Cross Multiplying for Ratio Equivalency

Cross Multiplying for Ratio Equivalency

by Brigitta Schultz

​Cross Multiplication

​Cross multiplication, which is a lot like the butterfly method, is a tool we can use to both find equivalent ratios and check for ratio equivalency.

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​Step 1: Set up the ratios as fractions set equal to each other. This is called a proportion. Be sure to look out for ratio labels so it is set up correctly (i.e. dogs/cats = dogs/cats).

​Step 2: Multiply the two numbers you know that are diagonal to each other.

​Step 3: Divide that product by "the extra" (the other number you know).

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​Then, you have your answer!

Multiple Choice

Step 1: the setup

Which of these is set up correctly?

In a supermarket, the ratio of tomatoes to apples is 4:7. If there are 91 apples, how many tomatoes are there?

• $$\frac{4}{7}=\frac{91}{?}$$  

• $$\frac{4}{91}=\frac{7}{?}$$  

• $$\frac{4}{7}=\frac{?}{91}$$  

Multiple Choice

Step 2: cross multiply

Which two values would I multiply together?

$$\frac{4}{7}=\frac{?}{91}$$  

• 4 and 7

• 7 and 91

• 4 and 91

Multiple Choice

Step 2: divide by "the extra"

Which value is "the extra?"

$$\frac{4}{7}=\frac{?}{91}$$  

• 91

• 7

• 4

​Checking Equivalency

Multiple Choice

Are these ratios equivalent?

$$\frac{13}{27}=\frac{65}{135}$$  

• 1,755 = 1,755, so yes they are equivalent.

• 1,755 = 1,755, so no they are not equivalent.

• 351 ≠ 8,775, so yes they are equivalent. 

• 351 ≠ 8,775, so no they are not equivalent.

Multiple Choice

Are these ratios equivalent?

$$\frac{17}{54}=\frac{96}{184}$$  

• Yes

• No

Multiple Choice

Are these ratios equivalent?

$$\frac{270}{522}=\frac{45}{87}$$  

• Yes

• No