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 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

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

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.

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?

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

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

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

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.

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

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

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

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