This document provides examples and worksheets on inverse proportions. It includes word problems asking how long it would take different numbers of men, cars, girls, etc. to complete certain jobs or travel certain distances if time or amounts are changed inversely. It also gives the formula for inverse proportion, a=k/b, and asks students to solve for variables using given values of k.

2. Presentation:
If 8 men can do a certain job in 12 days,
how many men will be required to do the same
job in 16 days?
1. What is asked in the problem?
2. What is the proportion?
3. What is the first ratio? Second ratio?
4. What do we need to consider in order to solve the problem?

3. Other example:
If a car traveling at the rate of 40 km/h
takes 10 hours to travel a certain distance,
how long would it take the same car to
travel the same distance at the rate of 50
km/h?

4. A proportion is said to be inverse if as
one term increases, the other term decreases
proportionately.

5. Worksheet #2:Inverse Proportion
Solve these problems using proportion.
1. An army camp has provisions for 240 men for 28 days. How long
will the provisions last if only 112 men are sent to the camp?
2. If 9 men can do a piece of work in 6 days, how long will it take 12
men to do the same work?
3. In a home economics class, 5 girls worked together and sewed a
dress in 7 days. How long would it have taken 3 girls to make the
same dress?
4. If 5 boys can decorate a hall for a program in 3 ½ hours, how long
will it take 7 boys to decorate it?
5. A contractor hired 150 men to pave a road in 30 days. How many
men would he hire to do the same work in 20 days?

6. 6. A tank of oil can be emptied in 16 minutes if 1 outlet valve is fully
opened. How long will it take to empty the tank if 2 outlet valves
are fully opened?
7. A truck can transport a supply of building materials in 4 hours
making 8 trips each hour. How long would the job take if 4 strips
were made each hour?
8. A housewife has sufficient charcoal to last 12 days provided she
uses only 2 buckets of charcoal a day. How long will the charcoal
last if she uses 3 buckets a day?
9. It took 20 men 2 ½ days to repair a street. How long might the job
have taken if only 15 men had been working?
10. Five fathers from the Parent-Teacher Association spent 14
evenings helping in a project in school. How many men could have
completed the same job in 10 evenings?

7. Solve the following problems.
1. If a is indirectly proportional to b, then a = k/b, where k is a
constant or a fixed number. If a = 8 when b = 6, find the value of k.
Using the value of k in number 1, find:
2. a if b = 2
3. a if b = 4
4. a if b = 12
5. b if a = 2
6. b if a = 3
7. b is a = 10