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Learn to write and solve proportions .

Understand proportions through examples featuring ratios and cross products. Practice solving proportions with detailed explanations.

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Learn to write and solve proportions .

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  1. Learn to write and solve proportions.

  2. Vocabulary proportion

  3. 2 4 4 8 2 6 __ __ __ __ __ __ = = = 1 2 2 4 1 3 2 4 __ __ 1 2 A proportion is an equation that shows two equivalent ratios. Reading Math Read the proportion = as “two is to one as four is to two.”

  4. 4 number of hearts __ number of stars 8 Additional Example 1: Modeling Proportions Write a proportion for the model. First write the ratio of hearts to stars. = Next separate the hearts and stars into two equal groups.

  5. 2 __ number of hearts number of stars 4 4 2 __ __ 8 4 Additional Example 1 Continued Now write the ratio of hearts to stars in each group. = A proportion shown by the model is = .

  6. 2 number of faces __ number of moons 6 Check It Out: Example 1 Write a proportion for the model. First write the ratio of faces to moons. = Next separate the faces and moons into two equal groups.

  7. 1 __ number of faces number of moons 3 2 1 __ __ 6 3 Check It Out: Example 1 Continued Now write the ratio of faces to moons in each group. = A proportion shown by the model is = .

  8. CROSS PRODUCTS Cross products in proportions are equal 4 2 3 9 9 3 14 2 __ __ __ ___ __ __ __ __ = = = = 8 4 5 15 6 2 7 1 6 •3 = 9 • 2 7 •2 = 14 • 1 8 • 2 = 4 • 4 5 • 9 = 3 • 15 16= 16 18 = 18 14 = 14 45= 45

  9. 5 n __ __ = 6 18 90 6n ___ ___ 6 6 Additional Example 2: Using Cross Products to Complete Proportions Find the missing value in the proportion. Find the cross products. 6 •n= The cross products are equal. 5 • 18 6n= 90 n is multiplied by 6. Divide both sides by 6 to undo the multiplication. = n = 15

  10. 3 n __ __ = 5 15 45 5n ___ ___ 5 5 Check It Out: Example 2 Find the missing value in the proportion. Find the cross products. 5 •n= The cross products are equal. 3 • 15 5n= 45 n is multiplied by 5. Divide both sides by 5 to undo the multiplication. = n = 9

  11. 1 tbsp f _____ ____ 6 gal 4 gal 1 tbsp f _____ ____ 6 gal 4 gal Additional Example 3: Measurement Application According to the label, 1 tablespoon of plant fertilizer should be used per 6 gallons of water. How many tablespoons of fertilizer would you use for 4 gallons of water? Let f be the amount of fertilizer for 4 gallons of water. = = Write a proportion. 6 •f= 1 • 4 The cross products are equal.

  12. tbsp tbsp ___ ___ gal gal gal gal ___ ___ tbsp tbsp Caution! In a proportion, the units must be in the same order in both ratios. = or =

  13. 4 6f __ ___ 6 6 2 __ 3 2 __ 3 Additional Example 3 Continued f is multiplied by 6. 6f= 4 Divide both sides by 6 to undo the multiplication. = Write your answer in simplest form. f = tbsp You would use tbsp of fertilizer for 4 gallons of water.

  14. 3 tbsp f _____ ____ 9 gal 2 gal 3 tbsp f _____ ____ 9 gal 2 gal Check It Out: Example 3 According to the label, 3 tablespoons of plant fertilizer should be used per 9 gallons of water. How many tablespoons of fertilizer would you use for 2 gallons of water? Let f be the amount of fertilizer for 2 gallons of water. = = Write a proportion. 9 •f= 3 • 2 The cross products are equal.

  15. 6 9f __ ___ 9 9 2 __ 3 2 __ 3 Check It Out: Example 3 Continued f is multiplied by 9. 9f= 6 Divide both side by 9 to undo the multiplication. = Write your answer in simplest form. f = tbsp You would use tbsp of fertilizer for 2 gallons of water.

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