Proportions relate two ratios as equal. To determine if something is a proportion, use one of two methods: 1. Put both sides in lowest terms - if the fractions are the same, it is a proportion. 2. Find the cross products - if the cross products of the numerators and denominators are equal, the ratios are equal and it is a proportion. When solving proportions with a variable, use cross multiplication to write an equation and then isolate the variable by dividing. Follow these steps: 1) cross multiply, 2) set the products equal, 3) divide to isolate the variable.

1. Proportions How do I solve a proportion?

2. Proportions – What are they?? Proportions are a way to relate information. They compare two ratios.

3. Proportions – What are they?? Proportion = a pair of equal ratios ×3 ×3

4. How do we tell if something really is a proportion? Method 1: Put both sides in lowest terms. ÷5 ÷5 ÷15 ÷15

5. How do we tell if something really is a proportion? Method 1: Put both sides in lowest terms. The fractions are the same, so it is a true proportion.

6. How do we tell if something really is a proportion? Method 2: Find the cross products.

7. Cross-Product Multiply the numerator of one ratios by the denominator of the other ratio. 6 × 1=6 3 ×2 =6

8. Cross-Product If the cross products are equal, the then ratios are equal, and it is a true proportion. 6 × 1=6 3 ×2 =6 The cross products are the same, so it is a true proportion.

9. Are these proportions equal? Method 1 – Lowest Terms ÷2 ÷2

10. Are these proportions equal? Method 1 – Lowest Terms No – they are not equal!!

11. Are these proportions equal? Method 2 – Cross Products 8 ×16 =128 9 ×14 =126 No – they are not equal!!

12. Are these proportions equal? YES – they are equal!!

13. Are these proportions equal? YES – they are equal!!

14. Are these proportions equal? No – they are not equal!!

15. Now, let’s try something harder Sometimes, we will only know 3 of the 4 values in a proportion. The missing value is a VARIABLE. Take a look…. Z is the variable

16. Now, let’s try something harder When we have a variable, we can still cross-multiply. 10×5 = 50 1×Z = 1Z

17. Now, let’s try something harder What do you think we are going to do now? 10×5 = 50 1×Z = 1Z Write the cross products equal to each other.

18. Now, let’s try something harder What do you think we are going to do now? 50 = 1Z Write the cross products equal to each other.

19. Now, let’s try something harder What do you think we are going to do next? 50 = 1Z It is an equation so we are going to do the inverse - DIVIDE.

20. Now, let’s try something harder What do you think we are going to do next? 50 = 1Z It is an equation so we are going to do the inverse - DIVIDE. 50 ÷ Z = 50 so Z = 50

21. Let’s try again Solve for the variable: 8×15 = 120 4×X = 4X 4X = 120 120÷4=30 so X = 30

22. Here are some steps: 1.) Cross multiply. 2.) Write the cross-products equal to each other. 3.) Divide the number by itself by the number with the variable. 4.) Write your answer as x = …

23. Now You TRY

24. Summarize Answer the EQ: How do I solve a proportion?