Fractions and percentages
Cut every part into smaller parts until the whole has 100 parts.
Surya's sunset orange
Surya mixes red and yellow paint to make a deep orange for a sunset. The red makes up 34 of the mixture. What percentage of the colour is red?
34 of the paint is red. What percentage is that?
What this lesson covers
The idea
A fraction becomes a percentage by finding its equivalent fraction with denominator 100, or simply by multiplying it by 100; a percentage z% can be written as z/100 or any fraction equivalent to it.
Surya's sunset orange
Surya mixes red and yellow paint to make a deep orange for a sunset. The red makes up 3/4 of the mixture. What percentage of the colour is red?
3/4 of the paint is red. What percentage is that?
- 34%
- 75%
- 43%
Make a hundred parts
A strip shows a fraction. Cut every part into smaller parts until the strip has 100 parts: the number of shaded parts is then the percentage. Then go the other way, from a percentage back to a fraction.
Equivalent fraction with denominator 100
A fraction becomes a percentage by finding its equivalent fraction with denominator 100, or simply by multiplying it by 100; a percentage z% can be written as z/100 or any fraction equivalent to it.
Method 1: make the denominator 100. Multiply the top and the bottom of 3/4 by 25: 3/4 = 75/100 = 75%
Method 2: a fraction is part of 1 and a percentage is part of 100, so multiply the fraction by 100: 3/4 × 100 = 75, so 3/4 is 75%.
Going back, z% is z/100 or any equal fraction. For 24%: 24/100 = 12/50 = 6/25 = 48/200
Notes
A fraction becomes a percentage by finding its equivalent fraction with denominator 100, or simply by multiplying it by 100; a percentage z% can be written as z/100 or any fraction equivalent to it.
Check yourself
Express 2/5 as a percentage.
Answer: 40 %
2 × 20 = 40 and 5 × 20 = 100, so 2/5 = 40/100, which is 40%. Or 2/5 × 100 = 40.
Express 7/20 as a percentage.
Answer: 35 %
7 × 5 = 35 and 20 × 5 = 100, so 7/20 = 35/100, which is 35%.
Which of these is not equal to 24%?
Write 35% as a fraction in its simplest form. What is the denominator?
Answer: 20
35/100: 35 and 100 are both divided by 5, giving 7/20. The denominator is 20.
- 24/10 — correct. Right! 24/10 is more than 2 wholes (240%). 24% is 24/100.
- 12/50. 12/50 = 24/100, so it is equal to 24%.
- 6/25. 6/25 = 24/100, so it is equal to 24%.
- 24/100. 24/100 is exactly 24%.