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**Lesson 4-1 Ratio and Proportion**

Objective: To find ratios and rates and to solve proportions.

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**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.

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**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

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**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

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**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.

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**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?

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

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

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**Example 4, page 184 Solve each proportion by using cross products.**

a) x/4 = 25/12 b) 24/3 = y/7 c) 54/d = 72/64

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**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.

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**Example 6, 185 Solve each proportion.**

(x+2)/14 = x/10 b) (y-15)/(y+4) = 35/7

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**Example 6, 185 (continued) Solve each proportion.**

c) 3/(w+6) = 5/(w-4) d) (d-7)/4 = (2d +1)/3

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**Summary Divide to find unit rates.**

Cross multiply to solve proportions or to verify a proportion.

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

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