Download RATIOS A ratio is a comparison of two numbers (quantities) using

RATIOS
A ratio is a comparison of two numbers (quantities) using division. Ratios are used to
show relationships between quantities and can be written in three ways.
1.
2.
3.
As a fraction a/b
With a colon (:) a:b
With words a to b
Example:
In class we have 2 teachers and 28 students. We can write the ratio of teachers to
students as-2/28
2:28
2 to 28
You can show different kinds of comparisons with a ratio.
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Ο
Ο
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Ο
Ο
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Part to part: The ratio of white dots to lined dots is 6/4; 6:4 or 6 to 4.
Part to whole: The ratio of white dots to the total number of dots is 6/10; 6:10 or 6 to 10.
Whole to whole: The ratio of the number of triangles to the number of dots is 0/10; 0:10
or 0 to 10.
To work with a ratio you usually use it in fraction form; you can simplify ratios. For
example, the ratio of white dots to lined dots in the diagram above can be simplified as
3/2, 3:2, or 3 to 2.
A ratio should NOT be written as a mixed number.
Example:
Charlie has 5 green shirts, 6 blue shirts, 8 red shirts, 2 yellow shirts, and 7 black shirts.
Whatever is first in the problem goes on TOP!
What is the ratio of:
Blue to red =
6
6:8
6 to 8
8
OR
3
3:4
3 to 4
4
Green to total =
5
28
5:28
Red to yellow and black =
2 + 7
5 to 28
8
9
8:9
8 to 9
Example:
What is the ratio of cats to dogs in a neighborhood that has 9 dogs and 3 cats?
Write the ratio of cats to dogs.
The ratio of cats to dogs is 3/9. Simplify and it is 1/3.
The ratio of cats to dogs in the neighborhood is 1/3, or there is 1 cat for every 3 dogs.
Example:
What is the ratio of girls to boys in a class of 20 students that has 12 boys?
Write the ratio using a colon.
Write the ratio of girls to boys.
The ratio of girls to boys is 8:12. Simplify and it is 2:3.
The ratio of girls to boys in the class is 2:3. There are 2 girls for every 3 boys.
Example:
Ms. Simpson’s class has 3 students with green eyes and 15 with brown eyes.
For every student that has green eyes, how many students have brown eyes?
The ratio of students with green eyes to students with brown eyes is 3/15.
Simplify 1/5.
For every student with green eyes, there are 5 students with brown eyes.
EQUIVALENT RATIOS
Ratios that name the same comparison (equivalent fractions are the same thing.)
2
=
1
=
4
28
14
56
You make equivalent fractions by multiplying and/or dividing.
A ratio can be written in simplest form.
8/6 or 8:6 can be written in simplest form as 4/3 or 4:3.
The ratios 8/6 and 4/3 are equivalent ratios.
Another way to tell whether two ratios or rates are equivalent is to CROSS MULTIPLY.
A rate is a ratio that compares two quantities with different units of measure.
To cross multiply, write the ratios as fractions. Then multiply the numerator of each ratio
and the denominator of the other ratio. The products are called the CROSS PRODUCTS
of the ratios. If the cross products are equal, the ratios are equivalent.
Example:
There are two copiers. Are the two machines making copies at the same rate?
5 copies in 8 minutes
16 copies in 24 minutes
1. Write as a fraction
5
8
16
24
2. Cross multiply
5
16
8
24 5 x 24
120 ≠
8 x16
128 The cross products are not equal, so the ratios
are not equivalent.
The two copiers are not making copies at the same rate.
You can cross multiply to find a missing value in a ratio or rate.
Example:
Emma is driving at a constant speed. She drives 4 miles in 5 minutes. If she continues
to drive at the same speed, how many miles will she drive in 15 minutes?
1. Write two ratios.
4
a
5
15
2. Cross multiply to find the missing term
4
a
5
15 4 x 15 = 5 x a
60 = 5a
60 = 5a
5
5
12 = a
Emma will drive 12 miles in 15 minutes.