Ratios, proportions, and percents are different ways to compare numbers. Ratios show the relationship between two or more numbers and can be written with a colon, as a fraction, or with the word "to". Proportions are two equivalent ratios written as part to whole. Percents tell a ratio out of 100 parts so 50% means 50 parts per 100.

1. Ratios
Proportions
Percents

2. Ratios
Proportions
Percents

4. Ratios
A ratio is a way to compare two or more
numbers
Ratios can be written as:
1). 2 numbers separated by a colon :
2). A fraction
3). With the word “to”
ratio
rate
ration
rational
unit rate

5. Ratios
Ratios look like fractions
because they are fractions
1 : 2=
= 1/6

6. Types of Ratio Comparisons
Part to Part
The ratio of strawberries to
oranges is 2 to 3.
The ratio of oranges to
strawberries is 3 to 2.

7. Types of Ratio Comparisons
Part to Whole
The ratio of kittens to total pets
is 3 to 8.
The ratio of puppies to all pets
is 5 to 8.

8. Ratio Examples
Ratio of squares to circles is 3/6
Ratio of squares to circles is 3 to 6
Part to
Part
Ratio of squares to circles is 3:6
Ratio of squares to total figures is 3:10
Ratio of circles to total figures is 6/10
Part to
Whole

9. Proportions
Proportions are two equivalent ratios,
written as Part to Whole
1/2
=
2/4
=
3/6
=
4/8

10. proportional
As one number or shape increases, the
other number or shape increases by
the same ratio
1/2
2/4
3/6
4/8

11. Proportions
Testing Proportions to see if they are
equivalent
Cross Multiply
to see if they
are equal
18
2
6
18
3
9
If they are the
same, they are
equivalent AND
proportional!
Use cross multiplication to test
proportions if you are given 2 fractions (or
more)

12. Proportions
Solving a proportion when you only have
some information
2
6
=
x
9
Step 1:
Find the unknown number.

13. Proportions
2
6
=
x
9
L oo k
Step 2:
L
k at the number directly above or
below the unknown number.
Circle this number.

14. Proportions
2
6
Step 3:
L
=
x
9
L oo k
k at the number directly across from
the circle
Draw a square around this number.

15. Proportions
2
6
=
x
9
Step 4:
Draw a triangle around the number
above or below the square.

16. Proportions
2
6
x
9
=
Step 5:
Fill in the template and solve

9
*
 6 * 2
x=3
=x
=x

17. Proportions
2 = x
6
9
Solving using backtracking:
Step 1: Cross multiply
2 * 9 = 6 *x
18 =
6x

18. Proportions
2 = x
6
9
Solving using backtracking:
Step 2: Tell the “story” of x
6
*
x
18

19. Proportions
2 = x
6
9
Solving using backtracking:
Step 3: Backtrack!
6
*
x
x=3
18
6

20. Percents
Percent means parts per 100,
and tells you a ratio "out of 100"
So 50% means 50 per 100

21. Ratios
Proportions
A
is a way to
compare
or more
numbers.
Ratios can be written as:
1) 2
separated
with a
(:)
Proportions are two
equivalent ratios.
Proportions are written as p
a r t to w h o le.
2) A
3) with the word
When given 2 proportions:
ratio of
to
is 3/6
ratio of
to
is 3 to 6
ratio of
to
is 3:6
Ratio of squares to
total figures is
When solving for an unknown:
Percents
Percent means parts
per
100, and tells you a ratio "out of
100"