Presentation on Inverse Proportion for Prep III N, E, W.

1. Direct and Inverse
Proportion
Chapter 2
(Book 2)
1

2. Direct
Proportion
2

3. Direct Proportion
Two quantities are directly proportional if
an increase in one quantity corresponds to a
constant increase in the other quantity, or if
a decrease in one quantity corresponds to a
constant decrease in the other quantity.
X Y
X Y
3

4. Example:
“Jim’s wages are directly proportional to
the hours he works”
Themore hours he works, the more
money he earns.
This could be written as:
4

5. Wages α Hours
Or...
Wages = k x Hours
k is the “constant of proportionality”
5

6. Direct Proportion Graphs
The table below shows the “cost of packets of Biscuits”
which is directly proportional to the “no. of packets.”
No. of Pkts 1 2 3 4 5 6
Cost (p) 20 40 60 80 100 120
We can construct a graph to represent this data.
What type of graph do we expect ?
6

7. Points to remember for graph:
For the data given in the previous slide
C
∝ N
1. For the above relation N is the independent variable and C is the
dependent variable.
2. On the graph we always take the independent variable on the X axis
and the dependant variable on the Y axis.
7

8. Direct Proportion
140
Notice that the points
120 lie on a straight line Graphs
Direct Proportion
passing through the
100 origin
80
60
40
20
This is true for any
two quantities which
0 are in Direct
0 1 2 3
Proportion. 5
4 6
8
No. of Packets

9. Direct Proportion Graph
KeyPoint
Two quantities which are in
Direct Proportion
always lie on a straight line
passing through the origin.
9

10. Direct Proportion Graphs
Example : Plot the points in the table below.
Are they in Direct Proportion?
X 1 2 3 4
y 3 6 9 12
We plot the points (1,3) , (2,6) , (3,9) , (4,12)
10

11. Direct Proportion Graphs
y 12
Plotting the points 11
10
(1,3) , (2,6) , (3,9) , (4,12) 9
8
7
Since we have a straight line 6
passing through the origin 5
x and y are in 4
Direct Proportion. 3
2
1
0 1 2 3 4 x
11

12. Inverse Proportion
12

13. Inverse Proportion
Two quantities are inversely
proportional if an increase in one
quantity corresponds to a constant
decrease in the other quantity, or if a
decrease in one quantity corresponds to a
constant increase in the other quantity.
X Y
X Y
13

14. Example:
“It takes 4 men 10 days to build a brick
wall. How many days will it take 20 men?”
The more men employed, the less time it
takes to build the wall
Inverse Proportion
14

15. Time is inversely
Proportional to Men
1
t∝ m
15

16. (The first step is to calculate the value of K and form the equation using the
known values)
t= k k
10 =
m 4
k = 4 ×10 = 40
t= 40 (The second step is to use the equation with the
value of K to calculate unknown values)
If we have 20 men, m = 20
m 40
t= = 2 days
20 16

17. Try this when:
M is inversely proportional to R
If M = 9 when R = 4
a. Find M when R =2
b. Find R when M = 3
17

18. Indirect Proportion Graphs
The table below shows the “number of days to make a
house” which is indirectly proportional to the “number of
men.”
Men (M) 5 10 15 20 25 30
Days (D) 300 150 100 75 60 50
We can construct a graph to represent this data.
What type of graph do we expect ?
18

19. Points to remember for graph:
For the data given in the previous slide
M
∝ 1/D
1. For the above relation M is the independent variable and D is the
dependent variable.
2. On the graph we always take the independent variable on the X axis
and the dependant variable on the Y axis.
19

20. Indirect Proportion Graphs
Notice that the
points lie on a
curved line
This is true for any
two quantities
which are in
Indirect Proportion.
20

21. Indirect Proportion Graph
KeyPoint
Two quantities which are
Indirectly Proportion
always make a curved graph.
21

22. If you have any further queries regarding the topic
or have any problems don’t hesitate to ask.
Best of Luck!
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