Fractions and decimal

$200 \div 6\frac{1}{4} =$

Solution

Write 200 as a fraction, and then express the mixed number $6\frac{1}{4}$ into an improper fraction.

$200 \div \frac{25}{4} = \frac{200}{1} \div \frac{25}{4}$

Change the division sign into a multiplication sign, and then reciprocate the divisor to be $\frac{4}{25}$.

Hence, $\frac{200}{1} \div \frac{25}{4} = \frac{200}{1} \times \frac{4}{25} = 8 \times 4 = 32$.

Therefore, $200 \div 6\frac{1}{4} = 32$.

$56 \div 2\frac{1}{8} =$

Solution

Write 56 as a fraction, and then change the mixed number $2\frac{1}{8}$ into an improper fraction.

$56 \div 2\frac{1}{8} = \frac{56}{1} \div \frac{17}{8}$

Change the division sign into a multiplication sign, and then change the divisor to be $\frac{8}{17}$: Hence, $\frac{56}{1} \div \frac{17}{8} = \frac{56}{1} \times \frac{8}{17} = \frac{448}{17} = 26\frac{6}{17}$.

Therefore, $56 \div 2\frac{1}{8} = 26\frac{6}{17}$.

Example 1

A teacher divided a half of a circular piece of paper into three equal parts. Three pupils were given one part each. What fraction of the circular piece of paper did each pupil get?

Solution

1. The instructions of the question can be written using numbers and division sign as follows:

$\frac{1}{2} \div 3 =$

2. When each half of a circular piece of paper is divided into three equal parts, a total of six parts are obtained.

3. In fraction one part from the 6 parts of the circular piece of paper is written as $\frac{1}{6}$.

Therefore, $\frac{1}{2} \div 3 = \frac{1}{6}$.

From this example, you can obtain $\frac{1}{6}$ from $\frac{1}{2} \div 3$, as follows:

The division sign should be changed to a multiplication sign, and 3 is written as its reciprocal and becomes $\frac{1}{3}$.

Thus, $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.

Therefore, each pupil got $\frac{1}{6}$ of the circular piece of paper.

Example 2

$\frac{2}{5} \div 2 =$

Solution

Write a whole number as a fraction with the denominator 1:

$\frac{2}{5} \div 2 = \frac{2}{5} \div \frac{2}{1}$

Multiply the dividend by the reciprocal of the divisor:

$\frac{2}{5} \div 2 = \frac{2}{5} \times \frac{1}{2} = \frac{2}{10} = \frac{1}{5}$.

Therefore, $\frac{2}{5} \div 2 = \frac{1}{5}$.

Example 3

$\frac{5}{3} \div 15 =$

Solution

Use the same steps as in Example 2:

$\frac{5}{3} \div 15 = \frac{5}{3} \div \frac{15}{1} = \frac{5}{3} \times \frac{1}{15} = \frac{5}{45} = \frac{1}{9}$.

Therefore, $\frac{5}{3} \div 15 = \frac{1}{9}$.