Using Tape Diagrams to Find Percent

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.

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

What part of the tape diagram shows 30%?

What part of the tape diagram shows 80%?

What part of the tape diagram shows 10%?

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

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.

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?

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

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.

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

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.

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

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

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.

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

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

Now try a few on your own.

What is 30% of 80? 80 ÷ 10 = 8 8

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

What is 70% of 200? 200 ÷ 10 = 20 20

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

What is 90% of 350? 350 ÷ 10 = 35 35

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

Now find the answers to some real-world problems.

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

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

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?

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.

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?

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.

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

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

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!

25%

25% is represented by one box.

75% is represented by three boxes.

What is 25% of 48? 48 ÷ 4 = 12 12

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

What is 75% of 120? 120 ÷ 4 = 30 30

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

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?

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

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?

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.

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.

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

12 is 40% of what number? STEP TWO 3 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?

12 is 40% of what number? STEP THREE 3 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.

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

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

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 is 60% of what number? STEP THREE 9 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.

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

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

32 is 80% of what number? STEP TWO 4 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?

32 is 80% of what number? STEP THREE 4 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.

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

Now try a few on your own.

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

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

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

Now find the answers to some real-world problems.

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?

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.

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?

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.

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?

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.

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