1. Direct Proportion

2. What is a direct proportion?
The more you eat,
the more you grow.
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.
The lesser the
number of items,
the smaller the
amount to pay.

3. What are other examples of direct proportion?
The more sugar you
add in the pastillas,
the sweeter it will be.

4. What are other examples of direct proportion?
The faster the speed,
the greater the distance.

5. What are other examples of direct proportion?
The more the number
of persons,
the more food is required.

6. What are other examples of direct proportion?
The less sleep you had,
the less energy
you have.

7. Let us try looking at one word problem.
Maita earns 450 pesos in selling apples on 4 Sundays. How many Sundays will it take her to earn 1,350 pesos?
Is this a problem involving direct proportion? Why do you say so?
Yes it is, because the more Sundays Maita sells apples, the more earnings she will have.

8. 4 450 X 1,350 No. of Sundays Earnings
Maita earns 450 pesos in selling apples on 4 Sundays.
How many Sundays will it take her to earn 1,350 pesos?
No. of Sundays
Earnings 4
450 X
1,350
To solve this problem, after knowing what is asked, it’s better to list the given facts or numbers using a table.
Let X represent the number asked for in the problem

9. How many Sundays will it take her to earn 1,350 pesos?
Maita earns 450 pesos in selling apples on 4 Sundays.
How many Sundays will it take her to earn 1,350 pesos?
No. of Sundays
Earnings 4
450 X
1,350
Solve for the value of X by using cross-multiplication. Indicate the proper label.

10. Maita earns 450 pesos in apples on 4 Sundays.
How many Sundays will it take her to earn 1,350 pesos?
No. of Sundays
Earnings 4
450 12
1,350
Therefore, Maita should sell apples on 12 Sundays to earn 1,350 pesos.

11. “ .. When you double the number of cakes
Number of cakes and total cost, are said to be in DIRECT Proportion, if :
“ .. When you double the number of cakes
you double the cost.”
Example : The cost of 6 cakes is $4.20. Find the cost of 5 cakes.
Cakes
Cost 6
4.20 5 X

12. 2 3 X 12 To make scrambled eggs for 3 people
we need 2eggs, 4g butter and 40 ml of milk.
How much of each for...
(a) 12 people (b) Just himself
Butter
people
Eggs
people 2 3 X 12
Milk
people

13. YOUR TURN

14. Solve the problems
1. 44 kg of bananas cost $176. How much would 32 kg cost?    2.  A car can travel 481 kilometers on 37 liters of gasoline. How much gasoline will it need to go 130 kilometers?  3. 34 kg of bananas cost $68. How much would 11 kg cost?    4.  A boat can travel 132 kilometers on 66 liters of gasoline. How much gasoline will it need to go 88 kilometers?
5. Chicken must be cooked for 50 minutes for every kg. How long does it take for a 4kg chicken to cook?
6. 25 strawberry sweets cost $358. How much would sweets cost?

15. RATIO PROBLEMS
  Isabelle shares out 12 chocolates. She gives Abbie 1 chocolate for every 4 chocolates she takes. How many sweets does Abbie get?
   Georgie is decorating her room. She mixes 1 tin of red paint with 3 tins of blue. She needs 12 tins of paint altogether. How many tins of blue paint does she need?
There are 2 strawberry sweets to every 3 orange sweets in a bag of 30 sweets. How many strawberry sweets are there?
There are 5 girls to every 2 boys in a class of 28 children. How many girls are there in the class?

16. 1. Organize the Information