1. Ratio
and
Proportion
Prepared by:
Josephine Libron

2. Objectives: Objectives 1. Define ratio and proportion
2. Identify ways in writing ratios
3. Find equal ratios
4. Solve problems involving ratio and proportion using Microsoft Office Word.

3. Is it good to compare things?

4. When quantities have different measurements, how can they be compared?

5. Ratio
Equal Ratios
Proportion
Solving Problems Involving Ratio and Proportion

6. Ratio
- is a comparison of two quantities

7. Example:
Rosa makes hats out of cartolina. For every 2 pieces of cartolina, she can make 7 hats.

8. There are two quantities compared:
Number of pieces of cartolina – 2
Number of hats

9. Two equal ratios form a PROPORTION.

10. Ratios and Proportions can be written as a Fraction
Ratios and Proportions can be written as a Fraction. We can also use the colon ( : ) in writing ratios and proportions.

11. 1.) As a fraction 2 7
2.) By using the colon (:) 2:7

12. Let’s Practice! Write the ratio or proportion using colon.
1.) 3 cups of sugar for every 5 cups of Flour
2.) 2 men for every 5 cups of rice
3.) 1 book for every 2 pupils
4.) 4/8 = ½
5.) 3/7 = 12/28

13. Let’s Check!
Let’s Check!
Click the Button to find the answers.

14. Answers:
1.) 3:5
2.) 2:5
3.) 1:2
4.) 4:8 = 1:2
5.) 3:7 = 12:28

15. Assignment:
Read in advance about Equal Ratios.

16. Equal Ratios Equal Ratios Equal Ratios
To find equal ratios, multiply or divide the given ratio by a fraction equal to 1.

17. Examples: 1. 2 3 Solution: Multiply 2 to the given ratio 2 2 x 2 = 4 3
Solution: Multiply 2 to the given ratio 2
2 x = 4
Therefore, = 4

18. 2. 8 24
Solution: Divide 8 to the given ratio 8
8 ÷ = 1
Therefore, 8 = 1

19. Let’s Practice! Let’s Practice! Let’s Practice!
A. Write a ratio equal to each
1.) 1/5
2.) 10/12
3.) 1:2
4.) 2:3
5.) 3:4

20. Let’s check!
Let’s Check!
Click the Button to find the answers

21. Answers
Answers
1.) ) 8 : 12 10
2.) ) 15 : 20 36
3.) 3 : 6

22. Let’s Apply Let’s Apply!
1. Girlie can make five rag dolls from six discarded socks. Write four ratios equal to this.

23. Proportion A proportion is a statement that two ratios are equal.
In a proportion, the product of the means is always equal to the product of the extremes =

24. To find the missing part of the proportion:
Multiply the given ratio by a fraction equal to 1 or use the cross product method
Multiply the means or the extremes. Then divide by the third given number

25. Examples:
1.) 8 = 32 n
Solution: Use the cross product method
32 x 7= 224
8 x n= 224
n= 224 ÷8
n= 28
therefore, 8 = 32

26. 2.) 3 : 5 = n : 25
Solution: Multiply the means or the extremes
3 : 5 = n : 25
3 x 25 = 75
5 x n = 75
n = 75 ÷ 5
n = 15
Therefore: 3:5= 15:25

27. Let’s Practice Let’s Practice! A. Find n. Use cross productsB.
Find n.
: 24 = n : 6
: 28 = n : 42

28. Let’s check!
Let’s Check!
Click the Button to find the answers

29. Answers
Answers
A. B.
1.) ) 5
2.) ) 18

30. Let’s Apply
1. Empty cans sell at P0.75 for 4. How many does Lina have to sell to earn P11.25?

31. Answer
: 4 = : n
4 x = 45
0.75 x n = 45
n = 45 ÷ 0.75
n = 60
Therefore, Lina have to sell 60 empty cans to earn P11.25.

32. Solving Problems Involving Ratio and Proportion

33. Remember:
There are basic steps in solving a problem :
Understand
Plan
Carry out the plan and
Check.

34. Problem
For every 3 meters of bamboo sticks, three boys can make 5 frames of Christmas lanterns. How many lantern frames can they make with 15 meters of bamboo sticks?

35. Think. What does the problem ask for? What are given?
The number of lantern frames that can be made from 15m of bamboo sticks
What are given?
3m of bamboo sticks
3 boys
5 lantern frames
15m of bamboo sticks
Will I need all the given numbers
The problem is about comparing number of sticks to number of frames. The number of boys is not needed.

36. How will I find the answer? What is the number sentence?
Plan.
How will I find the answer?
Compare the number of meters of bamboo to number of frames.
What is the number sentence?
3 = 15 n

37. Give the complete answer
Carry out the plan.
Solve = n
5(15) = 75
3 x n = 75
n = 75 ÷ 3
n = 25
Give the complete answer
The boys can make 25 lantern frames

38. Is the computation correct?
Check.
Is the answer sensible?
3 meters can make 5 lantern frames. There are five 3s in 15
5 x 5 = 25 (number of lantern frames) The answer is sensible.
Is the computation correct?
Check
3 x 25 = 75
The computation is correct.

39. Assignment :
Solve : (Show the basic steps in solving a problem).
1. Two out of three booths sell rag dolls. If there are 27 booths, how many of these sell rag dolls?

40. Assignment (ANSWERS)
A. What does the problem ask for?
The number of booths that sell rag dolls out of 27 booths.
B. What are given?
27 booths
3 booths
2 booths ( sell rag dolls )

41. D. Write the number sentence. 2 = n 3 27
C. How will you find the answer?
Compare the number of booths to the number of booths that sell rag dolls.
D. Write the number sentence.
2 = n

42. E. Show your solution.
2 = n
2 x 27 = 54
3 x n = 54
n = 54 ÷ 3
n = 18

43. F. Check your computation.
2 x 27 = 3 x 18
54 = 54
The computation is correct.

44. In 1 whole sheet of paper.
1. Make a summary of the whole lesson that has been tackled for the week.
2. Give an example of at least 5 real life problems involving ratio and proportion with the solutions following the basic steps in problem solving. (Write this in the Microsoft Word)