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

A comparison of two quantities by division

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

The ratio of rock to hip hop is 5 to 7, which can be written as follows:

as , 5 to 7, 5:7.

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.

Example 1A: Writing Ratios

rock to hip hop

57

There were 5 students that chose rock and 7 students that chose hip hop.

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.

Example 1B: Writing Ratios

hip hop to pop

78

There were 7 students that chose hip hop and 8 students that chose pop.

The ratio of hip hop to pop is 7 to 8, which can be written as follows:

as , 7 to 8, 7:8.

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.

Example 1C: Writing Ratios

rock to pop and hip hop

There were 5 students that chose rock and 7 + 8=15 students that chose hip hop and pop.

The ratio of rock to hip hop and pop is 5 to 15, which can be written as follows:

as , 5 to 15, 5:15.515

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

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

Remember!

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.

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

= 2001

The ratios in simplest form are , 200 to 1, 200:1.2001

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

Honey-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.

Example 3: Comparing Ratios

Honey-lemon Cherry

Drops 30 24

Ounces 10 6

Honey-lemon: dropsounces

= 3010

= 31

Cherry: dropsounces

= 246

= 41

Because 4 > 3 and the denominators are the same, the bag of cherry cough drops has the greater ratio of drops to ounces.

Write the ratios as fractions with common denominators.

Holt CA Course 1

5-1 RatiosCheck It Out! Example 1

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

= 31

The ratio of microscopes to students is 3 to 1.

Holt CA Course 1

5-1 Ratios

Mixed nuts 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 mixed nuts per ounce.

Check It Out! Example 3

Large Small

Mixed nuts 56 25

Ounces 8 5

Large:mixed nuts ounces

= 568

= 71

Small: mixed nuts ounces

= 255

= 51

Because 7 > 5 and the denominators are the same, the large package has the greater ratio of mixed nuts to ounces.

Write the ratios as fractions with common denominators.