1. 4. Inverse Proportion
By: Darawath Dina, Hokleng hong, Hakhour tech and Panha ath
Introduction to Inverse Proportions
 a relation between two quantities such that one
increases in proportion as the other decreases.
Investigation
Speed (x km/h)
10
20
30
40
60
120
Time taken
(y hours)
12
6
4
3
2
1
By investigating this table, you will be able to observe that:
As the speed of the car, x km/h, increases, the time taken, y hours, decreases
proportionally, ex. if x is doubled, then y will be halved;
By this table, it shows that if x is tripled, then y will be reduced to 1/3 of it’s
value.
This relationship is known as inverse proportion. We say that the spped of the
car, x km/h, is inversely proportional to the time taken, y hours.
SPEED
(X KM/H)
10
20
30
40
60
120
TIME TAKEN
(Y HOURS)
12
6
4
3
2
1
PRODUCT
XY PRODUCT
10 x 12
= 120
20 x 6
= 120
...
...
...
...
What can we observe about the product xy?
In inverse proportion, the product xy is a constant. In this case, xy = 120 =
distance travelled.
let the speed of the car be x1 = 20. then the corresponding time taken is y1 =6.
let the speed of the car be x2 = 40. then the corresponding time taken is y2 =3.
From the table, x1y2 = 20 x 6 =120 and x2y2 = 40 x 3 = 120.
Thus, x1y1 = x2y2 = 120 (constant)
by rearranging, we can get y2/y1 = x1/x2
in conclusion, If y is inversely proportional to x, then y2/y1 = x1/x2 = x2y2.
LET’S DO IT TOGETHER!
 PROBLEM: 10 identical taps can fill a tank in 4 hours.
Calculate the time taken for 8 such taps to fill the same
tank.
Solution:
 10 taps can fill the tanks in 4 hours
 1 tap can fill in (10 x 4) hours.
 8 taps can fill the tank in 10 x 4/8 = 5 hours
or we can use this solution:
 let the time taken for 8 taps to fill the tanks be y hours
 Then 8y = 10 x 4


y = 10 x 4/8
=5
 8 taps can fill the tank in 5 hours.
In Conclusion
Inverse proportion is when a unit (x) increases
while another unit (y) decreases.
We can find (x) or (y) by using the formula;
y2/y1 = x1/x2
 y1x1=y2x2
Ex. y1= x2y2/x1.