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Lesson 4.1.1

Ratios

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Lesson4.1.1 Ratios

California Standard:Number Sense 1.2Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).

What it means for you:You’ll learn what ratios are and the different ways you can represent them.

Key words:• ratio• fraction

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Lesson4.1.1 Ratios

You’ve probably come across ratios before — for example, making an orange drink by diluting about one part concentrated drink with about four parts water.

This way of stating how the amount of one thing compares with the amount of another thing is called a ratio.

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Ratios Are a Way of Comparing Amounts of Things

Lesson4.1.1 Ratios

A ratio is the amount of one thing compared with the amount of another thing.

In the diagram, the ratio of rabbits to cats is 5 to 3.

This is because there are 5 rabbits but only 3 cats.

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Example 1

Solution follows…

Lesson4.1.1 Ratios

What is the ratio of carrots to hamsters in the picture? And what is the ratio of hamsters to carrots?

SolutionCount the number of carrots. There are 3 carrots.Count the number of hamsters. There are 2 hamsters.

Make sure you get the order of the numbers right.The ratio of carrots to hamsters has the number of carrots first. The ratio of carrots to hamsters is 3 to 2.

In the same way, the ratio of hamsters to carrots is 2 to 3.

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Guided Practice

Solution follows…

Lesson4.1.1 Ratios

1. What is the ratio of tennis rackets to tennis balls in the picture opposite?

2. What is the ratio of tennis balls to tennis rackets in the picture?

3. There are ten people on a basketball court and two baskets. What is the ratio of people to baskets on the court?

4 to 3

3 to 4

10 to 2

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There Are Three Ways of Writing a Ratio

Lesson4.1.1 Ratios

The previous examples used words like “5 to 3” to write a ratio. But there are other ways to write ratios, and they all mean the same thing.

There are three ways you need to know about.

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5 to 3

5 : 3

This fraction tells you that there are 5 of one thing for every 3 of another.

The colon “:” is another way of writing “to” in ratios. You’d still say this “5 to 3”.

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Example 2

Solution follows…

Lesson4.1.1 Ratios

The ratio of dogs to cats in the picture is 4 to 3. How else could you write this ratio?

Write the ratio of cats to dogs in three different ways.

SolutionThere are three ways of writing ratios.You could also write the ratio of dogs to cats as 4 : 3 or .

The ratio of cats to dogs is 3 to 4, or 3 : 4, or .

43

34

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Guided Practice

Solution follows…

Lesson4.1.1 Ratios

4. The ratio of cars to people on a street is 1 : 2.How else can you represent this ratio?

5. The ratio of boys to girls in a class is .Express the ratio of girls to boys in three different ways.

6. What is the ratio of the width of the first rectangle shown below to the second?

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1 to 2, or12

3 to 2, or 3 : 2, or32

4 to 3, or 4 : 3, or43

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Ratios Don’t Have Any Units

Lesson4.1.1 Ratios

Ratios don’t have any units. A ratio is just one number compared with another, such as “3 to 2”.

Usually, ratios compare things measured in the same units. Then, the units cancel out when you divide the two quantities.

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Example 3

Solution follows…

Lesson4.1.1 Ratios

What is the ratio of the big square on the right to the smaller one?

Solution

To form the ratio of the areas, divide one by the other.

Ratio of big area to small area =

7 cm2 4 cm2

74

=

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Lesson4.1.1 Ratios

But if the units are different, the description of what the ratio shows is usually a bit more detailed.

The last example compared things that used the same units:

Ratio of big area to small area =

7 cm2 4 cm2

74

=

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Example 4

Solution follows…

Lesson4.1.1 Ratios

A walker hikes 7 miles in 3 hours. What is the ratio of the distance walked in miles to the time taken in hours?

Solution

Ratio of the distance walked in miles to the time taken in hours =

73

Distance walked in miles

Time taken in hours

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Guided Practice

Solution follows…

Lesson4.1.1 Ratios

Jess makes purple paint using 4 cans of blue paint to 1 can of red. It takes her 3 hours to paint her bedroom, and she uses all her paint.

7. What is the ratio of cans of blue paint to cans of red paint?

8. What is the ratio of cans of paint used to the time taken in hours?

4 : 1

5 : 3

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Independent Practice

Solution follows…

Lesson4.1.1 Ratios

In exercises 1–4, write the ratio shown in two equivalent ways.

1. 7 : 6

2. 3 to 8

3.

4. 7 : 11

117

7 to 6, 76

3 : 8, 38

11 to 7, 11 : 7

7117 to 11,

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Independent Practice

Solution follows…

Lesson4.1.1 Ratios

Exercises 5–7 are based on the circle graph on the right.

5. What is the ratio of people working in business to civil servants?

6. What is the ratio of unemployed people to people in business?

7. What is the ratio of people who are working and whose professions are known, to working people whose professions are unknown?

9 : 4

2 : 9

19 : 3

It shows the professions of 24 former pupils of a school.

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Lesson4.1.1 Ratios

Round Up

You’ve now met all of the basics of ratios.

Next, you’ll see how to use ratios in real life and how to simplify them to make your calculations easier.