--- title: "NCERT Solutions Class 7 Maths Ch 12 Another Peek Beyond the Point" url: https://www.swavid.com/maths/class/7/chapter/another-peek-beyond-the-point/ncert-solutions dateModified: 2026-10-07T15:12:00+00:00 --- # NCERT Solutions Class 7 Maths Ch 12 Another Peek Beyond the Point This chapter's questions cover decimal multiplication and division, place value concepts, and solving word problems involving decimals. They also include exercises on fraction-to-decimal conversions and real-world applications like calendar calculations. Free PDF (20 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-7/swavid-ncert-solutions-class-7-maths-chapter-12-another-peek-beyond-the-point-f52c10f00d.pdf ## Figure it Out ### Question 1 *3 marks · Short answer* Recall that a tenth is 0.1, a hundredth is 0.01, and so on. Find the following products in tenths, hundredths and so on: (a) $6 \times 4$ tenths = 24 tenths (b) $7 \times 0.3$ (c) $9 \times 5$ hundredths **Part (b)** 1. $7 \times 0.3 = 7 \times \frac{3}{10} = \frac{21}{10} = 2.1$ Answer (b): 2.1 **Part (c)** 1. $9 \times 5 \text{ hundredths} = 9 \times 0.05 = 0.45$ Answer (c): 0.45 **Answer:** The products are (b) 2.1 and (c) 0.45. > Common mistake: Confusing the place value of tenths and hundredths. ### Question 2 *3 marks · Short answer* Find the products: (a) $27.34 \times 6$ (b) $4.23 \times 3.7$ (c) $0.432 \times 0.23$ **Part (a)** 1. $27.34 \times 6 = \frac{2734}{100} \times 6 = \frac{16404}{100} = 164.04$ Answer (a): 164.04 **Part (b)** 1. $4.23 \times 3.7 = \frac{423}{100} \times \frac{37}{10} = \frac{15651}{1000} = 15.651$ Answer (b): 15.651 **Part (c)** 1. $0.432 \times 0.23 = \frac{432}{1000} \times \frac{23}{100} = \frac{9936}{100000} = 0.09936$ Answer (c): 0.09936 **Answer:** The products are (a) 164.04, (b) 15.651, and (c) 0.09936. > Common mistake: Incorrect placement of the decimal point in the product. ### Question 3 *3 marks · Short answer* Thejus needs 1.65 m of cloth for a shirt. How many metres of cloth are needed for 3 shirts? **Solution** 1. Given, cloth needed for $1$ shirt = $1.65\text{ m}$. 2. Total cloth needed for $3$ shirts = $1.65 \times 3\text{ m}$. 3. Multiplying the numbers: $165 \times 3 = 495$, and placing the decimal point for two decimal places gives $4.95\text{ m}$. 4. Thus, $4.95\text{ m}$ of cloth is needed for $3$ shirts. **Answer:** $4.95\text{ m}$ > Common mistake: Placing the decimal point incorrectly in the product. ### Question 4 *3 marks · Short answer* Meenu bought 4 notebooks and 3 erasers. The cost of each book was ₹15.50 and each eraser was ₹2.75. How much did she spend in all? **Solution** 1. Cost of $1$ notebook = ₹$15.50$, so the cost of $4$ notebooks = $4 \times 15.50 =$ ₹$62.00$. 2. Cost of $1$ eraser = ₹$2.75$, so the cost of $3$ erasers = $3 \times 2.75 =$ ₹$8.25$. 3. Total money spent = $62.00 + 8.25 =$ ₹$70.25$. **Answer:** ₹$70.25$ > Common mistake: Multiplying the prices with wrong quantities or making addition errors with decimals. ### Question 5 *3 marks · Short answer* The thickness of a rupee coin is 1.45 mm. What is the total height of the cylinder formed by placing 36 rupee coins one over the other? Write the answer in centimeters. **Solution** 1. Thickness of $1$ rupee coin = $1.45\text{ mm}$. 2. Total height of the cylinder formed by $36$ coins = $36 \times 1.45\text{ mm} = 52.20\text{ mm}$. 3. Since $10\text{ mm} = 1\text{ cm}$, convert the height to centimeters by dividing by $10$: $52.20 \div 10 = 5.22\text{ cm}$. **Answer:** $5.22\text{ cm}$ > Common mistake: Forgetting to convert millimeters to centimeters at the end. ### Question 6 *3 marks · Short answer* The price of 1 kg of oranges is ₹56.50. What is the price of 2.250 kg of oranges? Can we write 56.50 as 56.5 and 2.250 as 2.25 and multiply? Will we get the same product? Why? **Solution** 1. Price of $1\text{ kg}$ of oranges = ₹$56.50$, so the price of $2.250\text{ kg}$ = $56.50 \times 2.250 = 127.125\text{ (or } 127.13\text{)}$. 2. Yes, we can write $56.50$ as $56.5$ and $2.250$ as $2.25$ because trailing zeros in the decimal part do not change the value of a decimal number. 3. Yes, we will get the same product because $56.50 \times 2.250 = \frac{5650}{100} \times \frac{2250}{1000} = \frac{565}{10} \times \frac{225}{100} = 56.5 \times 2.25$, which yields the same numerator product and total decimal places. **Answer:** ₹$127.125$; yes, we get the same product because trailing zeros do not change the value. > Common mistake: Thinking that dropping trailing zeros changes the product. ### Question 7 *3 marks · Short answer* Dwarakanath purchases notebooks at a wholesale price of ₹23.6 per piece and sells each notebook at ₹30/-. How much profit does he make if he sells 50 books in a week? **Solution** 1. Wholesale price of $1$ notebook = ₹$23.60$, and selling price = ₹$30.00$. 2. Profit on $1$ notebook = $30.00 - 23.60 =$ ₹$6.40$. 3. Total profit on selling $50$ books in a week = $50 \times 6.40 =$ ₹$320.00$. **Answer:** ₹$320$ > Common mistake: Subtracting incorrectly or multiplying by the wrong number of books. ### Question 8 *3 marks · Short answer* Given that $18 \times 12 = 216$, find the products: (a) $18 \times 1.2$ (b) $18 \times 0.12$ (c) $1.8 \times 1.2$ (d) $0.18 \times 0.12$ (e) $0.018 \times 0.012$ (f) $1.8 \times 12$ In which of the cases above is the product less than 1? **Part (a)** 1. $18 \times 1.2 = 21.6$ Answer (a): 21.6 **Part (b)** 1. $18 \times 0.12 = 2.16$ Answer (b): 2.16 **Part (c)** 1. $1.8 \times 1.2 = 2.16$ Answer (c): 2.16 **Part (d)** 1. $0.18 \times 0.12 = 0.0216$ Answer (d): 0.0216 **Part (e)** 1. $0.018 \times 0.012 = 0.000216$ Answer (e): 0.000216 **Part (f)** 1. $1.8 \times 12 = 21.6$, product less than 1 in cases (b), (c), (d), and (e) Answer (f): 21.6 (less than 1 in b, c, d, e) **Answer:** (a) 21.6, (b) 2.16, (c) 2.16, (d) 0.0216, (e) 0.000216, (f) 21.6; less than 1 in (b), (c), (d), and (e) > Common mistake: Placing the decimal point incorrectly based on total decimal places. ### Question 9 *3 marks · Short answer* In which of the following multiplications is the product less than 1? Can you find the answer without actually doing the multiplications? (a) $7 \times 0.6$ (b) $0.7 \times 0.6$ (c) $0.7 \times 6$ (d) $0.07 \times 0.06$ **Solution** 1. When both numbers multiplied are between 0 and 1, their product is less than 1. 2. In (b) $0.7 \times 0.6$ and (d) $0.07 \times 0.06$, both numbers are less than 1. 3. Thus, the product is less than 1 in cases (b) and (d). **Answer:** Product is less than 1 in (b) $0.7 \times 0.6$ and (d) $0.07 \times 0.06$ > Common mistake: Multiplying fully instead of using the rule that the product of two numbers between 0 and 1 is less than both numbers. ### Question 10 *3 marks · Short answer* Multiplying the following numbers by 10, 100 and 1000 to complete the table. **Part (a)** 1. For 5.7: multiplied by 10 is 57, by 100 is 570, by 1000 is 5700 Answer (a): 57, 570, 5700 **Part (b)** 1. For 23.02: multiplied by 10 is 230.2, by 100 is 2302, by 1000 is 23020 Answer (b): 230.2, 2302, 23020 **Part (c)** 1. For 0.92: multiplied by 10 is 9.2, by 100 is 92, by 1000 is 920 Answer (c): 9.2, 92, 920 **Part (d)** 1. For 0.306: multiplied by 10 is 3.06, by 100 is 30.6, by 1000 is 306 Answer (d): 3.06, 30.6, 306 **Part (e)** 1. For 24.67: multiplied by 10 is 246.7, by 100 is 2467, by 1000 is 24670 Answer (e): 246.7, 2467, 24670 **Answer:** Completed table for numbers multiplied by 10, 100, and 1000. > Common mistake: Moving the decimal point in the wrong direction. ## Figure it Out ### Question 1 *3 marks · Short answer* Find the quotient by converting the denominator into 1, 10, 100 or 1000 and verify the solution by the long division method (division by place value). (a) $\frac{18}{5}$ (b) $\frac{415}{4}$ (c) $\frac{1217}{2}$ (d) $\frac{4827}{8}$ **Part (a)** 1. Convert the denominator to 10 by multiplying numerator and denominator by 2: $\frac{18 \times 2}{5 \times 2} = \frac{36}{10} = 3.6$. 2. Verify by long division: $18 \div 5 = 3.6$. Answer (a): $3.6$ **Part (b)** 1. Convert the denominator to 100 by multiplying numerator and denominator by 25: $\frac{415 \times 25}{4 \times 25} = \frac{10375}{100} = 103.75$. 2. Verify by long division: $415 \div 4 = 103.75$. Answer (b): $103.75$ **Part (c)** 1. Convert the denominator to 10 by multiplying numerator and denominator by 5: $\frac{1217 \times 5}{2 \times 5} = \frac{6085}{10} = 608.5$. 2. Verify by long division: $1217 \div 2 = 608.5$. Answer (c): $608.5$ **Part (d)** 1. Convert the denominator to 1000 by multiplying numerator and denominator by 125: $\frac{4827 \times 125}{8 \times 125} = \frac{603375}{1000} = 603.375$. 2. Verify by long division: $4827 \div 8 = 603.375$. Answer (d): $603.375$ **Answer:** The quotients are (a) 3.6, (b) 103.75, (c) 608.5, and (d) 603.375. > Common mistake: Errors in multiplying large numbers when finding equivalent fractions with denominators of 10, 100, or 1000. ### Question 2 *1 mark · MCQ* Choose the correct answer: (a) $\frac{1526}{4} =$ (b) $\frac{3567}{8} =$ **Part (a)** 1. Divide 1526 by 4 using long division to get 381.5. Answer (a): (iii) 381.5 **Part (b)** 1. Divide 3567 by 8 using long division to get 445.875. Answer (b): (iii) 445.875 **Answer:** (a) (iii) 381.5, (b) (iii) 445.875 > Common mistake: Incorrect placement of the decimal point after dividing the ones place. ### Question 3 *3 marks · Short answer* What is the quotient? (a) $132 \div 4 =$ (b) $13.2 \div 4 =$ (c) $1.32 \div 4 =$ (d) $0.132 \div 4 =$ **Part (a)** 1. Divide 132 by 4 to get 33. Answer (a): $33$ **Part (b)** 1. Divide 13.2 by 4 by placing the decimal point after the tens place to get 3.3. Answer (b): $3.3$ **Part (c)** 1. Divide 1.32 by 4 by shifting the decimal point one more place to the left to get 0.33. Answer (c): $0.33$ **Part (d)** 1. Divide 0.132 by 4 by shifting the decimal point further to get 0.033. Answer (d): $0.033$ **Answer:** The quotients are (a) 33, (b) 3.3, (c) 0.33, and (d) 0.033. > Common mistake: Miscounting the decimal places when the dividend decreases by powers of 10. ### Question 4 *3 marks · Short answer* What is the quotient? (a) $126 \div 8 =$ (b) $12.6 \div 8 =$ (c) $1.26 \div 8 =$ (d) $0.126 \div 8 =$ (e) $0.0126 \div 8 =$ **Part (a)** 1. Divide 126 by 8 using long division: $126 \div 8 = 15.75$. Answer (a): $15.75$ **Part (b)** 1. Divide 12.6 by 8 by shifting the decimal point one place left: $1.575$. Answer (b): $1.575$ **Part (c)** 1. Divide 1.26 by 8 by shifting the decimal point one more place left: $0.1575$. Answer (c): $0.1575$ **Part (d)** 1. Divide 0.126 by 8 by shifting the decimal point further left: $0.01575$. Answer (d): $0.01575$ **Part (e)** 1. Divide 0.0126 by 8 by shifting the decimal point another place left: $0.001575$. Answer (e): $0.001575$ **Answer:** The quotients are (a) 15.75, (b) 1.575, (c) 0.1575, (d) 0.01575, and (e) 0.001575. > Common mistake: Incorrect number of zeroes inserted after the decimal point when shifting places. ## Figure it Out ### Question 1 *3 marks · Short answer* Express the following fractions in decimal form: (a) $\frac{2}{5}$ (b) $\frac{13}{4}$ (c) $\frac{4}{50}$ (d) $\frac{5}{8}$ **Part (a)** 1. Multiply the numerator and denominator by $2$ to make the denominator $10$. 2. $\frac{2 \times 2}{5 \times 2} = \frac{4}{10} = 0.4$ Answer (a): $0.4$ **Part (b)** 1. Multiply the numerator and denominator by $25$ to make the denominator $100$. 2. $\frac{13 \times 25}{4 \times 25} = \frac{325}{100} = 3.25$ Answer (b): $3.25$ **Part (c)** 1. Multiply the numerator and denominator by $2$ to make the denominator $100$. 2. $\frac{4 \times 2}{50 \times 2} = \frac{8}{100} = 0.08$ Answer (c): $0.08$ **Part (d)** 1. Multiply the numerator and denominator by $125$ to make the denominator $1000$. 2. $\frac{5 \times 125}{8 \times 125} = \frac{625}{1000} = 0.625$ Answer (d): $0.625$ **Answer:** The decimal forms are (a) $0.4$, (b) $3.25$, (c) $0.08$, and (d) $0.625$. > Common mistake: Incorrectly multiplying numerator and denominator by different numbers. ### Question 2 *3 marks · Short answer* Find the quotients: (a) $24.86 \div 1.2$ (b) $5.728 \div 1.52$ **Part (a)** 1. Convert the divisor into a counting number by multiplying both dividend and divisor by $10$: $24.86 \div 1.2 = 248.6 \div 12$. 2. Perform long division: $248.6 \div 12 = 20.7166\dots$ 3. State the final quotient with appropriate rounding: $20.72$. Answer (a): $20.72$ **Part (b)** 1. Convert the divisor into a counting number by multiplying both dividend and divisor by $100$: $5.728 \div 1.52 = 572.8 \div 152$. 2. Perform long division: $572.8 \div 152 = 3.7684\dots$ 3. State the final quotient with appropriate rounding: $3.77$. Answer (b): $3.77$ **Answer:** (a) $20.7166\dots$ or $20.72$, (b) $3.7684\dots$ or $3.77$ > Common mistake: Forgetting to multiply both the dividend and the divisor by the same power of $10$ before performing long division. ## Figure it Out ### Question 3 *3 marks · Short answer* Evaluate the following using the information $156 \times 12 = 1872$. (a) $15.6 \times 1.2 = \text{__________}$ (b) $187.2 \div 1.2 = \text{__________}$ (c) $18.72 \div 15.6 = \text{__________}$ (d) $0.156 \times 0.12 = \text{__________}$ **Part (a)** 1. Given $156 \times 12 = 1872$, total decimal places in $15.6 \times 1.2$ is $1 + 1 = 2$. 2. Placing the decimal point two places from the right gives $18.72$. Answer (a): 18.72 **Part (b)** 1. Rewrite $187.2 \div 1.2$ as $\frac{187.2 \times 10}{1.2 \times 10} = \frac{1872}{12}$. 2. Dividing $1872$ by $12$ gives $156$. Answer (b): 156 **Part (c)** 1. Rewrite $18.72 \div 15.6$ as $\frac{18.72 \times 10}{15.6 \times 10} = \frac{187.2}{156}$. 2. Dividing $187.2$ by $156$ gives $1.2$. Answer (c): 1.2 **Part (d)** 1. Given $156 \times 12 = 1872$, total decimal places in $0.156 \times 0.12$ is $3 + 2 = 5$. 2. Placing the decimal point five places from the right gives $0.01872$. Answer (d): 0.01872 **Answer:** Evaluated values using $156 \times 12 = 1872$ > Common mistake: Counting incorrect number of decimal places in multiplication. ### Question 4 *3 marks · Short answer* Evaluate the following: (a) $25 \div \text{______} = 0.025$ (b) $25 \div \text{______} = 250$ (c) $25 \div \text{______} = 2.5$ (d) $25 \div 10 = 25 \times \text{_____}$ (e) $25 \div 0.10 = 25 \times \text{______}$ (f) $25 \div 0.01 = 25 \times \text{______}$ **Part (a)** 1. We have $25 \div \text{______} = 0.025$. 2. Dividing $25$ by $1000$ shifts the decimal point three places to the left, giving $0.025$. Answer (a): 1000 **Part (b)** 1. We have $25 \div \text{______} = 250$. 2. Dividing by a number smaller than $1$ or multiplying gives $250$, so we divide by $0.1$. Answer (b): 0.1 **Part (c)** 1. We have $25 \div \text{______} = 2.5$. 2. Dividing $25$ by $10$ gives $2.5$. Answer (c): 10 **Part (d)** 1. Division by a fraction is multiplication by its reciprocal, so $25 \div 10 = 25 \times \frac{1}{10}$. Answer (d): \frac{1}{10} \text{ (or } 0.1 \text{)} **Part (e)** 1. Since $0.10 = \frac{1}{10}$, $25 \div 0.10 = 25 \div \frac{1}{10} = 25 \times 10$. Answer (e): 10 **Part (f)** 1. Since $0.01 = \frac{1}{100}$, $25 \div 0.01 = 25 \div \frac{1}{100} = 25 \times 100$. Answer (f): 100 **Answer:** Completed equations for decimal division and multiplication > Common mistake: Confusing division by powers of 10 with multiplication. ### Question 5 *3 marks · Short answer* Find the quotient: (a) $2.46 \div 1.5 =$ (b) $2.46 \div 0.15 =$ (c) $2.46 \div 0.015 =$ Is the quotient obtained in $24.6 \div 1.5$ the same as the quotient obtained in $2.46 \div 0.15$? **Part (a)** 1. Convert divisor to a whole number: $2.46 \div 1.5 = \frac{2.46 \times 10}{1.5 \times 10} = \frac{24.6}{15}$. 2. Dividing $24.6$ by $15$ gives $1.64$. Answer (a): 1.64 **Part (b)** 1. Convert divisor to a whole number: $2.46 \div 0.15 = \frac{2.46 \times 100}{0.15 \times 100} = \frac{246}{15}$. 2. Dividing $246$ by $15$ gives $16.4$. Answer (b): 16.4 **Part (c)** 1. Convert divisor to a whole number: $2.46 \div 0.015 = \frac{2.46 \times 1000}{0.015 \times 1000} = \frac{2460}{15}$. 2. Dividing $2460$ by $15$ gives $164$. Answer (c): 164 **Part Comparison** 1. The quotient of $24.6 \div 1.5$ is $16.4$, while the quotient of $2.46 \div 0.15$ is $16.4$. 2. Yes, the quotients are the same because both dividend and divisor are multiplied by the same factor of $10$. Answer Comparison: Yes, they are the same. **Answer:** Quotients found and compared > Common mistake: Forgetting to multiply both dividend and divisor by the same power of 10. ### Question 6 *3 marks · Short answer* A 4 m long wooden block has to be cut into 5 pieces of equal length. What is the length of each piece? **Solution** 1. Given: Total length of the wooden block = $4\text{ m}$, number of equal pieces = $5$. 2. The length of each piece is obtained by dividing the total length by the number of pieces: $4 \div 5$. 3. Converting to a fraction or decimal: $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} = 0.8\text{ m}$. **Answer:** 0.8 m > Common mistake: Dividing 5 by 4 instead of 4 by 5. ### Question 7 *3 marks · Short answer* If the perimeter of a regular polygon with 12 sides is 208.8 cm, what is the length of its side? **Solution** 1. Perimeter of the regular polygon = $208.8 \text{ cm}$ 2. Number of sides = $12$ 3. Length of each side = $\frac{208.8}{12}$ 4. $208.8 \div 12 = 17.4$ 5. Length of each side = $17.4 \text{ cm}$ **Answer:** $17.4 \text{ cm}$ > Common mistake: Incorrect placement of the decimal point during division. ### Question 8 *3 marks · Short answer* 3 litres of watermelon juice is shared among 8 friends equally. How much watermelon juice will each get? Express the quantity of juice in millilitres. **Solution** 1. Given: Total quantity of juice = $3\text{ litres}$, number of friends = $8$. 2. Convert litres to millilitres: $3\text{ litres} = 3 \times 1000\text{ ml} = 3000\text{ ml}$. 3. The amount of juice each friend gets is $3000 \div 8 = 375\text{ ml}$. **Answer:** 375 ml > Common mistake: Forgetting to convert litres to millilitres before dividing. ### Question 9 *3 marks · Short answer* A car covers 234.45 km using 12.6 litres of petrol. What is the distance travelled per litre? **Solution** 1. Total distance covered = $234.45 \text{ km}$ 2. Petrol used = $12.6 \text{ litres}$ 3. Distance travelled per litre = $234.45 \div 12.6$ 4. $234.45 \div 12.6 = \frac{234.45 \times 10}{12.6 \times 10} = \frac{2344.5}{126}$ 5. $2344.5 \div 126 = 18.607 \dots \approx 18.61 \text{ km}$ **Answer:** $18.61 \text{ km}$ > Common mistake: Failing to convert the decimal divisor to a counting number before division. ### Question 10 *3 marks · Short answer* 13.5 kg of flour (aata) was distributed equally among 15 students. How much flour did each student receive? **Solution** 1. Given: Total flour = $13.5\text{ kg}$, Number of students = $15$. 2. Flour received by each student = $\text{Total flour} \div \text{Number of students} = 13.5 \div 15$. 3. Perform long division: $13.5 \div 15 = 0.9\text{ kg}$. **Answer:** $0.9\text{ kg}$ > Common mistake: Placing the decimal point incorrectly in the quotient. ## Figure it Out ### Question 1 *3 marks · Short answer* A 210 gram packet of peanut chikki costs ₹70.5, while a 110 gram packet of potato chips costs ₹33.25. Which is cheaper? **Solution** 1. Cost of $210\text{ g}$ of peanut chikki = $\text{₹}70.5$. 2. Cost of $1\text{ g}$ of peanut chikki = $\frac{70.5}{210} = \text{₹}0.3357$ per gram. 3. Cost of $110\text{ g}$ of potato chips = $\text{₹}33.25$. 4. Cost of $1\text{ g}$ of potato chips = $\frac{33.25}{110} = \text{₹}0.3023$ per gram. 5. Alternatively, find the cost of $100\text{ g}$ for each: peanut chikki costs $\frac{70.5}{2.1} = \text{₹}33.57$, while potato chips for $100\text{ g}$ costs $\frac{33.25}{1.1} = \text{₹}30.23$. 6. Comparing the unit costs, potato chips are cheaper per gram. **Answer:** The potato chips packet is cheaper. > Common mistake: Comparing total costs instead of unit cost per gram. ### Question 2 *3 marks · Short answer* Write the decimal number at the arrow mark: **Solution** 1. For the first number line, the interval between $3.1$ and $3.2$ is divided into $10$ equal parts, making each small division equal to $0.01$. 2. Counting from $3.1$, the arrow mark is at the $6^{\text{th}}$ subdivision. 3. So, the decimal number at the first arrow mark is $3.1 + 6 \times 0.01 = 3.16$. 4. For the second number line, the interval between $2.15$ and $2.17$ has $10$ subdivisions between $2.15$ and $2.17$, so each small division is $0.002$. 5. The arrow mark is at the $3^{\text{rd}}$ subdivision after $2.15$. 6. So, the decimal number at the second arrow mark is $2.15 + 3 \times 0.002 = 2.156$. **Answer:** The decimal numbers are $3.16$ and $2.156$. > Common mistake: Miscounting the number of subdivisions between the marked decimals. ### Question 3 *3 marks · Short answer* Shyamala bought 3 kg bananas at ₹30/- per kg. She counted 35 bananas in all. She sells each banana for ₹5/-. How much profit does she make selling all the bananas? **Solution** 1. Cost price of $3\text{ kg}$ of bananas at $\text{₹}30$ per $\text{kg} = 3 \times 30 = \text{₹}90$. 2. Total number of bananas = $35$, and each is sold for $\text{₹}5$. 3. Total selling price = $35 \times 5 = \text{₹}175$. 4. Profit = Selling price $-$ Cost price = $\text{₹}175 - \text{₹}90 = \text{₹}85$. **Answer:** ₹85 > Common mistake: Multiplying the number of bananas by the price per kg instead of the selling price per banana. ### Question 4 *3 marks · Short answer* A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long. How many books could be placed on the shelf? Was there any space left? If yes, how much? **Solution** 1. Thickness of one textbook = $2.5\text{ cm}$. 2. Total number of textbooks the teacher wants to place = $80$. 3. Total thickness required for 80 textbooks = $80 \times 2.5 = 200\text{ cm}$. 4. Length of the bookshelf = $160\text{ cm}$. 5. Since $200\text{ cm}$ is greater than $160\text{ cm}$, all 80 books cannot fit. 6. Maximum number of books that can be placed = $\frac{160}{2.5} = \frac{1600}{25} = 64$ books. 7. Space left = $160\text{ cm} - (64 \times 2.5\text{ cm}) = 160 - 160 = 0\text{ cm}$. **Answer:** 64 books could be placed on the shelf, and no space was left. > Common mistake: Subtracting bookshelf length from total required length instead of dividing by book thickness. ### Question 5 *1 mark · Fill in the blank* Fill in the following blanks appropriately: 5.5 km = _________ m 35 cm = ________ m 14.5 cm = _______ mm 68 g = ________ kg 9.02 m = ________ mm 125.5 ml = _______ l **Solution** 1. Convert each given quantity using standard relations: $1\text{ km} = 1000\text{ m}$, $1\text{ m} = 100\text{ cm}$, $1\text{ cm} = 10\text{ mm}$, $1\text{ kg} = 1000\text{ g}$, $1\text{ m} = 1000\text{ mm}$, $1\text{ l} = 1000\text{ ml}$. **Answer:** $5500\text{ m}, 0.35\text{ m}, 145\text{ mm}, 0.068\text{ kg}, 9020\text{ mm}, 0.1255\text{ l}$ > Common mistake: Moving the decimal point in the wrong direction during unit conversion. ### Question 6 *3 marks · Short answer* The following problem was set by Sridharacharya in his book, Patiganita. “$6\frac{1}{4}$ is divided by $2\frac{1}{2}$, and $60\frac{1}{4}$ is divided by $3\frac{1}{2}$. Tell the quotients separately." Can you try to solve it by converting the fractions into decimals? **Part (a)** 1. Convert the mixed fraction $6\frac{1}{4}$ into decimal: $6\frac{1}{4} = 6.25$. 2. Convert the mixed fraction $2\frac{1}{2}$ into decimal: $2\frac{1}{2} = 2.5$. 3. Divide the two decimals: $6.25 \div 2.5 = 2.5$. Answer (a): 2.5 **Part (b)** 1. Convert the mixed fraction $60\frac{1}{4}$ into decimal: $60\frac{1}{4} = 60.25$. 2. Convert the mixed fraction $3\frac{1}{2}$ into decimal: $3\frac{1}{2} = 3.5$. 3. Divide the two decimals: $60.25 \div 3.5 = 17.214$ (approx). Answer (b): 17.214 **Answer:** The quotients are 2.5 and 17.214. > Common mistake: Errors in converting mixed fractions to decimals. ### Question 7 *3 marks · Short answer* Fill the boxes in at least 2 different ways: (a) $\square \times \square = 2.4$ (b) $\square \times \square = 14.5$ **Part (a)** 1. Way 1: $1.2 \times 2 = 2.4$ 2. Way 2: $0.6 \times 4 = 2.4$ Answer (a): $1.2 \times 2 = 2.4$ and $0.6 \times 4 = 2.4$ **Part (b)** 1. Way 1: $2.9 \times 5 = 14.5$ 2. Way 2: $1.45 \times 10 = 14.5$ Answer (b): $2.9 \times 5 = 14.5$ and $1.45 \times 10 = 14.5$ **Answer:** Multiple correct answers possible; two ways shown for each part. > Common mistake: Placing the decimal point incorrectly in the product. ### Question 8 *3 marks · Short answer* Find the following quotients given that $756 \div 36 = 21$: (a) $75.6 \div 3.6$ (b) $7.56 \div 0.36$ (c) $756 \div 0.36$ (d) $75.6 \div 360$ (e) $7560 \div 3.6$ (f) $7.56 \div 0.36$ **Part (a)** 1. $75.6 \div 3.6 = \frac{75.6}{3.6} = \frac{756}{36} = 21$ Answer (a): 21 **Part (b)** 1. $7.56 \div 0.36 = \frac{7.56}{0.36} = \frac{756}{36} = 21$ Answer (b): 21 **Part (c)** 1. $756 \div 0.36 = \frac{756 \times 100}{36} = 21 \times 100 = 2100$ Answer (c): 2100 **Part (d)** 1. $75.6 \div 360 = \frac{75.6 \div 10}{36} = \frac{7.56}{36} = 0.21$ Answer (d): 0.21 **Part (e)** 1. $7560 \div 3.6 = \frac{7560 \times 10}{36} = 2100 \times 10 = 21000$ Answer (e): 21000 **Part (f)** 1. $7.56 \div 0.36 = \frac{7.56}{0.36} = \frac{756}{36} = 21$ Answer (f): 21 **Answer:** Quotients are 21, 21, 2100, 0.21, 2100, and 21 respectively. > Common mistake: Forgetting to balance decimal places in dividend and divisor. ### Question 9 *3 marks · Short answer* Find the missing cells if each cell represents a÷b: **Solution** 1. Divide each row value 'a' by the corresponding column value 'b' to fill the cells. 2. For row $b = 37$: $1517 \div 37 = 41$, $151.7 \div 37 = 4.1$, $15.17 \div 37 = 0.41$, $1.517 \div 37 = 0.041$, $15170 \div 37 = 410$. 3. For row $b = 3.7$: $1517 \div 3.7 = 410$, $151.7 \div 3.7 = 41$, $15.17 \div 3.7 = 4.1$, $1.517 \div 3.7 = 0.41$, $15170 \div 3.7 = 4100$. **Answer:** The missing values are computed using place value division. > Common mistake: Shifting the decimal point by the wrong number of places. ### Question 10 *5 marks · Long answer* Using the digits 2, 4, 5, 8, and 0 fill the boxes $\square.\square \square \times \square.\square$ to get the: (a) maximum product (b) minimum product (c) product greater than 150 (d) product nearest to 100 (e) product nearest to 5 **Part (a)** 1. To get the maximum product, we should place the largest available digits in the highest place values. 2. Form the decimal numbers $85.4$ and $2.0$. 3. Multiply $85.4 \times 2.0 = 170.8$. Answer (a): $85.4 \times 2.0 = 170.8$ **Part (b)** 1. To get the minimum product, we should form the smallest possible numbers using the non-zero digits at the highest place values. 2. Form the decimal numbers $2.04$ and $5.8$. 3. Multiply $2.04 \times 5.8 = 11.832$. Answer (b): $2.04 \times 5.8 = 11.832$ **Part (c)** 1. To obtain a product greater than 150, we need large leading digits. 2. Form the numbers $84.5$ and $2.0$. 3. Multiply $84.5 \times 2.0 = 169$, which is greater than 150. Answer (c): $84.5 \times 2.0 = 169$ **Part (d)** 1. To get a product nearest to 100, we test combinations around 100. 2. Consider $48.5 \times 2.0 = 97.0$ or $24.8 \times 4.0$ etc. 3. The combination $48.5 \times 2.0 = 97.0$ gives a product very close to 100. Answer (d): $48.5 \times 2.0 = 97$ **Part (e)** 1. To get a product nearest to 5, we test combinations that yield a small number. 2. Consider $2.04 \times 2.5$ or similar small decimal combinations. 3. Using $2.4 \times 2.05 = 4.92$, which is very close to 5. Answer (e): $2.4 \times 2.05 = 4.92$ **Answer:** The required products for the given conditions are determined by placing the digits 2, 4, 5, 8, and 0 into the template. > Common mistake: Placing zero incorrectly leading to a change in the number of decimal places. ### Question 11 *3 marks · Short answer* Sort the following expressions in increasing order: (a) $245.05 \times 0.942368$ (b) $245.05 \times 7.9682$ (c) $245.05 \div 7.9682$ (d) $245.05 \div 0.942368$ (e) $245.05$ (f) $7.9682$ **Solution** 1. Evaluate or deduce the approximate value of each expression: (a) $245.05 \times 0.942368 \approx 230.9$, (b) $245.05 \times 7.9682 \approx 1952.7$, (c) $245.05 \div 7.9682 \approx 30.75$, (d) $245.05 \div 0.942368 \approx 260$, (e) $245.05$, (f) $7.9682$. 2. Order the calculated values from smallest to largest: $7.9682$, $245.05 \div 7.9682$, $245.05 \times 0.942368$, $245.05$, $245.05 \div 0.942368$, $245.05 \times 7.9682$. 3. Write the final sorted sequence using original expression labels: (f), (c), (a), (e), (d), (b). **Answer:** (f), (c), (a), (e), (d), (b) > Common mistake: Assuming multiplication always increases a number and division always decreases it. ## Frequently asked questions ### How many total questions are there in NCERT Solutions for Class 7 Maths Chapter 12: Another Peek Beyond the Point? The chapter contains five separate Figure it Out sets with a total of 35 questions spread across them according to the new NCERT book for the 2026-27 session. You can find SwaVid's free PDF and step-by-step solutions for all these questions on this page only. ### Which topics are covered in the Class 7 Maths Chapter 12 exercises? The exercises cover various important concepts including decimal multiplication, decimal division, fraction to decimal conversion, profit calculation with decimals, and unit conversion. Students also practice evaluating missing terms in equations and working with decimals on a number line. ### What are the hardest question types in this chapter and how should I approach them? The long answer and multi-step word problems involving profit calculation, decimal division with decimal divisors, and comparing decimal operations are often considered the trickiest. To approach them, carefully break down the given information into smaller steps and double-check your decimal placements before final calculation. ### How can I write answers to get full marks in Class 7 Maths exams for this chapter? To secure full marks, you should clearly state the given values, write down the applicable formula or conversion rule, and show each step of the calculation neatly. Referring to SwaVid's free PDF and step-by-step solutions available on this page only will help you understand the ideal presentation format. ### Is the free PDF for this chapter available for download? Yes, complete solutions and the free PDF for Class 7 Maths Chapter 12 are available on this page only. They are designed as per the latest NCF 2023 curriculum for the 2026-27 session to help with your daily practice. ## Related pages - [Class 7 Maths chapters](https://www.swavid.com/maths/class/7) 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