This document provides lesson notes on using ratios and proportions to solve word problems. It includes examples of ratios and proportions, as well as sample word problems involving ratios and proportions that can be solved using equivalent fractions or setting up a proportion. The examples cover topics like comparing the number of workers to time taken to complete a job, calculating pay based on hours worked, and using given ratios and values to determine unknown amounts.

1. Lesson 34
OBJ: STUDENTS WILL SOLVE WORD PROBLEMS USING RATIONS AND
PROPORTIONS.

2. Notes
Ratio – a comparison of two numbers by division.
example: There are 9 girls and 15 boys in a class.
9 푔푖푟푙푠
15 푏표푦푠
or
15 푏표푦푠
9 푔푖푟푙푠
Proportion – a statement that two ratios are equal.
example:
2
4
=
6
12
2
4
=
1
2
6
12
=
1
2

3. Nora is paid $12 an hour. Is her pay proportional
to the number of hour she works?
푃푎푦 ($)
푇푖푚푒 (ℎ푟)
12
1
Hours Pay 푷풂풚
푯풐풖풓풔
1 12 12
1
2 24 24
2
=
3 36
4 48

4. The table shows the number of workers and the number of
minutes needed to complete the job. Is the relationship
proportional?
푇푖푚푒
푤표푟푘푒푟푠
60
1
Number
working
Time
(minutes)
푇푖푚푒
푤표푟푘푒푟푠
1 60 60
1
2 30
3 20

5. Solve the Proportion
Equivalent Fractions
24
8
2
6
=
=
푚
5
8
푥
5
12
=
10
푥
푚
7
=
10
14
Fish Hook
24
8
=
푚
5
2
8
=
6
푥
5
12
=
10
푥
푚
7
=
10
14

6. Solve the Proportion
The ratio of boys to girls in the class is 3 to 4. If there are 12 girls, how many
boys are there?
The ratio of the length to width of a rectangular room is 5 to 4. If the room is
20 feet long, how wide is the room?
The teacher-student ratio in the primary grades is 1 to 20. If there are 100
students in the primary grades, how many teachers are there?