Converting a decimal to a mixed number and an improper fraction in simplest form: Basic

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Definition

Rules to convert a decimal to a mixed number and an improper fraction in simplest form.

• We read the decimal as whole number part, tenths, hundredths and so on and write it as a mixed number.

• Then we simplify the proper fraction of the mixed number and write it in lowest terms.

• Using algorithm, we convert the mixed number to an improper fraction.

Example 1

Convert 6.8 to a mixed number and an improper fraction in simplest form.

Solution

Step 1:

The decimal 6.8 is read as 6 and 8 tenths.

So, it can be written as a mixed number $6\frac{8}{10}$.

Step 2:

The mixed number has a whole number part 6 and a fractional part 8/10 which can be reduced to lowest terms as $\frac{4}{5}$. So, $6\frac{8}{10} = \frac{4}{5}$.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 5 is multiplied with whole number 4 and the product is added to the numerator 4 to give 6 × 5 + 4 = 34.

Step 4:

This becomes the numerator of the improper fraction and 5 is retained as the denominator of the improper fraction. We get $\frac{34}{5}$

So, $6.8 = 6\frac{4}{5} = \frac{34}{5}$ in simplest form

Example 2

Convert 15.25 to a mixed number and an improper fraction in simplest form

Solution

Step 1:

The decimal 15.25 is read as 15 and 25 hundredths. So, it is written as a mixed number $15\frac{25}{100}$.

Step 2:

The mixed number has a whole number part 15 and a fractional part $\frac{25}{100}$ which is reduced to simplest form as $\frac{1}{4}$. So, $15\frac{25}{100} = 15\frac{1}{4}$.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 4 is multiplied with whole number 15 and the product is added to the numerator 1 to give 15 × 4 + 1 = 61.

Step 4:

This becomes the numerator of the improper fraction and 4 is retained as the denominator of the improper fraction. We get $\frac{61}{4}$

Step 5:

So, $15\frac{25}{100} = 15\frac{1}{4} = \frac{61}{4}$ in simplest form