Find the following quotients given that : (a) (b) (c) (d) (e) (f)

Question

Homi · Accepted Answer

We can multiply or divide both numbers in a division by the same number. This does not change the quotient.

Step 1 — The main division fact

We are given a very helpful division fact. This fact tells us that 756 divided by 36 equals 21. We will use this fact to solve all parts.

$756 \div 36 = 21$

Step 2 — Solving part (a)

We need to find the value of $75.6 \div 3.6$ . Let us write this as a fraction.

$\frac{75.6}{3.6}$

To remove the decimal points, we can multiply both numbers by 10. Multiplying both numbers by 10 does not change the answer.

$\frac{75.6 \times 10}{3.6 \times 10}$

$= \frac{756}{36}$

We know from the given fact that $756 \div 36$ is 21.

$\boxed{\textbf{21}}$

Step 3 — Solving part (b)

We need to find the value of $7.56 \div 0.36$ . Let us write this as a fraction.

$\frac{7.56}{0.36}$

To remove the decimal points, we can multiply both numbers by 100. Multiplying both numbers by 100 does not change the answer.

$\frac{7.56 \times 100}{0.36 \times 100}$

$= \frac{756}{36}$

We know from the given fact that $756 \div 36$ is 21.

$\boxed{\textbf{21}}$

Step 4 — Solving part (c)

We need to find the value of $756 \div 0.36$ . Let us write this as a fraction.

$\frac{756}{0.36}$

To make the bottom number 36, we multiply it by 100. We must also multiply the top number by 100.

$\frac{756 \times 100}{0.36 \times 100}$

$= \frac{75600}{36}$

We can write 75600 as $756 \times 100$ .

$= \frac{756 \times 100}{36}$

We know that $756 \div 36$ is 21.

$= 21 \times 100$

$\boxed{\textbf{2100}}$

Step 5 — Solving part (d)

We need to find the value of $75.6 \div 360$ . Let us write this as a fraction.

$\frac{75.6}{360}$

We want to get 756 on top and 36 on the bottom. To get 756 from 75.6, we multiply by 10. If we multiply the top by 10, we must also multiply the bottom by 10.

$\frac{75.6 \times 10}{360 \times 10}$

$= \frac{756}{3600}$

We can write 3600 as $36 \times 100$ .

$= \frac{756}{36 \times 100}$

We know that $756 \div 36$ is 21.

$= \frac{21}{100}$

$\boxed{\textbf{0.21}}$

Step 6 — Solving part (e)

We need to find the value of $7560 \div 3.6$ . Let us write this as a fraction.

$\frac{7560}{3.6}$

To make the bottom number 36, we multiply it by 10. We must also multiply the top number by 10.

$\frac{7560 \times 10}{3.6 \times 10}$

$= \frac{75600}{36}$

We can write 75600 as $756 \times 100$ .

$= \frac{756 \times 100}{36}$

We know that $756 \div 36$ is 21.

$= 21 \times 100$

$\boxed{\textbf{2100}}$

Step 7 — Solving part (f)

We need to find the value of $7.56 \div 0.36$ . This is the same problem as part (b). Let us write this as a fraction.

$\frac{7.56}{0.36}$

To remove the decimal points, we can multiply both numbers by 100. Multiplying both numbers by 100 does not change the answer.

$\frac{7.56 \times 100}{0.36 \times 100}$

$= \frac{756}{36}$

We know from the given fact that $756 \div 36$ is 21.

$\boxed{\textbf{21}}$

Answer

(a) 21 (b) 21 (c) 2100 (d) 0.21 (e) 2100 (f) 21

Question 32

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