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

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 simppfy the proper fraction of the mixed number and write it in lowest terms.

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

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 $6frac{8}{10}$.

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, $6frac{8}{10} = frac{4}{5}$.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 5 is multipped 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, $6.8 = 6frac{4}{5} = frac{34}{5}$ in simplest form

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 $15frac{25}{100}$.

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, $15frac{25}{100} = 15frac{1}{4}$.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 4 is multipped 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, $15frac{25}{100} = 15frac{1}{4} = frac{61}{4}$ in simplest form