Question

compare the fraction pairs below using <, >, or =..
\\(\frac{2}{5}\\) \\(\bigcirc\\) \\(\frac{4}{10}\\)
\\(\frac{6}{9}\\) \\(\bigcirc\\) \\(\frac{7}{12}\\)

Explanation:

First Fraction Pair ($\frac{2}{5}$ and $\frac{4}{10}$)

Step1: Simplify or find common denominator

To compare $\frac{2}{5}$ and $\frac{4}{10}$, we can simplify $\frac{4}{10}$ or find a common denominator. Simplifying $\frac{4}{10}$ by dividing numerator and denominator by 2: $\frac{4\div2}{10\div2}=\frac{2}{5}$.

Step2: Compare the fractions

Now we have $\frac{2}{5}$ and $\frac{2}{5}$, so they are equal.

Step1: Find a common denominator

The least common denominator of 9 and 12 is 36. Convert $\frac{6}{9}$: $\frac{6\times4}{9\times4}=\frac{24}{36}$. Convert $\frac{7}{12}$: $\frac{7\times3}{12\times3}=\frac{21}{36}$.

Step2: Compare the numerators

Since 24 > 21, $\frac{24}{36} > \frac{21}{36}$.

Answer:

$\frac{2}{5} = \frac{4}{10}$

Second Fraction Pair ($\frac{6}{9}$ and $\frac{7}{12}$)