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Presentation on Inverse Proportion for Prep III N, E, W.
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Direct and Inverse Direct and Inverse ProportionProportion
Direct and Inverse Direct and Inverse ProportionProportion
Chapter 2
(Book 2)
1
Direct Direct
ProportionProportion
2
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
Example:
“Jim’s wages are directly proportional to the hours he works”
The more hours he works, the more money he earns.
This could be written as:
4
HoursWages Or...
Wages = k x Hours
k is the “constant of proportionality”
5
Direct Proportion GraphsDirect 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
Points to remember for graph: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.
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Direct Proportion
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6
No. of Packets
Cos
t (p
)
Direct Proportion GraphsNotice that the points lie on a straight line passing through the
origin
This is true for any two quantities which
are in Direct Proportion.
8
Direct Proportion GraphDirect Proportion Graph
KeyPoint
Two quantities which are in Direct Proportion
always lie on a straight linepassing through the origin.
9
Direct Proportion GraphsDirect Proportion Graphs
Example : Plot the points in the table below. Are they in Direct Proportion?
We plot the points (1,3) , (2,6) , (3,9) , (4,12)
XX 11 22 33 44
yy 33 66 99 1212
10
Direct Proportion GraphsDirect Proportion Graphs
1
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12)
0 1 2 3 4
101112
23456789
Since we have a straight linepassing through the origin
x and y are in Direct Proportion.
x
y
11
Inverse ProportionInverse Proportion
12
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 YYX
13
Inverse ProportionInverse Proportion
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
14
Time is inverselyProportional to Men
t ∝ m
1
15
t = m
k4
10k
40104 k
t = m
40If we have 20 men, m = 20
t = 20
40= 2 days
(The first step is to calculate the value of K and form the equation using the known values)
(The second step is to use the equation with the value of K to calculate unknown values)
16
Try this when:Try this when:
M is inversely proportional to RIf M = 9 when R = 4a. Find M when R =2b. Find R when M = 3
17
Indirect Proportion GraphsIndirect Proportion Graphs
The table below shows the “number of days to make a house” which is indirectly proportional to the “number of men.”
We can construct a graph to represent this data.
What type of graph do we expect ?
18
Men (M) 5 10 15 20 25 30
Days (D) 300 150 100 75 60 50
Points to remember for graph: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
Indirect Proportion Graphs
20
Notice that the points lie on a
curved line
This is true for any two quantities which are in
Indirect Proportion.
Indirect Proportion GraphIndirect Proportion Graph
KeyPoint
Two quantities which are Indirectly Proportion
always make a curved graph.
21
Best of Luck!Best of Luck!
If you have any further queries regarding the topic
or have any problems don’t hesitate to ask.
22