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Proportions

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Proportions

  1. 1. Proportions How do I solve a proportion?
  2. 2. Proportions – What are they?? <ul><li>Proportions are a way to relate information. </li></ul><ul><li>They compare two ratios. </li></ul>
  3. 3. Proportions – What are they?? <ul><li>Proportion = a pair of equal ratios </li></ul>×3 ×3
  4. 4. How do we tell if something really is a proportion? <ul><li>Method 1: Put both sides in lowest terms. </li></ul>÷5 ÷5 ÷15 ÷15
  5. 5. How do we tell if something really is a proportion? <ul><li>Method 1: Put both sides in lowest terms. </li></ul>The fractions are the same, so it is a true proportion.
  6. 6. How do we tell if something really is a proportion? <ul><li>Method 2: Find the cross products. </li></ul>
  7. 7. Cross-Product <ul><li>Multiply the numerator of one ratios by the denominator of the other ratio. </li></ul>6 × 1=6 3 ×2 =6
  8. 8. Cross-Product <ul><li>If the cross products are equal, the then ratios are equal, and it is a true proportion. </li></ul>6 × 1=6 3 ×2 =6 The cross products are the same, so it is a true proportion.
  9. 9. Are these proportions equal? <ul><li>Method 1 – Lowest Terms </li></ul>÷2 ÷2
  10. 10. Are these proportions equal? <ul><li>Method 1 – Lowest Terms </li></ul>No – they are not equal!!
  11. 11. Are these proportions equal? <ul><li>Method 2 – Cross Products </li></ul>8 ×16 =128 9 ×14 =126 No – they are not equal!!
  12. 12. Are these proportions equal? YES – they are equal!!
  13. 13. Are these proportions equal? YES – they are equal!!
  14. 14. Are these proportions equal? No – they are not equal!!
  15. 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. 16. Now, let’s try something harder When we have a variable, we can still cross-multiply. 10×5 = 50 1×Z = 1Z
  17. 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. 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. 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. 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. 21. Let’s try again Solve for the variable: 8×15 = 120 4×X = 4X 4X = 120 120÷4=30 so X = 30
  22. 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. 23. Now You TRY
  24. 24. Summarize Answer the EQ: How do I solve a proportion?

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