Equivalent fractions are different fractions that represent the same part of a whole having the same value. This equivalence results from multiplying or dividing the numerator and the denominator by the same number.
Let us determine whether ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ are equivalent.
Since ${\dfrac{1}{2}}$ = ${\dfrac{5}{10}}$, the given fractions are equivalent.
Cross Multiplying
Now, by cross-multiplying the fractions ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ fractions, we get
Since both the products are equal, the fractions ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ are equivalent fractions.
Converting to Decimals
Finding their decimal numbers is also a way to verify whether the given fractions are equivalent.
Converting ${\dfrac{5}{10}}$ and ${\dfrac{1}{2}}$ to the decimal form, we get
Solved Examples
Verify whether the fractions ${\dfrac{12}{18}}$ and ${\dfrac{16}{24}}$ are equivalent.
Solution:
In the given fractions, the denominators are 18 and 24 LCM of 18 and 24 are 72 Now, for making the denominators of the given fractions equal, we get ${\dfrac{12\times 4}{18\times 4}}$ = ${\dfrac{48}{72}}$ ${\dfrac{16\times 3}{24\times 3}}$ = ${\dfrac{48}{72}}$ Thus the fractions ${\dfrac{12}{18}}$ and ${\dfrac{16}{24}}$ are equivalent.
Is ${\dfrac{8}{12}}$ an equivalent fraction of ${\dfrac{2}{3}}$
Solution:
Here, On dividing the numerator and the denominator of ${\dfrac{8}{12}}$ by 4, we get ${\dfrac{8\div 4}{12\div 4}}$ = ${\dfrac{2}{3}}$ Thus, ${\dfrac{8}{12}}$ is an equivalent fraction of ${\dfrac{2}{3}}$
