1. Variations

2. Variation A change in one factor brings about a change
in the related factor. These changes are
termed as variation.

3. Examples of Variation What happens when......... You buy more pens ↑ ?
Costs you more ↑
Number of
students are
more ↑?
More number
of teachers ↑
Speed of the
car increases ↑?
Time taken to reach
destination
decreases ↓
Number of people
working increases ↑?
Time taken to
finish work
decreases ↓

4. Direct Variation Answer: As the number of people living in the house
What happens when
When you buy more pens , do you
think that the total cost will
increase or decrease?
Answer: As you buy more pens ↑, total cost also increases ↑.
When the number of people living in
house decreases, do you think that the
total weekly expense will increase or
decrease?
Answer: As the number of people living in the house
decreases ↓, the weekly expense also decreases ↓.

5. Direct Variation Now, look at the following tables:
Cost of 1 chocolate (Rs) 5
20 ↑
30 ↑
Cost of 10 chocolates (Rs)
5 x 10 = 50
20 x 10 = 200 ↑
30 x 10 = 300↑
For one to many, we need to multiply
As the cost of 1 chocolate increases ↑, the cost of 10
chocolates also increases ↑ correspondingly.
Cost of 5 Shirts (Rs)
3000
2000
1000 ↓ ↓
Cost of 1 Shirt (Rs) ↓ ↓
As the cost of 5 shirts decreases ↓ , the cost of 1 shirt
also decreases ↓ correspondingly.
For many to one, we need to divide

6. Direct Variation increase (↑ ) in the other quantity
  When an increase (↑ ) in one quantity brings about an
increase (↑ ) in the other quantity
and similarly a decrease (↓) in one quantity brings about
a decrease (↓) in the other quantity,
then the two quantities are said to be in direct variation.

7. Some Direct variation examples:
No of students in a class ↑
No of teachers ↑
Distance travelled by
the car ↑
Time taken by the car ↑
No of chocolates purchased↓
Total expenses ↓
Amount deposited in the bank ↑
Interests for that amount ↑

8. Inverse Variation
What happens when
When the speed of the car
Increases , do you think that the
time taken to reach the destination
will increase or decrease?
Answer: As the speed of the car increases ↑, the time taken
to reach the given destination definitely decreases ↓.
When the number of men
decreases, do you think the days
taken to complete the required job
will increase or decrease?
Answer: As the number of men decreases ↓, the days taken
to complete the required job will definitely increases ↑.

9. Inverse Variation When an increase (↑) in one quantity produces a
proportionate decrease (↓) in another quantity
and similarly if a decrease (↓) in one quantity produces
a proportionate increase (↑) in another quantity
we say that the two quantities are in inverse variation.

10. Some Inverse variation examples:
Planting of trees ↓
Temperature ↑
Speed of the car ↑
Time taken to travel ↓
No of lines per page ↑
No of pages ↓

11. Example 1: Identify the statement below is direct or inverse variations?
Time and distance covered
Solution:
As time increases(↑) distance covered also increases(↑),
Similarly if time decreases (↓) distance covered also decreases(↓),
Hence it is Direct variation.

12. Example 2: Identify the statement below is direct or inverse variations?
Number of men and time to complete a job
Solution:
As the number of men increases (↑), the days taken to complete a job will
decrease (↓)
Similarly as the number of men decreases (↓), the days taken to complete
a job will increase (↑),
Hence it is Inverse variation.

13. Try these
Identify the statement below is direct or inverse variations?
Number of pencil and its cost
Number of lines per page and number of pages in book
length of side of a square and its area
Speed and time to cover a distance