What is the Division of Fractions? | In general, division is a method of sharing something equally into separate groups. In mathematics, division of a fraction by another fraction is done by multiplying one fraction by the reciprocal of the second fraction. The reciprocal of a fraction is a fraction in which the numerator and denominator are interchanged.
Dividing Fractions by Fractions
Let us take an example to see the method of dividing fractions by fractions. We need to divide 3/8 by 9/16.
Then, we will interchange the values of the numerator and denominator of the second fraction and multiply it with the first fraction.
Therefore, 3/8 ÷ 9/16 = 3/8 × 16/9 = 48/72 = 2/3
∴ The solution for 3/8 ÷ 9/16 = 2/3.
Division Of Fractions With Whole Numbers
In the case of the division of fractions with whole numbers, we need to multiply the denominator of the fraction with the whole number. For example, divide 2/5 (fraction) by 4 (whole number)
Therefore, 2/5 ÷ 4 = 2/5 × 1/4 = 2/20 = 1/10
Thus, 2/3 ÷ 4 gives the result of 1/10.
Division of Fractions With Decimal Numbers
Decimal numbers can be considered as a fraction having the base 10. To perform the division of fractions by decimals, we have to convert the decimal in the fractional form and then perform the division of fractions.
For example, for the division 2/3 ÷ 0.4, we can write 0.4 in fractional form as 4/10 or 2/5. Then divide 2/3 by 2/5 to get the result. Therefore, 2/3 ÷ 0.4 = 2/3 ÷ 2/5 = 2/3 × 5/2 = 10/6 = 5/3.
Multiplying Fractions
The multiplication of fractions with different or same denominators can easily be performed. The fractions to be multiplied should be in proper fractions or improper fractions form, but not mixed fractions. Multiplying fractions can be done by following simple steps.
- Multiply the numerators of both fractions.
- Multiply the denominators of both fractions.
- Simplify the resultant fraction to its lowest form.
For example, let us multiply the following fractions: 4/5 × 3/8.
Step 1: Multiply the numerators: 4 × 3 = 12,
Step 2: Multiply the denominators: 5 × 8 = 40.
Step 3: The resultant fraction is: 12/40 and its simplest form is 3/10.
So the result of the multiplication 4/5 × 3/8 = 3/10
Alternative Method
The multiplication of fractions can be performed using another method in which we simplify the given fractions among themselves and then multiply the numerators, and then the denominators to get the final resultant fraction. You can also learn more fraction-related concepts through cuemath.com.
For example, we need to multiply 15/25 × 12/16
Follow the steps below to multiply the fractions using the above method.
- These fractions are simplified as: 15/25 = 3/5 and 12/16 = 3/4
- Multiply the numerators of both fractions: 3 × 3 = 9
- Multiply the denominators of both fractions: 5 × 4 = 20
- Therefore, the result that we get is 9/20
Some important points:
- If the two fractions to be multiplied are not in their simplest forms, then first simplify them and then multiply to make the calculation easier. For example, 16/24 x 21/30 will be difficult to multiply directly. So, we simplify the individual fraction first. Thus 16/24 = 2/3 and 21/30 = 7/10. Now, we multiply the simplified fractions and get the result as, 2/3 x 7/10 = 14/30 = 7/15
- Simplification can also be done across the two given fractions. Find out if there is any common factor between the numerator of one fraction and the denominator of the other fraction. Then you can simplify them before multiplying and then complete the multiplication. For example, 5/27 x 18/35 can be simplified to 1/3 x 2/7 before multiplication. Thus the final result will be 2/21.
