
4.04/4.05 Applications of Ratios and Percents
Presentation
•
Mathematics
•
7th Grade
•
Medium
Maria Vo
Used 1+ times
FREE Resource
16 Slides • 15 Questions
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Applications of Ratios and Percents
4.04/4.05
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Objectives
After completing this lesson, you will be able to say:
•I can use proportional relationships to solve multi-step ratio problems.
•I can use proportional relationships to solve multi-step percent problems
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Poll
Let's start with a simple question!
Did you just wake up?
Yes
No
I haven't slept yet
4
Poll
Would you rather live without heat and AC or live without social media?
Live without heat
Live without social media
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Multiple Choice
What is a ratio?
A comparison of quantities
A comparison of measurements with a denominator of 1
A part per hundred
6
Multiple Choice
What is a unit rate?
A comparison of quantities
A comparison of quantities with different units (with a denominator of 1)
A part per hundred
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Let's Start!
Mr. Peabody needs to pour cement for his new time machine, “The Way Back”. Currently, his crew has completed 500 square feet in the last 40 days. The total area will be 800 square feet… at this rate how long will it take to complete the project?
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Multiple Choice
How should I set up the ratio?
"500 square feet in the last 40 days. The total area will be 800 square feet… "
40500
80500
80040
40800
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Now we should find the unit rate...
40 days500 sq feet=1 dayx
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Multiple Choice
What is the unit rate for 40500 ?
50040 or 0.08
1500 or 500
140 or 40
40500 or 12.5
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Multiple Choice
How should I use the unit rate 112.5 to solve for how long it'll take to cover 800 square feet?
Add 12.5 and 800
Subtract 12.5 and 800
Multiply 12.5 and 800
Divide 12.5 and 800
Set up a proportion!
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Summary!
40 days500 ft2 =1 day12.5 ft2
1 day12.5 ft 2=x days800 ft2
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Complex Fractions
Mr. Peabody’s Workers have been painting his lab for ¼ of the month… they painted 1/3 of his lab. How many months will it take them to paint the entire lab?
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Multiple Choice
How should I set up this complex fraction?
Mr. Peabody’s Workers have been painting his lab for ¼ of the month… they painted 1/3 of his lab.
41÷31
31÷41
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41÷31=3141
31of the lab41month is the rate that we are working with.
We want to find out how much it would take for 1 month so we will divide using KCF (Keep, Change, Flip)
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Multiple Choice
What should 41÷31 look like after we use KCF (Keep, Change, Flip)
41 × 31
31 × 41
41 × 13
31 ×14
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Multiple Choice
41 × 13
Let's multiply
43
34
54
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Summary of Complex Fractions
41 month÷ 31lab = 41 × 13 = 43 month!
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Extra Example
If 3/4 of a ton of sand covers 1/5 of a playground, how many tons of sand are required to cover the entire playground?
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Multiple Choice
If 3/4 of a ton of sand covers 1/5 of a playground, how many tons of sand are required to cover the entire playground?
203
415
94
49
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Multiple Choice
What does the term "Percent" means?
a part in every hundred
divide by 100
every cent
how many cents
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Percent of Increase or Decrease
Daisy calculated that she would spend $250 on school supplies this year. She actually spent $195 on school supplies. What is Daisy’s percent of error?
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Multiple Choice
How should I set up this problem based on the formula?
"She spend $250 on school supplies this year. She actually spent $195 on school supplies."
195∣195−250∣×100
250∣195−250∣×100
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195∣195−250∣×100
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195∣195−250∣×100
195∣−5∣×100
1955=0.0256 ×100=2.56%
Remember that we multiply by 100 to get percents.
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How about another one?
Roger spent 20 hours doing yard work last week. This week he spent 26 hours doing yard work. He says that she spent 130% more time doing yard work this week. Is he correct?
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Open Ended
Roger spent 20 hours doing yard work last week. This week he spent 26 hours doing yard work. He says that she spent 130% more time doing yard work this week. Is he correct?
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Answer to "Roger spent 20 hours doing yard work last week. This week he spent 26 hours doing yard work. He says that she spent 130% more time doing yard work this week. Is he correct?"
20∣20−26∣×100
20 ∣−6∣×100 = 206 = 0.3 ×100 = 30%
No, he is not because he only spent 30% more time.
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Now for something a little different
Jamie read 50 pages of her 400-page book in 6 hours. At this rate, how long will it take her to read the entire book?
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Multiple Choice
Marcus painted 51 of his bedroom in 31 of an hour. At this rate, how long would it take him to finish the room?
151
35
53
81
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Answer!
51÷ 31 = 51 × 13 = 53hours
Applications of Ratios and Percents
4.04/4.05
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