To change ratios into percentages easily, just follow these simple steps:

What are Ratios?

Ratios show how two things are related.

For example, a ratio of 3:2 means that for every 3 parts of one thing, there are 2 parts of another.

If you add them up, the total parts in this ratio is 3 + 2 = 5 parts.

Turning Ratios into Fractions

1. Write the Ratio as a Fraction: Take the first number (the top part) of the ratio and put it over the total parts (the bottom part).

Using our 3:2 example:

• The fraction would be:
  ( \frac{3}{3 + 2} = \frac{3}{5} )

Finding the Percentage

2. Change the Fraction into a Percentage: To get a percentage, multiply the fraction by 100.

Continuing with our example:

• The percentage would be:
  ( \frac{3}{5} \times 100 = 60% )

A Simple Formula

For any ratio like ( a:b ), you can use this formula to find the percentage of ( a ):

• Percentage of ( a = \frac{a}{a + b} \times 100 )

An Example Calculation

Let’s look at the ratio 4:1:

1. Total parts = 4 + 1 = 5
2. The fraction is ( \frac{4}{5} )
3. The percentage is ( \frac{4}{5} \times 100 = 80% )

Try These Practice Problems

• Convert these ratios into percentages:

  1. 5:3
     • Total parts = 5 + 3 = 8
     • Percentage = ( \frac{5}{8} \times 100 = 62.5% )
  2. 1:4
     • Total parts = 1 + 4 = 5
     • Percentage = ( \frac{1}{5} \times 100 = 20% )

Tips for Success

• Always try to simplify the ratio first if you can. This makes the math easier.
• Get to know some common fractions and their percentage values (like ( \frac{1}{2} = 50% ) and ( \frac{1}{4} = 25% )) to speed up your conversions.
• Practice with different ratios to get better and faster at figuring out percentages.