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# Percentages, Decimals, and Fractions

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Percentages, Decimals, and Fractions are closely related together, but some students find it hard to relate them together.

The relationship between percentages and decimals is simple; you can just multiply the decimal by 100.

For example, 0.5 * 100 = 50 = 50% of 100

0.352 * 70 = 35.2% of 70

1.42 * 20 = 142% of 20

If you want to find 4.5% of 100 you need to multiply 0.045 to 100

0.045 * 100 = 4.5

The relationship between decimal and fraction is also very simple. The decimal is equal to the numerator divided by the denominator.

For example, ¼ = 0.25

2/5 = 0.4

3/8 = 0.375

7/10 = 0.7

The relationship between percentage and fraction is simple. Percentage is numerator divided by denominator multiplied by 100.

¼ = 25%

2/5 = 40%

3/8 = 37.5%

7/10 = 70%

Example question is 20% of x is equal to 50% of 20. What is x?

20% of x = 0.2x. and 50% of 20 = 0.5 * 20 = 10

=> 0.2x = 10

x = 50

or 20% of x = 1/5 * x  and 505 of 20 = ½*20 = 10

1/5 * x = 10

x = 50

Like this, you should be able to switch percentage into decimal or fraction easily.