Question

Which of the following are the pairs of equivalent fractions?
(i) $\frac{5}{6}\text{and}\frac{20}{24}$
(ii) $\frac{3}{8}\text{and}\frac{15}{40}$
(iii) $\frac{4}{7}\text{and}\frac{16}{21}$
(iv) $\frac{2}{9}\text{and}\frac{14}{63}$
(v) $\frac{1}{3}\text{and}\frac{9}{24}$
(vi) $\frac{2}{3}\text{and}\frac{33}{22}$

Answer 1

(i) $\frac{5}{6}\text{and}\frac{20}{24}$

Now we know that, $5\times 4=20$

$\Rightarrow \frac{5}{6}\times \frac{4}{4}=\frac{20}{24}$

Hence, they are equivalent fractions.

(ii) $\frac{3}{8}\text{and}\frac{15}{40}$

Now we know that, $3\times 5=15$

$\Rightarrow \frac{3}{8}\times \frac{5}{5}=\frac{15}{40}$

Hence, they are equivalent fractions.

(iii) $\frac{4}{7}\text{and}\frac{16}{21}$

Now we know that, $4\times 4=16$

$\Rightarrow \frac{4}{7}\times \frac{4}{4}=\frac{16}{28}\ne \frac{16}{21}$

Hence, they are not equivalent fractions.

(iv) $\frac{2}{9}\text{and}\frac{14}{63}$

Now we know that, $2\times 7=14$

$\Rightarrow \frac{2}{9}\times \frac{7}{7}=\frac{14}{63}$

Hence, they are equivalent fractions.

(v) $\frac{1}{3}\text{and}\frac{9}{24}$

Now we know that, $1\times 9=9$

$\Rightarrow \frac{1}{3}\times \frac{9}{9}=\frac{9}{27}\ne \frac{9}{24}$

Hence, they are not equivalent fractions.

(vi) $\frac{2}{3}\text{and}\frac{33}{22}$

Now, $2$ multiplied by any whole number is not equal to $33$. Therefore, we will use the method of cross multiplication to check.

LHS: $2\times 22=44$

RHS: $33\times 3=99$

Since, $44\ne 99\Rightarrow$ LHS $\ne$ RHS.

Hence, they are not equivalent fractions.