1. Using Tape Diagrams to Find Percent

2. We will be using tape diagrams to find the percent of a number
We will be using tape diagrams to find the percent of a number. Start by drawing a simple tape diagram.
Divide the tape diagram into 10 sections.

3. Each section will represent 10%.
10 sections = 100%

4. What part of the tape diagram shows 30%?

5. What part of the tape diagram shows 80%?

6. What part of the tape diagram shows 10%?

7. What is 40% of 90? Now let’s use tape diagrams to solve
some percent problems.
What is 40% of 90?
Remember: Every box on the tape diagram represents the same amount

8. What part of the tape diagram shows 40%?
What is 40% of 90?
STEP ONE
What part of the tape diagram shows 40%?
Mark it off with a line.

9. What is 40% of 90?
STEP TWO
Now think about the tape diagram in a different way.
The entire tape diagram represents the total number.
In this problem: 90
There are 10 boxes on the tape diagram.
If the entire diagram represents 90, what number should be written in each box?

10. Each box represents a value of 9.
What is 40% of 90?
90 ÷ 10 = 9
Each box represents a value of 9. 9

11. What is 40% of 90? 9
STEP THREE
Look at the boxes you marked off earlier.
40% is represented by 4 boxes.
Now you can figure out the answer to the problem.

12. What is 40% of 90? 9
4 x 9 = 36
40% of 90 is 36

13. What part of the tape diagram shows 60%?
What is 60% of 120?
STEP ONE
What part of the tape diagram shows 60%?
Mark it off with a line.

14. What number should be written in each box?
What is 60% of 120?
STEP TWO
The total number is 120.
There are 10 boxes on the tape diagram.
What number should be written in each box?
120 ÷ 10 = 12

15. 60% is represented by 6 boxes.
What is 60% of 120? 12
STEP THREE
60% is represented by 6 boxes.
6 x 12 = 72
60% of 120 is 72

16. What part of the tape diagram shows 20%?
What is 20% of 40?
STEP ONE
What part of the tape diagram shows 20%?
Mark it off with a line.

17. What number should be written in each box?
What is 20% of 40?
STEP TWO
The total number is 40.
There are 10 boxes on the tape diagram.
What number should be written in each box?
40 ÷ 10 = 4 4

18. 20% is represented by 2 boxes.
What is 20% of 40? 4
STEP THREE
20% is represented by 2 boxes.
2 x 4 = 8
20% of 40 is 8

19. Now try a few on your own.

20. What is 30% of 80?
80 ÷ 10 = 8 8

21. 30% is represented by 3 boxes.
What is 30% of 80? 8
30% is represented by 3 boxes.
3 x 8 = 24
30% of 80 is 24

22. What is 70% of 200?
200 ÷ 10 = 20 20

23. 70% is represented by 7 boxes.
What is 70% of 200? 20
70% is represented by 7 boxes.
7 x 20 = 140
70% of 200 is 140

24. What is 90% of 350?
350 ÷ 10 = 35 35

25. 90% is represented by 9 boxes.
What is 90% of 350? 35
90% is represented by 9 boxes.
9 x 35 = 315
90% of 350 is 315

26. Now find the answers to some
real-world problems.

27. Jamison is buying a new skateboard for $60. He has a coupon for 30% off. How much money will he save with his coupon?

28. 30% is represented by 3 boxes.
60 ÷ 10 = 6 6
30% is represented by 3 boxes.
3 x 6 = 18
Jamison will save $18.

29. The Hall Family spent $40 at a restaurant for dinner
The Hall Family spent $40 at a restaurant for dinner. They have a coupon for 20% off the total cost. How much will they spend for dinner?

30. 40 ÷ 10 = 4 4 20% is represented by 2 boxes. 2 x 4 = 8
The coupon will save them $8.
40 – 8 = 32
Dinner will cost the Hall Family $32.

31. Leticia is saving money for a new computer that will cost $500
Leticia is saving money for a new computer that will cost $500. So far, she has saved 80% of what she needs. How much more money does Leticia need to save?

32. 500 ÷ 10 = 50 50 80% is represented by 8 boxes. 8 x 50 = 400
Leticia has saved $400.
500 – 400 = 100
Leticia needs to save $100 more to buy the computer.

33. So far, we’ve done percents such as
10% 20% 30% 40%
60% 70% 80% 90%

34. Divide the number in half!
What about
25% or 75%?
(50% is easy peesy)
How can you find 50%?
Divide the number in half!

35. So far we’ve always divided the tape diagram into 10 pieces.
When you are finding
25% or 75%,
divide the tape diagram into 4 pieces.
(50% is easy peesy)
How can you find 50%?
Divide the number in half!

36. 25%

37. 25% is represented by one box.

38. 75% is represented by three boxes.

39. What is 25% of 48?
48 ÷ 4 = 12 12

40. What is 25% of 48? 12
1 square represents 25%.
25% of 48 is 12

41. What is 75% of 120?
120 ÷ 4 = 30 30

42. What is 75% of 120? 3 squares represents 75%. 3 x 30 = 90
75% of 120 is 90

43. Morgan wants to buy a new video game system that costs $240
Morgan wants to buy a new video game system that costs $240. He has a coupon for 25% off. How much will he pay if he uses his coupon?

44. 240 ÷ 4 = 60 One section represents 25%.
Morgan’s coupon will save him $60.
240 – 60 = 180
The video game system will cost $180.

45. Roy is saving his money for a remote-controlled airplane that costs $120. He has saved 75% of the money. How much more does Roy need to save?

46. Three sections represents 75%.
120 ÷ 4 = 30 30
Three sections represents 75%.
3 x 30 = 90
Roy has saved $90.
120 – 90 = 30
Roy needs to save $30 more.

47. Now let’s think about percent in a different way.
Let’s do some problems where we already know the percent, but we need to find the total number.

48. Mark off 40% on the tape diagram.
12 is 40% of what number?
STEP ONE
Mark off 40% on the tape diagram.

49. 12 is 40% of what number? STEP TWO3 3 3 3
12 ÷ 4 = 3
STEP TWO
The four sections that represent 40% have a value of 12.
What is the value of each box?

50. 12 is 40% of what number? STEP THREE3 3 3 3 3 3 3 3 3 3
STEP THREE
All the boxes in the tape diagram have the same value, so all the boxes represent 3.

51. All 10 boxes have a value of 3.
12 is 40% of what number? 3 3 3 3 3 3 3 3 3 3
STEP FOUR
All 10 boxes have a value of 3.
10 x 3 = 30
12 is 40% of 30

52. Mark off 60% on the tape diagram.
54 is 60% of what number?
STEP ONE
Mark off 60% on the tape diagram.

53. 54 is 60% of what number? STEP TWO The six sections that represent 60%9 9 9 9 9 9
54 ÷ 6 = 9
STEP TWO
The six sections that represent 60%
have a value of 54.
What is the value of each box?

54. 54 is 60% of what number? STEP THREE9 9 9 9 9 9 9 9 9 9
STEP THREE
All the boxes in the tape diagram have the same value, so all the boxes represent 9.

55. All 10 boxes have a value of 9.
54 is 60% of what number? 9 9 9 9 9 9 9 9 9 9
STEP FOUR
All 10 boxes have a value of 9.
10 x 9 = 90
54 is 60% of 90

56. Mark off 80% on the tape diagram.
32 is 80% of what number?
STEP ONE
Mark off 80% on the tape diagram.

57. 32 is 80% of what number? STEP TWO4 4 4 4 4 4 4 4
32 ÷ 8 = 4
STEP TWO
The eight sections that represent 80%
have a value of 32.
What is the value of each box?

58. 32 is 80% of what number? STEP THREE4 4 4 4 4 4 4 4 4 4
STEP THREE
All the boxes in the tape diagram have the same value, so all the boxes represent 4.

59. All 10 boxes have a value of 4.
32 is 80% of what number? 4 4 4 4 4 4 4 4 4 4
STEP FOUR
All 10 boxes have a value of 4.
10 x 4 = 40
32 is 80% of 40

60. Now try a few on your own.

61. 35 is 70% of what number? 35 ÷ 7 = 5 5 x 10 = 50 35 is 70% of 50 5 5 5

62. 18 is 90% of what number? 18 ÷ 9 = 2 2 x 10 = 20 18 is 90% of 20 2 2 2

63. 15 is 75% of what number? 15 ÷ 3 = 5 4 x 5 = 20 15 is 75% of 20 5 5 5

64. Now find the answers to some
real-world problems.

65. Tristan bought a new video game for $24 with a coupon for 25% off
Tristan bought a new video game for $24 with a coupon for 25% off. How much would the video game have cost without the coupon?

66. Since the game was 25% off, that means he paid for 75% of the game.8 8 8 8
24 ÷ 3 = 8
4 x 8 = 32
The video game cost $32 before the coupon.

67. Liliana spent $64 on a new coat. She had a coupon that gave her 20% off. How much was the original price of the coat?

68. Since the coat was 20% off, that means she paid for 80% of the coat.
64 ÷ 8 = 8
10 x 8 = 80
The coat cost $80 before the coupon.

69. Jackie took her 2 friends out to lunch
Jackie took her 2 friends out to lunch. She had a coupon for 10% off their total bill. She paid $27. How much was the bill before the coupon?

70. Since the lunch was 10% off, that means she paid for 90% of the lunch.3 3 3 3 3 3 3 3 3 3
27 ÷ 9 = 3
10 x 3 = 30
The lunch cost $30 before the coupon.

71. Now you can use tape diagrams to solve percent problems.
Super job!
Now you can use tape diagrams to solve percent problems.