50+ Operations With Rational Numbers worksheets for 7th Class on ... - Free Printable

Let's solve each of the first 5 questions from your quiz step by step. These involve operations with rational numbers (fractions and mixed numbers).

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Question 1:

$$
1\frac{2}{9} + \frac{2}{3}
$$

Step 1: Convert the mixed number to an improper fraction.
$$
1\frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9}
$$

Step 2: Add $\frac{11}{9} + \frac{2}{3}$

Find a common denominator. The least common denominator (LCD) of 9 and 3 is 9.

Convert $\frac{2}{3}$:
$$
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
$$

Now add:
$$
\frac{11}{9} + \frac{6}{9} = \frac{17}{9}
$$

Convert back to mixed number:
$$
\frac{17}{9} = 1\frac{8}{9}
$$

✔ Answer: C $1\frac{8}{9}$

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Question 2:

$$
\frac{4}{5} - \frac{1}{3}
$$

Find LCD of 5 and 3 → 15

Convert:
- $\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$
- $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$

Subtract:
$$
\frac{12}{15} - \frac{5}{15} = \frac{7}{15}
$$

✔ Answer: C $\frac{7}{15}$

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Question 3:

$$
8\frac{4}{5} - \frac{7}{8}
$$

Convert mixed number:
$$
8\frac{4}{5} = \frac{5 \times 8 + 4}{5} = \frac{40 + 4}{5} = \frac{44}{5}
$$

Now subtract: $\frac{44}{5} - \frac{7}{8}$

LCD of 5 and 8 → 40

Convert:
- $\frac{44}{5} = \frac{44 \times 8}{5 \times 8} = \frac{352}{40}$
- $\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}$

Subtract:
$$
\frac{352}{40} - \frac{35}{40} = \frac{317}{40}
$$

Convert to mixed number:
$$
\frac{317}{40} = 7\frac{37}{40} \quad (\text{since } 40 \times 7 = 280,\ 317 - 280 = 37)
$$

✔ Answer: D $7\frac{37}{40}$

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Question 4:

$$
\frac{4}{5} \times \frac{1}{3}
$$

Multiply numerators and denominators:
$$
\frac{4 \times 1}{5 \times 3} = \frac{4}{15}
$$

✔ Answer: D $\frac{4}{15}$

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Question 5:

$$
2\frac{1}{4} \times \frac{8}{15}
$$

Convert mixed number:
$$
2\frac{1}{4} = \frac{4 \times 2 + 1}{4} = \frac{9}{4}
$$

Now multiply:
$$
\frac{9}{4} \times \frac{8}{15} = \frac{9 \times 8}{4 \times 15} = \frac{72}{60}
$$

Simplify:
- Divide numerator and denominator by 12: $\frac{72 \div 12}{60 \div 12} = \frac{6}{5}$

Convert to mixed number:
$$
\frac{6}{5} = 1\frac{1}{5}
$$

✔ Answer: C $1\frac{1}{5}$

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✔ Final Answers:

1. C $1\frac{8}{9}$
2. C $\frac{7}{15}$
3. D $7\frac{37}{40}$
4. D $\frac{4}{15}$
5. C $1\frac{1}{5}$

Let me know if you'd like help with the remaining questions!