Equivalent Ratios, Fractions, Decimals, and Percents

Ratio A ratio compares one thing to another using numbers. For example, the ratio of boys to girls in Mr. Johnson’s elementary class is 12 to 13. There are 12 boys and 13 girls in Mr. Johnson’s class. That ratio can be written in a few different ways. 12 to 13 12:13 12/13

Your Turn There are 4 green apples and 6 red apples in a bag. What is the ratio of green apples to red apples? 4 to 6, 4:6, 4/6 What is the ratio of red apples to green apples? 6 to 4, 6:4, 6/4

Ratios Can Be Written as Fractions You probably noticed that one way to write a ratio is as a fraction with one number written in the numerator and the other written in the denominator. 2:3 is the same thing as 2/3. 4:5 is the same thing as 4/5. 3:6 is the same thing as 3/6, which reduces to 1/2.

Fractions Can Be Written as Decimal Numbers A fraction is simply a division problem. 3/4 is the same thing as 3 divided by 4. When we do that math, we find that we need to extend the dividend by adding a decimal point and zeroes until be find the point of termination. 3 divided by 4 results in a decimal number of 0.75 (seventy-five hundredths). Therefore, we know 3:4 is the same as 3/4 which is the same as 0.75.

Decimal Numbers Can Be Converted to Percents A percent is a ratio expressing how many out of 100. (Cent comes from the Latin word centum meaning 100.) When we divided 3 by 4, we found it to be equivalent to the decimal number 0.75 (seventy- five hundredths). We can write seventy-five hundredths as 75/100 OR 75 out of 100 which can be written as 75%. We now know that 3:4 is equivalent to 3/4 and 0.75 and 75%.

Finding Equivalencies Find the fraction, decimal, and percent equivalencies of these ratios. RatioFractionDecimalPercent 1:4 1:2 1:3 3:4 3:10 1:8 1:5 4:5 7:10