CBSE Class 7 Mathematics Rational Numbers Worksheet Set A - Free Printable

Let's solve each question one by one with detailed explanations.

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Question 2: Which is greater?

a) $-\frac{4}{3}$ or $-\frac{8}{7}$

Solution:

We compare two negative fractions. The greater number will be the one closer to zero (i.e., the one with smaller absolute value).

- $|-\frac{4}{3}| = \frac{4}{3} \approx 1.333$
- $|-\frac{8}{7}| = \frac{8}{7} \approx 1.143$

Since $\frac{8}{7} < \frac{4}{3}$, then $-\frac{8}{7} > -\frac{4}{3}$

✔ Answer: $-\frac{8}{7}$ is greater.

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Question 3: Arrange in ascending order:

$\frac{5}{15}, -\frac{3}{5}, -\frac{4}{10}, \frac{3}{30}$

Step 1: Simplify all fractions

- $\frac{5}{15} = \frac{1}{3} \approx 0.333$
- $-\frac{3}{5} = -0.6$
- $-\frac{4}{10} = -\frac{2}{5} = -0.4$
- $\frac{3}{30} = \frac{1}{10} = 0.1$

Now list them:

- $-0.6$, $-0.4$, $0.1$, $0.333$

So ascending order:
$-\frac{3}{5}, -\frac{4}{10}, \frac{3}{30}, \frac{5}{15}$

✔ Answer: $-\frac{3}{5}, -\frac{4}{10}, \frac{3}{30}, \frac{5}{15}$

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Question 4: Find the value of the following:

#### a) $\frac{7}{15} \div \frac{9}{-28}$

Division: $\frac{7}{15} \div \frac{9}{-28} = \frac{7}{15} \times \frac{-28}{9}$

Multiply:
$$
= \frac{7 \times (-28)}{15 \times 9} = \frac{-196}{135}
$$

Simplify: GCD of 196 and 135 is 1 → already simplified.

✔ Answer: $-\frac{196}{135}$

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#### b) $-\frac{8}{11} \div \frac{16}{22}$

Note: $\frac{16}{22} = \frac{8}{11}$

So: $-\frac{8}{11} \div \frac{8}{11} = -1$

✔ Answer: $-1$

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#### c) $-2\frac{1}{8} + (-\frac{6}{10})$

Convert mixed number: $-2\frac{1}{8} = -\frac{17}{8}$

Simplify $-\frac{6}{10} = -\frac{3}{5}$

Now add: $-\frac{17}{8} + (-\frac{3}{5}) = -\frac{17}{8} - \frac{3}{5}$

LCM of 8 and 5 is 40:

$$
= -\left(\frac{17 \times 5}{40} + \frac{3 \times 8}{40}\right) = -\left(\frac{85 + 24}{40}\right) = -\frac{109}{40}
$$

✔ Answer: $-\frac{109}{40}$

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#### d) $(-4\frac{1}{5}) \div \frac{2}{7}$

Convert: $-4\frac{1}{5} = -\frac{21}{5}$

Now divide: $-\frac{21}{5} \div \frac{2}{7} = -\frac{21}{5} \times \frac{7}{2} = -\frac{147}{10}$

✔ Answer: $-\frac{147}{10}$

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Question 5: Find 4 rational numbers between $-\frac{1}{3}$ and $-4$

First, note that $-4 < -\frac{1}{3}$ since $-4 = -\frac{12}{3}$, and $-\frac{12}{3} < -\frac{1}{3}$

So we need numbers between $-4$ and $-\frac{1}{3}$

Let’s find common denominator or use decimal approximations:

- $-4 = -4.0$
- $-\frac{1}{3} \approx -0.333$

We can pick any 4 rational numbers between $-4$ and $-0.333$. For example:

- $-3$
- $-2$
- $-1$
- $-0.5$

Or as fractions:

- $-3 = -\frac{3}{1}$
- $-2 = -\frac{2}{1}$
- $-1 = -\frac{1}{1}$
- $-\frac{1}{2}$

✔ Answer: $-3, -2, -1, -\frac{1}{2}$ (any four rational numbers in that range)

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Question 6: Multiply $\frac{8}{13}$ by the reciprocal of $-\frac{17}{26}$

Reciprocal of $-\frac{17}{26}$ is $-\frac{26}{17}$

Now multiply:
$$
\frac{8}{13} \times \left(-\frac{26}{17}\right) = -\frac{8 \times 26}{13 \times 17}
$$

Note: $26 = 2 \times 13$, so:
$$
= -\frac{8 \times 2 \times 13}{13 \times 17} = -\frac{16}{17}
$$

✔ Answer: $-\frac{16}{17}$

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Question 7: The sum of two numbers is $-8$. If one of the numbers is $-\frac{17}{9}$, find the other.

Let the other number be $x$

Then:
$$
x + \left(-\frac{17}{9}\right) = -8
\Rightarrow x = -8 + \frac{17}{9}
$$

Convert $-8 = -\frac{72}{9}$

$$
x = -\frac{72}{9} + \frac{17}{9} = -\frac{55}{9}
$$

✔ Answer: $-\frac{55}{9}$

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Question 8: What should be subtracted from $-\frac{8}{15}$ so as to get $-\frac{5}{6}$?

Let the number to be subtracted be $x$

Then:
$$
-\frac{8}{15} - x = -\frac{5}{6}
\Rightarrow -x = -\frac{5}{6} + \frac{8}{15}
$$

Find common denominator: LCM of 6 and 15 is 30

$$
-\frac{5}{6} = -\frac{25}{30},\quad \frac{8}{15} = \frac{16}{30}
\Rightarrow -x = -\frac{25}{30} + \frac{16}{30} = -\frac{9}{30} = -\frac{3}{10}
$$

So $x = \frac{3}{10}$

✔ Answer: $\frac{3}{10}$

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Question 9: By what number should we multiply $-\frac{16}{21}$ so that their product is $\frac{4}{7}$?

Let the number be $x$

Then:
$$
-\frac{16}{21} \times x = \frac{4}{7}
\Rightarrow x = \frac{4}{7} \div \left(-\frac{16}{21}\right) = \frac{4}{7} \times \left(-\frac{21}{16}\right)
$$

$$
= -\frac{4 \times 21}{7 \times 16} = -\frac{84}{112}
$$

Simplify: divide numerator and denominator by 28 → $84 ÷ 28 = 3$, $112 ÷ 28 = 4$

So $-\frac{3}{4}$

✔ Answer: $-\frac{3}{4}$

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Question 10: Solve: $\frac{-5}{8} \div \left(-\frac{1}{2} + \frac{1}{4}\right)$

First simplify inside the parentheses:

$$
-\frac{1}{2} + \frac{1}{4} = -\frac{2}{4} + \frac{1}{4} = -\frac{1}{4}
$$

Now:
$$
\frac{-5}{8} \div \left(-\frac{1}{4}\right) = \frac{-5}{8} \times \left(-\frac{4}{1}\right) = \frac{20}{8} = \frac{5}{2}
$$

✔ Answer: $\frac{5}{2}$

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## ✔ Final Answers Summary:

| Q.No | Answer |
|------|--------|
| 2 | $-\frac{8}{7}$ is greater |
| 3 | $-\frac{3}{5}, -\frac{4}{10}, \frac{3}{30}, \frac{5}{15}$ |
| 4a | $-\frac{196}{135}$ |
| 4b | $-1$ |
| 4c | $-\frac{109}{40}$ |
| 4d | $-\frac{147}{10}$ |
| 5 | $-3, -2, -1, -\frac{1}{2}$ (example) |
| 6 | $-\frac{16}{17}$ |
| 7 | $-\frac{55}{9}$ |
| 8 | $\frac{3}{10}$ |
| 9 | $-\frac{3}{4}$ |
| 10 | $\frac{5}{2}$ |

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