Chapter 4 Another Peek Beyond the Point (Class 7 - Latest Maths NCERT (Ganita Prakash II) Solutions)

Question 1. 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

Question 2. Find the products:

(a) $27.34 \times 6$

(b) $4.23 \times 3.7$

(c) $0.432 \times 0.23$

Question 3. Thejus needs $1.65\text{ m}$ of cloth for a shirt. How many metres of cloth are needed for $3$ shirts?

Question 4. Meenu bought $4$ notebooks and $3$ erasers. The cost of each book was $\textsf{₹} 15.50$ and each eraser was $\textsf{₹} 2.75$. How much did she spend in all?

Question 5. The thickness of a rupee coin is $1.45\text{ mm}$. What is the total height of the cylinder formed by placing $36$ rupee coins one over the other? Write the answer in centimeters.

Question 6. The price of $1\text{ kg}$ of oranges is $\textsf{₹} 56.50$. What is the price of $2.250\text{ kg}$ 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?

Question 7. Dwarakanath purchases notebooks at a wholesale price of $\textsf{₹} 23.6$ per piece and sells each notebook at $\textsf{₹} 30/-$. How much profit does he make if he sells $50$ books in a week?

Question 8. 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 $1$?

Question 9. 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) $0.07 \times 0.06$

Question 10. Multiplying the following numbers by $10, 100$ and $1000$ to complete the table.

Question 1. 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) $\frac{4827}{8}$

Question 2. Choose the correct answer:

(a) $\frac{1526}{4} =$

(i) $38.15$

(ii) $380.15$

(iii) $381.5$

(iv) $381.05$

(b) $\frac{3567}{8} =$

(i) $4458.75$

(ii) $44.5875$

(iii) $445.875$

(iv) $4458.75$

Question 3. What is the quotient?

(a) $132 \div 4 =$

(b) $13.2 \div 4 =$

(c) $1.32 \div 4 =$

(d) $0.132 \div 4 =$

Question 4. What is the quotient?

(a) $126 \div 8 =$

(b) $12.6 \div 8 =$

(c) $1.26 \div 8 =$

(d) $0.126 \div 8 =$

(e) $0.0126 \div 8 =$

Question 1. Express the following fractions in decimal form:

(a) $\frac{2}{5}$

(b) $\frac{13}{4}$

(c) $\frac{4}{50}$

(d) $\frac{5}{8}$

Question 2. Find the quotients:

(a) $24.86 \div 1.2$

(b) $5.728 \div 1.52$

Question 3. 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) $0.156 \times 0.12 = \text{__________}$

Question 4. 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) $25 \div 0.01 = 25 \times \text{______}$

Question 5. 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 $2.46 \div 0.15$?

Question 6. A $4\text{ m}$ long wooden block has to be cut into $5$ pieces of equal length. What is the length of each piece?

Question 7. If the perimeter of a regular polygon with $12$ sides is $208.8\text{ cm}$, what is the length of its side?

Question 8. $3$ litres of watermelon juice is shared among $8$ friends equally. How much watermelon juice will each get? Express the quantity of juice in millilitres.

Question 9. A car covers $234.45\text{ km}$ using $12.6$ litres of petrol. What is the distance travelled per litre?

Question 10. $13.5\text{ kg}$ of flour (aata) was distributed equally among $15$ students. How much flour did each student receive?

Question 1. A $210$ gram packet of peanut chikki costs $\textsf{₹} 70.5$, while a $110$ gram packet of potato chips costs $\textsf{₹} 33.25$. Which is cheaper?

Question 2. Write the decimal number at the arrow mark:

Question 3. Shyamala bought $3\text{ kg}$ bananas at $\textsf{₹} 30/-$ per kg. She counted $35$ bananas in all. She sells each banana for $\textsf{₹} 5/-$. How much profit does she make selling all the bananas?

Question 4. A teacher placed textbooks that are $2.5\text{ cm}$ thick on a bookshelf. The teacher wanted to place $80$ textbooks on the shelf. The bookshelf is $160\text{ cm}$ long. How many books could be placed on the shelf? Was there any space left? If yes, how much?

Question 5. Fill in the following blanks appropriately:

$1\text{ cm} = 10\text{ mm}$

$1\text{ m} = 100\text{ cm}$

$1\text{ km} = 1000\text{ m}$

$1\text{ kg} = 1000\text{ g}$

$1\text{ g} = 1000\text{ mg}$

$1\text{ l} = 1000\text{ ml}$

$5.5\text{ km} = \text{_________ m}$

$35\text{ cm} = \text{________ m}$

$14.5\text{ cm} = \text{_______ mm}$

$68\text{ g} = \text{________ kg}$

$9.02\text{ m} = \text{________ mm}$

$125.5\text{ ml} = \text{_______ l}$

Question 6. 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?

Question 7. Fill the boxes in at least $2$ different ways:

(a) $\text{_____} \times \text{_____} = 2.4$

(b) $\text{_____} \times \text{_____} = 14.5$

Question 8. 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) $7.56 \div 0.36$

Question 9. Find the missing cells if each cell represents $a \div b$:

Question 10. Using the digits $2, 4, 5, 8$, and $0$ fill the boxes $\text{_____} . \text{_____} \times \text{_____} . \text{_____}$ to get the:

(a) maximum product

(b) minimum product

(c) product greater than $150$

(d) product nearest to $100$

(e) product nearest to $5$

Question 11. 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) $7.9682$