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Understanding Proportions: Concepts, Examples, and Applications in Math

Proportions are equations that demonstrate the equivalence of two ratios. For instance, "two is to one as four is to two." This overview includes examples such as determining costs for books and CDs based on given ratios, as well as distance calculations while driving at a constant speed. Additionally, it covers using cross products to find missing values in proportions and emphasizes the importance of having matching units in both ratios. Practical scenarios illustrate the application of proportions in real-life situations.

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Understanding Proportions: Concepts, Examples, and Applications in Math

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  1. Proportions #27

  2. 2 4 4 8 2 6 __ __ __ __ __ __ = = = 1 2 2 4 1 3 2 4 __ __ 1 2 Vocabulary 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.”

  3. Example 1: Modeling Proportions Julio spent $10 to buy 4 books at a garage sale. How much would Julio pay for 8 books at the garage sale?

  4. Example 2 Paul spent $15 on 3 CDs at a store where all CDs are the same price. How much would it cost for Paul to buy 9 CDs?

  5. Example 3 Beth drove 120 miles in 2 hours. She continues driving at the same rate and does not stop. How far will she have driven in 6 hours?

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

  7. 5 n __ __ = 6 18 Example 4: Using Cross Products to Complete Proportions Find the missing value in the proportion.

  8. 3 4 __ __ = 9 n Example 5: Using Cross Products to Complete Proportions Find the missing value in the proportion.

  9. 3 n __ __ = 5 15 Example 6 Find the missing value in each proportion. 3 • 15

  10. 2 6 __ __ = 13 n Example 7 Find the missing value in each proportion. 2 •n= 6 • 13 2n= 78 n = 39

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

  12. Example 8 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?

  13. Example 9 To make a certain shade of pink paint, mix 8 gallons of white paint with 3 gallons of red paint. How many gallons of white paint would you mix with 15 gallons of red paint to make this shade of pink?

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