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

$2 frac{1}{2} = frac{left ( 2 imes 2 + 1 ight )}{2} = frac{5}{2}$

Step 2:

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

$frac{5}{2} = frac{left ( 5 imes 5 ight )}{2 imes 5} = frac{25}{10}$

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

$3 frac{3}{4} = frac{left ( 3 imes 4 + 3 ight )}{4} = frac{15}{4}$

Step 2:

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

$frac{15}{4} = frac{left ( 15 imes 25 ight )}{left ( 4 imes 25 ight )} = frac{375}{100}$

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

$7 frac{2}{5} = frac{left ( 7 imes 5 + 2 ight )}{5} = frac{37}{5}$

Step 2:

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

$frac{37}{5} = frac{left ( 37 imes 2 ight )}{left ( 5 imes 2 ight )} = frac{74}{10}$

Step 3:

Shifting the decimal one place to the left we get

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

Step 4:

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