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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.