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Proportions

Proportions. How do I solve a proportion?. Proportions – What are they??. Proportions are a way to relate information. They compare two ratios. Proportions – What are they??. Proportion = a pair of equal ratios. ×3. ×3. How do we tell if something really is a proportion?.

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Proportions

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  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 ÷15 ÷5 ÷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. 3×2=6 6×1=6

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

  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 50 ÷ Z = 50 so Z = 50 It is an equation so we are going to do the inverse - DIVIDE.

  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?

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