Rational Numbers Quiz - ICSE Class 8 Mathematics
Free practice quiz: Rational Numbers (ICSE Class 8 Mathematics). 57 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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If $\frac{a}{b} = \frac{3}{5}$ and $\frac{b}{c} = \frac{10}{7}$, what is the value of $\frac{a}{c}$?
- $\frac{3}{7}$
- $\frac{6}{7}$
- $\frac{21}{50}$
- $\frac{7}{6}$
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Answer: B. $\frac{6}{7}$
To find $\frac{a}{c}$, we can multiply the given ratios: $\frac{a}{c} = \frac{a}{b} \times \frac{b}{c} = \frac{3}{5} \times \frac{10}{7} = \frac{3 \times 10}{5 \times 7} = \frac{30}{35}$. Simplifying this fraction by dividing the numerator and denominator by their greatest common divisor, which is 5, we get $\frac{30 \div 5}{35 \div 5} = \frac{6}{7}$.
The sum of two rational numbers is $\frac{-7}{8}$. If one of the numbers is $\frac{1}{4}$, what is the other number?
- $\frac{-9}{8}$
- $\frac{-5}{8}$
- $\frac{-7}{32}$
- $\frac{-1}{8}$
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Answer: A. $\frac{-9}{8}$
Let the other rational number be $x$. According to the problem, $\frac{1}{4} + x = \frac{-7}{8}$. To find $x$, we subtract $\frac{1}{4}$ from $\frac{-7}{8}$: $x = \frac{-7}{8} - \frac{1}{4}$. To perform the subtraction, we need a common denominator, which is 8. Convert $\frac{1}{4}$ to $\frac{2}{8}$: $x = \frac{-7}{8} - \frac{2}{8} = \frac{-7-2}{8} = \frac{-9}{8}$.
If $\frac{x}{y} = 2$ and $\frac{y}{z} = 3$, what is $\frac{x}{z}$?
- 6
- 5
- 3/2
- 2/3
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Answer: A. 6
We are given $\frac{x}{y} = 2$ and $\frac{y}{z} = 3$. To find $\frac{x}{z}$, we can multiply these two ratios: $\frac{x}{z} = \frac{x}{y} \times \frac{y}{z} = 2 \times 3 = 6$.
What is the multiplicative inverse of $-\frac{2}{7}$?
- $\frac{2}{7}$
- $\frac{7}{2}$
- $-\frac{7}{2}$
- $\frac{-2}{7}$
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Answer: C. $-\frac{7}{2}$
The multiplicative inverse (or reciprocal) of a rational number is the number that, when multiplied by the original number, results in 1. For a rational number $\frac{p}{q}$, its multiplicative inverse is $\frac{q}{p}$, provided $p \neq 0$ and $q \neq 0$. The multiplicative inverse of $-\frac{2}{7}$ is $\frac{7}{-2}$, which is equivalent to $-\frac{7}{2}$.
Simplify: $\frac{3}{5} \div \frac{6}{5}$
- $\frac{18}{25}$
- $\frac{1}{2}$
- 2
- $\frac{25}{18}$
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Answer: B. $\frac{1}{2}$
To divide by a rational number, multiply by its reciprocal. The reciprocal of $\frac{6}{5}$ is $\frac{5}{6}$. So, $\frac{3}{5} \div \frac{6}{5} = \frac{3}{5} \times \frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30}$. Simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 15: $\frac{15 \div 15}{30 \div 15} = \frac{1}{2}$.