DIRECT AND INVERSE PROPORTIONS

1. PROPORTION
A S T E P - B Y- S T E P G U I D E T O D I R E C T A N D
I N V E R S E P R O P O R T I O N

2. STARTER
1. Solve for k:
a) 18=9k
b) 3=2k
c) 72=9k
d) 8=
k
3
e) 3=
k
7
f) 5=
k
9
2. If a=2b,
Find a when b=3
Find b when a = 7
3. If c=1.5d
Find c when d=12
Find d when c=15
4. If T=8V
Find T when V=7
Find V when T=24
5. If a=
24
𝑏
Find a when b=6
Find b when a=2
6. If D=
21
𝐸
Find D when E=21
Find E when D=42
7. If f=
45
𝑔
Find f when g=15
Find g when f=9
k=2
k=1.5
k=8
k=24
k=21
k=45
a=6
b=3.5
c=18
d=10
T=56
V=3
a=4
b=12
D=1
E=0.5
f=3
g=5
Strength or Target?

3. DIRECT
PROPORTION
A is directly proportional to B
A “is proportional to” B
A 𝛼 B
A = k x B
A = kB
What the question would
say
Read as…
In maths…
Write it as a general
formula we can work
with…
INVERSE
PROPORTION
A is inversely proportional to
B
A “is proportional to”
1
𝐵
A 𝛼
1
𝐵
A = k x
1
𝐵
A =
𝑘
𝐵
VS
“k” is the constant that links our two numbers.
We use it, and a specific case, to find a specific formula for all numbers
with a specific relationship.
You can skip straight to writing down the general formula in a question.

4. DIRECT
PROPORTION
A = kB
10 = k x 5
k =
10
5
k = 2
A = 2B
Start with the general
formula
Substitute in values in the question
Solve for k…
Write the specific formula
INVERSE
PROPORTION
A =
𝑘
𝐵
10 =
𝑘
5
10 x 5 = k
k = 50
A =
50
𝐵
VS
A is directly proportional to B.
When A=10, B=5.
1. Find the equation linking A and
B.
A is inversely proportional to B.
When A=10, B=5.
1. Find the equation linking A and
B.
We can use the general formula to find the specific formula for this relationship.
We can use the specific formula to find other values in the relationship, when one variable is a

5. A is inversely proportional to B.
When A=10, B=5.
1. Find the equation linking A and
B.
A =
50
𝐵
2. Find A when B = 2.
A =
50
𝐵
A =
50
2
A = 25
3. Find B when A=5
A =
50
𝐵
5 =
50
𝐵
B =
50
= 10
A is directly proportional to B.
When A=10, B=5.
1. Find the equation linking A and
B.
A = 2B
2. Find A when B=2.
A = 2B
A = 2 x 2
A = 4
3. Find B when A=5
A = 2B
5 = 2B
B =
5
= 2.5
DIRECT
PROPORTION
Start with the specific
formula
Substitute in values in the question
INVERSE
PROPORTIONVS
Start with the specific
formula
Substitute in values in the question
Solve for B

6. THANK YOU
NAME-NAVNEET SHARMA
CLASS-VIII-B
R.NO-23
TOPIC-DIRECT AND INVERSE
PROPORTION