Converting a Mixed Number With a Denominator of 2, 4, or 5 to a Decimal

A mixed number is a whole number and a proper fraction combined. So, a mixed number consists of two parts, the whole number part and the fractional part. For example, in mixed number $2 \frac{2}{5}$ , the whole number part is 2 and the fractional part is $\frac{2}{5}$.

In this lesson, we convert given mixed number with a denominator of 2, 4 or 5 into a decimal.

Rules to convert a mixed number with a denominator of 2, 4 or 5 into a decimal.

• At first, we convert a mixed number with a denominator of 2, 4 or 5 into a fraction using the algorithm method.

• Then, we write its equivalent fraction such that the denominator is a power of ten.

• We then shift the decimal that many places to the left as there are zeros after 1 in the denominator.

Convert $2 \frac{1}{2}$ into a decimal.

Solution

Step 1:

At first, we convert the mixed number into a fraction using the algorithm

$2 \frac{1}{2} = \frac{\left ( 2\times 2 + 1 \right )}{2} = \frac{5}{2}$

Step 2:

Then we write an equivalent fraction of 5/2 with a denominator 10.

$\frac{5}{2} = \frac{\left ( 5\times 5 \right )}{2 \times 5} = \frac{25}{10}$

Step 3:

Shifting the decimal one place to the left we get

$\frac{25}{10} = \frac{25.0}{10} = 2.5$

Step 4:

So, $2 \frac{1}{2} = 2.5$

Convert $3 \frac{3}{4}$ into a decimal.

Solution

Step 1:

At first, we convert the mixed number into a fraction using the algorithm

$3 \frac{3}{4} = \frac{\left ( 3\times 4 + 3 \right )}{4} = \frac{15}{4}$

Step 2:

Then we write an equivalent fraction of 15/4 with a denominator 100.

$\frac{15}{4} = \frac{\left ( 15 \times 25 \right )}{\left ( 4 \times 25 \right )} = \frac{375}{100}$

Step 3:

Shifting the decimal two places to the left we get

$\frac{375}{100} = \frac{375.0}{100} = 3.75$

Step 4:

So, $3 \frac{3}{4} = 3.75$

Convert $7 \frac{2}{5}$ into a decimal.

Solution

Step 1:

At first, we convert the mixed number into a fraction using the algorithm

$7 \frac{2}{5} = \frac{\left ( 7\times 5 + 2 \right )}{5} = \frac{37}{5}$

Step 2:

Then we write an equivalent fraction of 37/5 with a denominator 10.

$\frac{37}{5} = \frac{\left ( 37 \times 2 \right )}{\left ( 5 \times 2 \right )} = \frac{74}{10}$

Step 3:

Shifting the decimal one place to the left we get

$\frac{74}{10} = \frac{74.0}{10} = 7.4$

Step 4:

So, $7 \frac{2}{5} = 7.4$