## Solving Ratios with a Tape Diagram

Once students understand how the tape diagram works, they are ready to start solving ratio problems using this visual tool.  You can print and laminate ratio cards, or have students draw boxes.

We are going to look at 2 examples on how to use the tape diagram to solve ratio problems.  The first example is when we are given one of the parts and the second example is when we are given the total.

Example 1:  The ratio of boys to girls is 2:3.  If there are 10 boys, how many girls are there?

Have students represent the ratio with their tape diagram cards and label boys and girls. If there are 10 boys, that means each of the two cards must be worth 5.  Since all of the ratio cards have to be the same in order to have an equivalent ratio, put a 5 on every card.  This means that there must be 15 girls. Example 2:  The ratio of cats to dogs in a shelter is 5:1.  If there are 24 animals, how many cats are there?

Have students represent the ratio with their tape diagram cards and label cats and dogs. This time, we were given the total number of animals.  That means that the 6 total cards is representing 24.  Therefore, each card must be worth 4, because 24 divided by 6 is 4.  Our final answer is 20 cats. I hope this visual model is an effective strategy for your students!
~MN

## Intro to Using a Tape Diagram for Ratios

Tape diagrams are a great visual tool for understanding ratios.  Students can easily draw tape diagrams or you can print and laminate tape diagram cards and have students write on them with dry erase markers.  I like using the tape diagram cards because sometimes students have a hard time making equal size boxes.

Example 1

Have students represent the ratio 2:3 using the tape diagram cards or by drawing 2 boxes and underneath, 3 boxes. When we write on the tape diagram cards, we must write the same number in each card in order to keep our ratios equivalent.  This is super important!  Let’s write 2 in each box.  That would give us 4 in the top ratio and 6 in the bottom ratio.  Therefore, a ratio of 4:6.  That means that the ratio of 2:3 equals the ratio of 4:6. If we write a 3 in each box, that would give us a ratio of 6 to 9.  If we write a 4 in each box, that would give us a ratio of 8:12.  All of the ratios when simplified equal 2:3.  Example 2

Let’s look at another example.  Represent the ratio 6:5. Have students write a number of their choice in the boxes to represent equivalent ratios.  Have students share their results.  Some possible answers would be 12:10, 18:15, 24:20.   Discuss with students how it is important to keep the order of the ratio the same.  If the first number is larger than the second, it should stay that way when you find your equivalent ratios.  Also, we do not convert ratios into mixed numbers.

Once students have a strong understanding of how the tape diagram works, they are ready to start solving ratio problems using the tape diagram.

~MN