Dividing Decimal as Fractions

Dividing decimals can be made easier by understanding how to convert them into fractions.

Here’s a step-by-step explanation on how to divide decimals by converting them into fractions:

Identify the place value of the decimal:
For instance, the decimal 0.75 can be read as seventy-five hundredths, which translates to the fraction 75/100. Similarly, 0.5 is fifty hundredths, or 50/100.
Simplify the fractions if possible:
- 75/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 25.
- So, 75/100=(75÷25)/(100÷25)=3/4.
- 50/100 simplifies to 1/2.

Let’s say you want to divide 0.75 by 0.5. After converting to fractions, the problem becomes: 3/4÷1/2

To divide by a fraction, multiply by its reciprocal.

The reciprocal of 1/2 is 2/1.

So the problem becomes: 3/4×2/1

Simplify 6/4 by dividing the numerator and the denominator by their greatest common divisor, which is 2: (6÷2)/(4÷2)=3/2

To convert 3/2 back to a decimal, divide 3 by 2:

3÷2=1.5

So, 0.75 divided by 0.5 equals 1.5.

Example 1: 0.6 ÷ 0.2
- Convert to fractions: 6/10÷2/10
- Simplify: 3/5÷1/5
- Use reciprocal: 3/5×5/1=(3×5)/(5×1)=15/5
- Simplify: 15/5=3
- So, 0.6 ÷ 0.2 = 3
Example 2: 1.2 ÷ 0.4
- Convert to fractions: 12/10÷4/10
- Simplify: 6/5÷2/5
- Use reciprocal: 6/5×5/2=(6×5)/(5×2)=30/10
- Simplify: 30/10=3
- So, 1.2 ÷ 0.4 = 3

By converting decimals to fractions and following these steps, you can divide decimals with ease and accuracy.

MathsMD