4Mathematics INSTRUCTION

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©Curriculum Associates, LLC Copying is not permitted. 77Lesson 9 Ratios Involving Complex Fractions

Use with Ready Instruction Lesson 9

Dear Family,

A complex fraction is a fraction with another fraction in the numerator, the denominator, or both. Your child is learning to simplify these expressions in order to solve ratio problems that involve fractions. They are also learning how to interpret these simplified ratios and use them to solve real-world problems.

This work is an extension of their previous work with unit rates. Two common examples of unit rates include gas prices ($3.15 per gallon) and speed limits (40 miles per hour). Notice that the price for gas is given as dollars per 1 gallon and that the speed is given as miles per 1 hour. This is why we call these unit rates.

If you know a unit rate, you can make other calculations. For example, if you know the price per gallon of gas, you could figure out the cost of 15 gallons of gas. But in the real world, you might not always be given the unit rate.

For example,

Two different-size bottles of the same brand of orange juice are on

sale at the grocery store. The 1-gallon bottle is on sale for $6.50

and the 3 ··

4 -gallon bottle is on sale for $5.10. Which size container

of orange juice is the better deal?

You may already have an idea of how to answer this question. The next page shows, the problem worked out using various approaches that your child is currently learning, including working with complex fractions.

Working with rates and ratios paves the way for the study of proportional relationships, which is central to the study of many topics in algebra and geometry. Students will be introduced to this concept later this year, and then continue to study this in the eighth grade. Because many real-world situations involve fractions, students will need to be prepared to work with complex fractions within rates, ratios, and proportions.

Your child is learning how to work with ratios with complex fractions.

©Curriculum Associates, LLC Copying is not permitted. 79Lesson 9 Ratios Involving Complex Fractions

Name:

Vocabularyrate an equivalent ratio that compares the first quantity in a ratio to only one of the second quantity

unit rate the part of the rate that is being compared to 1.

Find Unit Rates

Study the example problem showing how to find a unit rate. Then solve problems 1–6.

1 How much would it cost to buy 8 pounds of grapefruit?

2 Leila uses 5 cups of grated zucchini to make 2 loaves of zucchini bread. How many cups of zucchini does she need to make 1 loaf?

3 Jenna walks 4 miles in 1 hour. At this rate, how many

miles can she walk in 3 1 ·· 2 hours?

Example

Six pounds of grapefruit cost $3.60. What is the cost per pound?

A double number line can help you find rate and unit rate.

Start with the ratio you know: $3.60 to 6. Then find equivalent ratios.

Price

Pounds

$0.600 $1.20 $1.80 $3.60$3.00$2.40

0 1 2 3 4 5 6

You can also divide: $3.60 4 6 5 $0.60. The cost per pound, or unit rate, is $0.60.

Ratios Involving Complex Fractions

Lesson 9 Use after Ready Instruction page 79