractions to mixed fractions. SwaVid's free PDF provides detailed explanations for each of these topics.

### Which types of questions are considered the most challenging in Class 6 Fractions and how should I approach them?

Word problems involving fraction subtraction and questions on Brahmagupta's method for addition and subtraction can be tricky for students. To approach them correctly, carefully identify the fractional units, convert them to common denominators where necessary, and write out each step clearly.

### How can I write answers in the Class 6 Maths exam to score full marks?

To secure full marks, always state the given fraction values, show clear working for steps like finding equivalent fractions or simplifying to lowest terms, and label your final answers properly. Referring to the solved examples in SwaVid's free PDF on this page will help you structure your answers effectively.

### Is a free PDF of the NCERT solutions for this chapter available for download?

Yes, a comprehensive and free PDF containing accurate solutions for all the exercises in the new NCERT book for the 2026-27 session is available right here on this SwaVid page. You can use it to verify your answers and practice concepts like number line representation and equivalent fractions.

## Related pages

- [Class 6 Maths chapters](https://www.swavid.com/maths/class/6)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student