Inverse Proportion!
Good morning Everyone!!
The topic for today is Inverse Proportion
Learning Objectives:
All Learners can confidently tell the difference between direct and inverse proportion
Most Learners can solve word Problems after identifying the difference and using the Unitary
method.
What is Inverse Proportion?
Inverse proportion occurs when one value increases and the other decreases. For example, more
workers on a job would reduce the time to complete the task. Ten men can build a wall in 10 days,
does not mean 20 men will take 20 days. Actually 20 men will finish the work earlier. If I double the
number of workers, I will only need half the time to finish the work.
Then, 20 men will only take 5 days !
It works the other way too.
If 6 men finish a job in 20 days. How long will it take 3 men to do the same job ? If I half the number
of men they will take double the time. So 3 men will take 40 days.
Now, That was easy because I can draw a relationship between 6 and 3 (half, so then I double)
How long will 1 man take?
1 man will take 6 x 20 = 120 days to the same job
How long will 5 men take?
This is where we use a common method to help us solve the question in 1 step
I will make two columns (Just like in direct proportion)
Men
days
6
20
5
?
Now in inverse proportion I will not use cross multiplication. I will Use horizontal lines
Men
6
days
_________________20
5 ________________
?
The line that has numbers on both sides always goes on the top and the number that is alone goes at
the bottom.
Hence
6
x
5
20
=
12 0
= 24 days
5
How Do you check if it is direct proportion where I use cross multiplication or Inverse proportion
where I use Horizontal multiplication?
Its Simple.
2 men share a pizza and get 6 slices each. How many slices each will 3 men get?
Now ask yourself. Has the number of men increased – Yes. Will the number of Slices Increase? NO it
will decrease.
When one value Increases and the other decreases Or vice versa. It is called Inverse proportion.
In direct proportion, as the first variable increases (decreases), the second variable also increases
(decreases). Example: 9 pens costs K108. Find the cost of 12 pens. Has the number of pens
increased? Yes. Will the cost Increase? Yes. Similarly, you can also find the cost of 6 pens. If number
of pens decrease, cost will also decrease. In direct proportion we will use cross multiplication.
Now, we will solve the first Exercise to see if you all have understood Inverse Proportion.
Exercise 1
1. It takes 6 men 6 days to build a wall. How long will it take 9 men to build the same wall?
2. Three men can paint a wall in 10 hours. How many men would be required to paint the same
wall in 7½ hours?
3. A ship has sufficient food to supply 600 passengers for 3 weeks. How long would the food
last for 800 people?
4. A bag of rice is sufficient for 12 men for 1 week. How long will two bags last for 8 men?
5. Three friends are about to go camping so they pack water that will be sufficient for 4 days.
Just as they are about to go 3 other friends join in. How long will the water now last them?
6. The time taken to boil the water is inversely proportional to the power of the water heater.
When the power is 1000 watts it takes 240 seconds to boil the water. How long will It take
when the power is 800 watts?
7. It takes 30 minutes for the passengers on a plane to check in when 5 staff members are
working. How long will it take if 8 staff members are working?
8. This time 9 friends are about to go camping and they pack enough water was 3 days. When
they are about to leave 3 friends back out. How long will the water now last them?
9. It takes a plane 5 hours to fly NYC to LA if it flies at 500mph. How long will it take if it flies at
600mph. Give your answer in hours and mins ( eg 3 hours and 45 mins )
10. If six builders take 80day to paint the entire building from inside and outside. How many
more builders will be required if you have get the job done in only 16 days?
11. It takes 14 hours for a tap with a flow of 18 litres per minutes to fill a reservoir with water.
How long will it take if its flow is reduced to 7 litres per minute?
Now try these:
12. If it takes 6 men 4 days to a dig a whole 3 metres deep, How long will it take 10 men to dig a
whole 7 metres deep?
13. A wall can be built by 6 men working 8 hours per day for 5 days. How many days will it take 4
men to build the wall if they work only for 5 hours per day ?
14. 12 men can finish tiling a room with 800 tiles in 5 days. How long will it take 8 men to tile a
room with 600 tiles?
15. 15 men and 8 women can complete a task in 90 days. How long will it take 12 men and 12
women to do the same task?
End of worksheet
Complete the work and upload on your Class dojo portfolio. When you do upload please answer
these questions for me. Your feedback is valuable
Check:
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•
•
Do you understand the difference between direct and inverse proportion?
Do you Understand how to solve word problems using Inverse proportion?
Will you be able to confidently solve word problems that involve both direct and inverse
proportion in the same worksheet?