Ratios and proportions compare relationships between quantities. A ratio can be written as a fraction a/b or using a colon a:b. A proportion uses two equal ratios and sets their cross products equal using the means-ends property to solve for missing values. There are two types of word problems involving ratios - those that give a ratio and actual value to use in a proportion, and those that give a ratio and total to multiply the ratio terms to determine the actual values.

1. Ratios and Proportions
Section
7-1
Jim Smith
3108.4.37

2. A RATIO IS A COMPARISION OF 2 QUANTITIES.
A RATIO MAY BE WRITTEN AS A FRACTION a/b
OR a:b. WE WANT TO USE THE REDUCED FORM
OF THE FRACTION BUT NOT WHOLE NUMBERS.
WHEN COMPARING MORE THAN 2 QUANTITIES,
USE COLONS a:b:c.

3. For a recent project, a teacher purchased 250 pieces
of red construction paper and 114 pieces of blue
construction paper. What is the ratio of red to blue?
A baseball player made six hits in nine innings.
What is the ratio of hits to innings?
Use the number line below to determine
the ratio of AD to EI.
0 10 20 30 40 50
0
A B C D E F G H I J K

4. A PROPORTION IS FORMED WHEN WE PUT
2 RATIOS EQUAL TO EACH OTHER. THE CROSS
PRODUCTS OF THIS PROPORTION ARE EQUAL.
BC
AD
D
C
B
A


THIS IS CALLED
THE MEANS AND EXTREMES PROPERTY.
THIS LETS US FIND A MISSING
VALUE IN ONE OR BOTH RATIOS.

5. 3
5
4
2
6
5
7
4
3
5
4
2
5
9
4
7
5
3










x
x
x
x
x
x
x
1.
2.
3.
4.
5.

6. THERE ARE 2 TYPES OF WORD PROBLEMS
TYPE 1- GIVES A RATIO AND AN ACTUAL
“PART” OF THE RATIO.
WE USE A PROPORTION TO SOLVE THESE.
THE RATIO OF GIRLS TO BOYS IN THE FRESHMAN CLASS IS 6:5.
IF THERE ARE 250 BOYS HOW MANY GIRLS ARE IN THE CLASS?
AT WHITEWATER JUNIOR HIGH SCHOOL, THERE ARE 360
STUDENTS AND 39 TEACHERS. WHAT IS THE RATIO OF STUDENTS
TO EACH TEACHER ROUNDED TO THE NEAREST TENTH?

7. TYPE 2- GIVES A RATIO AND A “ TOTAL”.
IF WE TAKE A RATIO IN ITS REDUCED FORM
AND MULTIPLY THE TOP AND BOTTOM BY
THE SAME NUMBER, EVENTUALLY WE
WILL GET THE ACTUAL OR ORIGINAL
NUMBERS OF THE COMPARISON.

8. THE RATIO OF BOYS TO GIRLS IN THE
JUNIOR CLASS IS 8:9. IF THERE ARE 510
STUDENTS IN THE CLASS, HOW MANY
BOYS ARE IN THE JUNIOR CLASS?

9. THE SIDES OF A TRIANGLE HAVE
A RATIO OF 9:6:5 AND A PERIMETER OF 100.
WHAT IS THE MEASURE OF THE 3 SIDES?
THE ANGLES OF A TRIANGLE HAVE
A RATIO OF 13:21:16. WHAT IS THE
MEASURE OF THE 3 ANGLES?