The Three Amigas: Ratios, Proportions, & Percents
What is a Ratio?
A ratio is a comparison of two quantities using division.
You can write ratios using three different forms.
3 to 4
3
4
3 : 4
A bag of 25 marbles contains 8 blue, 10 green, 5 red, and 2 yellow marbles.
8
The ratio of blue marbles to total marbles is
or 8:25 or 8 to 25
25
!
10
The ratio of green marbles to total marbles is
to 10:25 or 10 to 25.
25
10 2
= or 2:5 or 2 to 5**
**We can also reduce ratios the way we reduce fractions.
25 5
8
4
The ratio of blue to yellow marbles is or
or 4 to 1 or 4:1
2
1
**Ratios must have two numbers and improper ratios are okay!**
What are Proportions?
Proportions are made up of two ratios showing they are
equivalent using an equal sign.
10 2
= is a proportion
15 3
7 21
= is a proportion
3 9
How do I know if I have a proportion?
The Cross-Products determine if two ratios are equivalent.
Cross-Products are when you
! multiply the diagonal factors of the
! ratios, if they are both equal then
you have a proportion!
I am a Proportion:
I am not a Proportion:
10 2
=
15 3
10! 3=30
15!2 = 30
2 x
=
5 10
15 9
=
8 3
15! 3= 45
8!9 = 72
How do I find a proportion?
Remember your cross products need to be equal
4
2 • 10 needs to equal 5 • x
5
20
20 = 5 • x
) =4=x
20
00
!
Cross Multiply and Divide!
Percents and Proportions
The $1,000,000 (Million Dollar) Proportion is:
%
is
=
100 of
Susie got a 70% on her math test. There were 40 questions on the test. How many
did she answer correctly?
!
Question: 70% is how many questions out of 40?
70% ?
=
Proportion:
100 40
Method: Cross Multiply and Divide
70 x 40 = 280
280 ÷ 10 = 28
Answer: Susie answered 28 questions out of 40 questions correctly.
In one serving of chicken broth there are 25 calories, 10 of those calories are
from fat. What percent of the calories in a serving is from fat?
Question: 10 calories is what percent of 25 calories?
? % 10
=
Proportion:
100 25
Method: Cross Multiply and Divide
100 x 10 = 1,000
1,000 ÷ 25 = 40
Answer: 40% of the soup is fat calories
An egg has 20 grams of fat. This is 25% of the amount of fat the government recommends per day.
How many grams of fat does the government recommend per day?
Question: 20 grams is 2% of how many fat grams we need?
25% 20
=
Proportion:
100
?
Method: Cross Multiply and Divide
100 x 7 = 700
700 ÷ 2 = 350
Answer: The government recommends only 80 grams of fat per day.