Lesson 4-1Ratio 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 divisionWritten 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)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 184Solve 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, 185Solve each proportion.

a) (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