This document discusses direct and inverse proportion. It defines direct proportion as two quantities increasing or decreasing together such that their ratio remains constant. An example shows how to calculate the amount of sugar needed given the amount of water. Inverse proportion means one quantity increases as the other decreases, keeping their product constant. An example calculates how long food will last for additional hens. Direct proportion uses a formula of x/y=k while inverse proportion uses xy=k. Examples are provided to demonstrate calculating unknown values using these formulas.

1. STANDARD SEVEN
TERM – I
MATHEMATICS
DIRECT AND INVERSE PROPORTION
BY
DARSHINI.A

2. CONTENTS
• Introduction
• Direct Proportion
• Relevant Examples
• Inverse Proportion
• Relevant Examples

3. Introduction
A proportion states that two ratios (or fractions) are the same.
Example:
We can easily see from the above picture that 2/3 = 4/6.

4. In other words, 2 eggs out of 3 cups of flour is equal to 4 eggs out of 6
cups of flour.
There is no difference in the ratios. Therefore, they are proportional.

5. Recalling Proportion and its variation
There are many situations in our daily lives where we must see how
one quantity changes in response to other.
By increasing (or decreasing), two quantities /(X/) and /(Y/) show their
proportionality in terms of their quantities and amounts.
According to proportional rules, the quantity changes the amount
concerning each other.

6. Example

7. (i) The total cost will increase if the number of items purchased
increases.
(ii) The more money is deposited in a bank, the more interest is earned.
(iii) As the speed of the vehicle increases, the amount of time taken to
cover the same distance decreases.
(iv) For a given job, the greater the number of workers, the less time it
will take to complete the work.

8. DIRECT PROPORTION

9. In direct proportion, two quantities x and y are said to increase (or
decrease) together in such a way that the ratio of their respective
values is constant.
That is to suggest that if x/y= k is positive, then x and y will differ
directly. That is, x and y are in direct proportion.

12. Example:
If 1 part of sugar requires 75mL of water, how much amount of sugar
should we mix with 1800mL of water?
Solution:
Let the parts of sugar mix with 1800mL water be x.
Practically, if 1 part of a sugar requires 75mL, of water, then 1800mL of
water requires more sugar.
Increase in quantity of water increases the quantity of sugar. So it is in
direct proportion.

13. Substitute the known values in the formula.
175 = x/1800
75 × x = 1 × 1800
x= 1800/75
x= 24
Hence, 24 parts sugar should be mixed with the water of 1800mL.

14. INVERSE PROPORTION
Two quantities x and y are found to be inversely proportional when an
increase of x causes y (and vice versa) to decrease proportionally. The
product of their corresponding values remains constant.
That is, if xy=k, then it is stated x and y vary inversely proportional.

17. Example
A farmer has enough food to feed 20 hens in his field for 6 days. How
much longer would the food last if the field contained an additional 10
hens?

18. SOLUTION:
Let the number of days be x.
Total number of hens =20 + 10= 30.
The length of time that food is consumable reduces as hen numbers
rise.
As a result, the relationship between the number of hens and the
number of days are inversely proportional.

19. Substitute the known values.
20/30 = x/6
 2/3 = x/6
 3 × x = 2 × 6
 3x= 12
 x= 12/3
 x=4
 Hence, the food will last for four days.

20. Let’s summarize:
• A proportion states that two ratios (or fractions) are the same.
• Two quantities 'a’ and 'b’ are said to be in direct proportion, if they
increase or decrease together.
• The symbol used to represent direct proportion is “∝”
• Two quantities ‘a’ and ‘b’ are said to be in inverse proportion, if an
increase in quantity a , there will be a decrease in quantity b and
vice versa.
• The statement a is inversely proportional to b is written as ‘a ∝ 1/b’