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Lesson 4-1 Ratio and Proportion

Lesson 4-1 Ratio and Proportion. Objective: To find ratios and rates and to solve proportions. Real-World Connection. These skills are very useful in comparative shopping and for determining time in bicycle rates, as we’ll see in Example 5. VOCABULARY.

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Lesson 4-1 Ratio and Proportion

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  1. Lesson 4-1Ratio and Proportion Objective: To find ratios and rates and to solve proportions.

  2. Real-World Connection • These skills are very useful in comparative shopping and for determining time in bicycle rates, as we’ll see in Example 5.

  3. VOCABULARY • Ratio – a comparison of two numbers by division Written three ways: a/b or a:b or a to b • Rate – a comparison of quantities in different units of measure • Unit rate – a rate with a denominator of 1 • Unit analysis – deciding which conversion factor to use when converting from one unit to another • Conversion: requires multiplication or division to change from one unit to another

  4. VOCABULARY (continued) • Proportion – an equation that states two ratios are equal; a/c = b/d • Extremes – a and d in a proportion • Means -- c and b in a proportion • Cross products – ad and bc of a proportion

  5. Cross Products of a Proportion • If a/b = c/d, then ad = bc. • For example: Is 2/3 = 8/12 a proportion? • Solution: Find the cross-products. • 2(12) = 3(8) • 24 = 24 • Yes, this is a proportion.

  6. Example 1, page 182 • A) Find the unit rates for the other two sizes. • B) Which of the three sizes has the lowest cost per ounce?

  7. Example 2, page 183 • A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.

  8. Example 3, page 183 • Solve t/9 = 5/6.

  9. Example 4, page 184Solve each proportion by using cross products. • a) x/4 = 25/12 b) 24/3 = y/7 • c) 54/d = 72/64

  10. Example 5, page 184 • Suppose you walk 2 miles in 35 minutes. • A) Write a proportion to find how far you would walk in an hour if you were to continue at the same rate. • B) Solve the proportion.

  11. Example 6, 185Solve each proportion. • (x+2)/14 = x/10 b) (y-15)/(y+4) = 35/7

  12. Example 6, 185 (continued)Solve each proportion. c) 3/(w+6) = 5/(w-4) d) (d-7)/4 = (2d +1)/3

  13. Summary • Divide to find unit rates. • Cross multiply to solve proportions or to verify a proportion.

  14. ASSIGNMENT • #4-1, page 185, odds 1– 71, and odds 77-99

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