ratios and proportional relationships 1. objective: you will be able to… explain what a ratio is...

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Ratios and Proportional Relationships

© 2013 Meredith S. Moody

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Objective: You will be able to…

Explain what a ratio is in your own wordsExplain what a proportion is in your own wordsExplain what a rate is in your own wordsUse ratio language to describe a ratio

relationship between two quantitiesUse proportion language to describe a ratio

relationshipUse rate language to describe a ratio

relationshipUse ratio, proportion, and rate reasoning to

solve problems


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VocabularyRatio: A relationship between two

quantities

Proportion: Two or more related quantities whose ratios can be simplified to the same fraction

Rate: A ratio that compares two quantities with different units


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Example 1: RatioA small group of students in a math class

has 1 girl and 3 boys The ratio of girls to boys can be

expressed four different ways:◦ Using the “:” sign 1:3 (read as 1 to 3)◦ Using fractions 1/3 (read as 1 to 3)◦ As a decimal .33 ◦ As a percent 33%


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Example 2: ProportionThe small group of students from the previous

slide is proportional to the math class as a wholeThis means that for every 1 girl there are 3 boysIf the class has 20 students, how many girls are

there? How many boys?The ratio 1:3 is proportional to the whole classYou can build the proportion until your total = 201:3 2:6 3:9 4:12 5:15There are 5 girls and 15 boys in the entire classWe use proportions to find values of larger or

smaller quantities


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Example 2: RateThe most common example of a rate is

speedThe number of miles a car can travel per

hour is a ratio between two numbers with different units miles vs. hours

If a car travels 30 miles every hour, the rate can be expressed as 30:1 30miles:1hour(read as 30 miles per hour)


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Guided practice 1: Expressing ratios

The math class from example 1 has 20 students. 5 are girls and 15 are boys Instead of expressing the ratio in terms of

girls:boys, we can express the ratio in terms of girls:total students OR

boys:total studentsWhat is the ratio of girls to total students?

◦ 5:20 OR 5/20 ( ¼ ) OR .25 OR 25%What is the ratio of boys to total students?

◦ 15:20 OR 15/20 ( ¾ ) OR .75 OR 75%


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Guided practice 2: Proportions The math class ratio of girls:total students is

proportional to the whole school’s ratio of girls:total students.

The whole school has 1000 students How many girls are there in the school? Class ratio = 5:20 How many times would I have to add 20 to get to the

total (1000) number of students in the school?◦ 50

What is repeated addition?◦ Multiplication

Treat the ratio like a fraction and create an equivalent fraction

There are 250 girls in the school

520×5050

=2501000


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Guided practice 3: RatesCity A and City B are 120 miles apartSusan drove from City A to City B in 2 hoursCity C and City D are 200 miles apartJoe drove from City C to City D in 3 hoursWho drove at a faster rate?What is Susan’s rate?120 miles:2 hours 120/2 60/1 60mphWhat is Joe’s rate? 200 miles:3 hours 200/3 66.7/1 66.7mphJoe’s rate is greater, so Joe drove faster


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Check!Write down, in your own words, what a

ratio is◦ Share your explanation with a neighbor

Write down, in your own words, what a proportion is◦ Share your explanation with a neighbor

Write down, in your own words, what a rate is◦ Share your explanation with a neighbor


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You try! Express your ratios all 4 ways

What is the ratio of strawberries to oranges?◦ 3:5 OR 3/5 OR .6 OR 60%

What is the ratio of oranges to strawberries?◦ 5:3 OR 5/3 OR 1.67 OR 167%

What is the ratio of strawberries to total fruits?◦ 3:8 OR 3/8 OR .375 OR 37.5%

What is the ratio of oranges to total fruits?◦ 5:8 OR 5/8 OR .625 OR 62.5%


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You try! ProportionsThe fruit ratio in the previous

scenario is proportional to the fruit ratio at the entire market

There are 120 total strawberries and oranges at the market

How many strawberries are there?◦

How many oranges are there?◦


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You try! RatesA basket of 30 strawberries costs $1.50A crate of 50 oranges costs $5.00Which fruit is more expensive?(hint:) Find the rate (cost) of each fruitStrawberries: 30(strawberries)/$1.50

1(strawberry) / $0.05◦ The strawberries cost $ 0.05 each

($0.05 per strawberry)Oranges: 50(oranges)/$5.00

1(orange) / $0.10◦ The oranges cost $0.10 each

($0.10 per orange)The oranges are more expensive


ratios and proportional relationships 1. objective: you will be able to… explain what a ratio is...

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