Holt CA Course 1

5-1 Ratios

Warm UpWarm UpCalifornia StandardsCalifornia StandardsLesson PresentationLesson Presentation

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Holt CA Course 1

5-1 Ratios

Warm UpWrite each fraction in simplest terms.

1.

3640

3.

5. 1580

2. 2135

4. 4290

6. 5684

23

35

23

910

715

316

812

Holt CA Course 1

5-1 Ratios

NS1.2 Interpret 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 to b, a:b).

California Standards

a b

Holt CA Course 1

5-1 Ratios

Vocabularyratio

Holt CA Course 1

5-1 Ratios

In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the ratio . A ratio is a comparison of two numbers or quantities.

1725

Kathlene can write her ratio of baskets madeto attempts in three different ways.

17172525

17 to 2517 to 25 17:2517:25

Holt CA Course 1

5-1 Ratios

Sometimes a ratio can be simplified. To simplify a ratio, first write it in fraction form and then simplify the fraction.

Holt CA Course 1

5-1 Ratios

To compare ratios, write them as fractions with common denominators. Then compare the numerators.

Holt CA Course 1

5-1 Ratios

A fraction is in simplest form when the GCD of the numerator and denominator is 1.

Remember!

Holt CA Course 1

5-1 Ratios

Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.

Additional Example 1A: Writing Ratios

rock to hip hop

57

The ratio of rock to hip hop can be written as , 5 to 7, 5:7.

There are 5 who choose rock and 7 who choose hip hop.

rock hip hop = 5

7

Holt CA Course 1

5-1 Ratios

Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.

Additional Example 1B: Writing Ratios

hip hop to pop

hip hop pop

78

The ratio of hip hop to pop can be written as , 7 to 8, 7:8.

= 7 8

There are 7 who choose hip hop and 8 who choose pop.

Holt CA Course 1

5-1 Ratios

Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.

Additional Example 1C: Writing Ratios

rock to pop and hip hop rock t

pop & hip hop

= 5 15

There are 5 who choose rock, 8 who choose pop, and 7 who choose hip hop.

The ratio of rock to pop and hip hop can be written as 5

15, 5 to 15, 5:15.

Holt CA Course 1

5-1 Ratios

On average, most people can read about 600 words in 3 minutes. Write the ratio of words to minutes in all three forms. Write your answer in simplest form.

Additional Example 2: Writing Ratios in Simplest Form

wordsminutes Write the ratio as a fraction.

600 ÷ 33 ÷ 3

= 6003

Simplify.

For every minute, there are 200 words read.

wordsminutes =

wordsminutes = 200

1The ratio of words to minutes is 200 to 1.

Holt CA Course 1

5-1 RatiosHoney-lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Tell which package has the greater ratio of drops to ounces.

Additional Example 3: Comparing Ratios

Honey-lemon CherryDrops 30 24Ounces 10 6

Honey-lemon: dropsounces

= 3010 = 3

1

Cherry: dropsounces = 24

6= 4

1Because 4 > 3 and the denominators are the same, the drops to ounces is greater in the bag of cherry cough drops.

Write the ratios as fractions with common denominators.

Holt CA Course 1

5-1 RatiosCheck It Out! Example 1A

snow boarding rock climbing

69

The ratio of snow boarding to rock climbing can be written as , 6 to 9, 6:9.

= 6 9

There are 6 who choose snow boarding and 9 who choose rock climbing.

Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.

snow boarding to rock climbing

Holt CA Course 1

5-1 Ratios

At Casitas Middle School, there are 456 microscopes for 152 students. Write the ratio of microscopes to students in all three forms. Write your answer in simplest form.

Check It Out! Example 2

microscopesstudents

Write the ratio as a fraction.

456 ÷ 152152 ÷ 152

= 456152

Simplify.

For every microscope, there are 3 students.

microscopesstudents =

microscopesstudents = 3

1The ratio of microscopes to students is 3 to 1.

Holt CA Course 1

5-1 Ratios

Jelly beans come in small packages of 25 per 5 ounce package and large packages of 56 per 8 ounce package. Tell which bag has the greater ratio of jelly beans per ounce.

Check It Out! Example 3

Large SmallJelly Beans 56 25Ounces 8 5

Large: Jelly beans ounces

= 568 = 7

1

Small: Jelly beans ounces = 25

5= 5

1Because 7 > 5 and the denominators are the same, the large package has the greater ratio of jelly beans to ounces.

Write the ratios as fractions with common denominators.

Holt CA Course 1

5-1 RatiosLesson Quiz: Part I

A coin bank contains 16 quarters, 12 dimes, and 8 nickels. Write the given ratio in all three forms.

1. nickels to quarters

2. dimes to nickels

3. nickels and dimes to quarters

816 , 8 to 16, 8:16 or 1

2 , 1 to 2, 1:2

2016 , 20 to 16, 20:16 or 5

4 , 5 to 4, 5:4

128 , 12 to 8, 12:8 or , 3 to 2, 3:23

2

Holt CA Course 1

5-1 RatiosLesson Quiz: Part II

4. There are 220 calories in 5 crackers. Write the ratio of calories to crackers in simplest form.

5. On a school trip, Bus 1 has 3 teachers and 14 students. Bus 2 has 4 teachers and 28 students. Which bus has the greater ratio of teachers to students?

Bus 1

44 calories 1 cracker , 44 to 1, 44:1