Question

Write the fractions in increasing order?

$\frac{2}{9},\frac{7}{12},\frac{13}{20}$ and $\frac{1}{4}$

Answer 1

Step 1: Converting the fractions into like fractions

Given fractions are $\frac{2}{9},\frac{7}{12},\frac{13}{20}$and $\frac{1}{4}$

To express these fractions in increasing order, first, we have to convert them into like fractions.

We must make all the denominators the same by taking the LCM of all the denominators, that is $9,12,20$ and $4$.

$$\begin{gathered} 9=3\times 3 \\ 12=2\times 2\times 3 \\ 20=2\times 2\times 5 \\ 4=2\times 2 \end{gathered}$$

From the above choose each factor with the highest factor.

LCM$\left(9,12,20,4\right)$$=$$2\times 2\times 3\times 3\times 5$

LCM$\left(9,12,20,4\right)$$=$$180$

Now make the denominators as $180$ for all the fractions.

$$\begin{gathered} \frac{2}{9}=\frac{2\times 20}{9\times 20}=\frac{40}{180} \\ \frac{7}{12}=\frac{7\times 15}{12\times 15}=\frac{105}{180} \\ \frac{13}{20}=\frac{13\times 9}{20\times 9}=\frac{117}{180} \\ \frac{1}{4}=\frac{1\times 45}{4\times 45}=\frac{45}{180} \end{gathered}$$

Step 2: Arranging the fractions in increasing order

Since the denominators of all the same now, we will arrange the fractions in order using the numerators.

Now arrange the above fractions in increasing or ascending order.

$\frac{40}{180}<\frac{45}{180}<\frac{105}{180}<\frac{117}{180}$

Therefore, according to question fractions in increasing order are $\frac{2}{9},\frac{1}{4},\frac{7}{12},\frac{13}{20}$