Question & Answer
QUESTION

Write 10 equivalent rational numbers for $\dfrac{1}{2}$.

ANSWER Verified Verified
Hint: Use the fact that equivalent fractions are the fractions with different values of numerators and denominators that represent the same value or proportion of the whole. Multiply the numerator and denominator of the given fraction with the same integer, other than zero to write the equivalent fractions.

Complete step-by-step answer:
We have to write 10 equivalent fractions of $\dfrac{1}{2}$.
We know that the equivalent fractions are the fractions with different values of numerators and denominators that represent the same value or proportion of the whole.
To calculate the equivalent fractions of $\dfrac{1}{2}$, multiply the numerator and denominator of the given fraction with the same integer.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by 2, we have $\dfrac{1\times 2}{2\times 2}=\dfrac{2}{4}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by 3, we have $\dfrac{1\times 3}{2\times 3}=\dfrac{3}{6}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by 4, we have $\dfrac{1\times 4}{2\times 4}=\dfrac{4}{8}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by 5, we have $\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -1, we have $\dfrac{1\times -1}{2\times -1}=\dfrac{-1}{-2}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -2, we have $\dfrac{1\times -2}{2\times -2}=\dfrac{-2}{-4}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -3, we have $\dfrac{1\times -3}{2\times -3}=\dfrac{-3}{-6}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -4, we have $\dfrac{1\times -4}{2\times -4}=\dfrac{-4}{-8}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -5, we have $\dfrac{1\times -5}{2\times -5}=\dfrac{-5}{-10}$.
Multiplying the numerator and denominator of $\dfrac{1}{2}$ by -6, we have $\dfrac{1\times -6}{2\times -6}=\dfrac{-6}{-12}$.
Hence, the equivalent fractions for the fraction $\dfrac{1}{2}$ are $\dfrac{2}{4},\dfrac{3}{6},\dfrac{4}{8},\dfrac{5}{10},\dfrac{-1}{-2},\dfrac{-2}{-4},\dfrac{-3}{-6},\dfrac{-4}{-8},\dfrac{-5}{-10},\dfrac{-6}{-12}$.

Note: Fraction represents equal parts of a whole or a collection. One must keep in mind that the denominator of a fraction can never be zero. That’s why we can’t multiply any fraction by 0 to write its equivalent fractions.