How To Find Percents Using Double Number Line

Double number lines can be used to show equivalencies in a visual way. The number lines are the same length and the tick marks line up, but they are numbered differently and used to find percents using double number line. They can show ⅔ is equal to 4/6. 

They can show equivalent ratios such as 2 apples for every 3 oranges is equivalent to 10 apples for every 15 oranges.

Double number lines can also provide a visual strategy when working with percents. 

Ways To Find Percents Using Double Number Line:

Finding the Part

This number line models a problem where we are asked to find 75% of 60. Since 75% is ¾ of 100%, we will divide our number line into 4 equal parts. From the information given, we know that 60 will line up with 100%.

Next we need to divide 60 into 4 equal parts. One strategy would be to divide it in half and then in half again. Since 60/4=15. Each tick mark represents an increase of 15. Once we have filled in the values, we can see that the tick mark for 75% lines up with 45. So, 75% of 60 is 45.

Finding the Whole

This double number line models a problem where we are given that 12 is 40% of a certain number. We can use a number line that is divided into 5 equal parts to have a tick mark representing 40%. We would be asked to find the number representing the whole, or 100%. From the information given, we know the 12 lines up with 40%.

We need to determine what numbers to use for the tick marks on our second number line. Using the information given, we can see that there are two equal parts between 0 and 12. If we divide 12 by 2 we get 6, so each tick mark increases by 6. Once we fill in these values, we can see that the tick mark for 100% lines up with 30. So 12 is 40% of 30.

Finding the Percent

This double number line models a problem where we are asked what percent 24 is of 40. We know from the information given that 40 is our whole and should line up with 100%.

Next we need to compare the part, which is  24, to the whole. 24/40 is equivalent to 6/10. This tells us that both number lines should be divided into 10 equal parts. It also tells us that the 24 will be at the sixth mark. 

In this problem, the values of the other tick marks don’t matter. We can see that 24 is equivalent to 60% of 40.

Although double number lines are not very helpful for percents such as 37% or 58%, they are a useful visual for making sense of many percent problems.

Also read: How To Solve Ratios Using Ratio Strategies

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Frequently Asked Questions on Solving Percent Problems