Question

(a) What is the name given to the set of fractions: $\frac{1}{3},\frac{2}{6},$$\frac{4}{12},\frac{8}{24}?$

(b) Why are they called so?

(c) By what number the numerator and denominator are multiplied to obtain the next fraction?

Answer 1

Step1: Find the name of the set of fractions $\frac{1}{3},\frac{2}{6},$$\frac{4}{12},\frac{8}{24}$.

Given fractions: $\frac{1}{3},\frac{2}{6},$$\frac{4}{12},\frac{8}{24}$.

We know

$\frac{2}{6}=\frac{1}{3}$

$\frac{4}{12}=\frac{1}{3}$

$\frac{8}{24}=\frac{1}{3}$

Therefore, $\frac{1}{3}=\frac{2}{6}=\frac{4}{12}=\frac{8}{24}$

Hence, the set of fractions: $\frac{1}{3},\frac{2}{6},$$\frac{4}{12},\frac{8}{24}$is an equivalent fraction.

Step2: Why are they called an equivalent fraction.

Since $\frac{1}{3},\frac{2}{6},\frac{4}{12},\frac{8}{24}$are equivalent fractions.

Multiplying the denominator and numerator of a fraction by the same number does not change its value.

Step3: What number the numerator and denominator are multiplied to obtain the next fraction.

To obtain the next fraction we multiply the numerator and denominator by $2$.

Thus, $\frac{1}{3}\times \frac{2}{2}=\frac{2}{6}$

$\frac{2}{6}\times \frac{2}{2}=\frac{4}{12}$

$\frac{4}{12}\times \frac{2}{2}=\frac{8}{24}$

Hence, to obtain the next fraction we multiply the numerator and denominator by $2$.