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Today’s Lesson:
What: mental percentages and the
percent proportionWhy: To solve several different types of percentage problems using both mental math and the percent proportion formula.
How to compute percentages using the power of your mind (who needs a calculator anyway???):
Percentage
How do I do it??? Example(s)
10% Slide the decimal ONE to the left!
10% of 5,280 = 528
1% Slide the decimal TWO to the left!
1% of 400 = 4
20% Find 10%-- then DOUBLE it!!
20% of 70 = 14
* Since 10% is 7, we double 7 to get 14!
5% Find 10%-- then cut it in HALF!!
5% of 48 = 2.4
* Since 10% is 4.8, we take half of that number, which is 2.4!
15% Find 10%, find 5%-- ADD them together!!
15% of 40 = 6
* Since 10% is 4 and 5% is 2-- add 4 and 2 to get 6!
50% Cut the number in HALF!!
50% of 82 = 41
*Since 41 is HALF of 82!
25% Find 50%-- then cut it in HALF!!
25% of 18 = 4.5
* Since 50% of 18 is 9, we take half of 9 !
Find 10% of . . .
1. 800 = _____ 2. 255 = _____
You try . . .
5. 2,500 = _____ 6. 48.89 = _____
3. 2.23 = _____ 4. 32.5 = _____
7. 199.9 = _____ 8. 2,527 = _____
80 25
0.223 3.25
250 4.889
19.99 252.7
Miscellaneous . . .
1.
20% of 90
2. 20% of 420
3.
5% of 440
4.
5% of 82
5.
15% of 80
6.
15% of 1,000
7.
1% of 325.5
8.
1% of 8
9.
50% of 70
10.
50% of $6.24
11.
25% of 20
12.
25% of 4.40
18 84 22 4.1
12 150 3.255 0.08
35 $3.12 5 1.10
% part “is”
100 whole “of”
=
We can use the above formula to solve ANY type of percentage problem. WHY??? Because, using this formula allows us to find the missing percentage, find the missing part, or find the missing _________________________.
We place _________ in the correct position, according to what we need to find.
The Percent proportion formula . . .
whole
x
How do we set the proportion up??? Like this . . .
5 out of 85 is what percent? =
Find 25% of 75: =
20 is 10% of what number? =
Solving for the percent . . .
Solving for the part . . .
Solving for the whole . . .
% part “is”
100 whole “of”
=
Real-Life Scenarios:
1) Collin scored an 88% on the test. If
there were 40 total questions, how many did Collin answer correctly?
x ≈ 35 questions
% part “is”
100 whole “of”
=
2) Jane scored a 94% on the test. If she answered 47 questions correctly, how many total questions were on the test?
x = 50 questions
% part “is”
100 whole “of”
=
3) On the Unit 8 Test, Holly got 40 questions correct out of 45 total questions. What was her percentage score?
x ≈ 89%
% part “is”
100 whole “of”
=
4) Hannah made $40 from babysitting. She spends $8 at the dollar store. What percent of her babysitting money did she spend?
x = 20%
% part “is”
100 whole “of”
=
5) Henry earned $45 mowing lawns.
This is 25% of his total savings. What is his total savings?
x = $180
% part “is”
100 whole “of”
=
6) Callie spent 30% of her savings on
an i-Pod. If the i-Pod was $120, how much did she have in savings to begin with?
x = $400
END OF LESSON
The next slides are student copies of the notes for this lesson. These notes were handed out in class
and filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”)
represent the homework assigned for that day.
Math-7 NOTES DATE: ______/_______/_______What: mental percentages and the percent proportionWhy: To solve several different types of percentage problems using both mental math and the percent proportion formula.
NAME:
How to compute percentages using the power of your mind :(who needs a calculator anyway???)
Percentage
How do I do it??? Example(s)
10% Slide the decimal ONE to the left!
10% of 5,280 = 528
10% of $423.74 = $42.37
1% Slide the decimal TWO to the left!
1% of 400 = 4
20% Find 10%-- then DOUBLE it!! 20% of 70 = 14
* Since 10% is 7, we double 7 to get 14 !
5% Find 10%-- then cut it in HALF!!
5% of 48 = 2.4
* Since 10% is 4.8, we take half of that number, which is 2.4 !
15% Find 10%, find 5%-- ADD them together!!
15% of 40 = 6
* Since 10% is 4 and 5% is 2-- add 4 and 2 to get 6 !
50% Cut the number in HALF!! 50% of 82 = 41
* Since 41 is HALF of 82 !
25% Find 50%-- then cut it in HALF!!
25% of 18 = 4.5
* Since 50% of 18 is 9, we take half of 9 !
Find 10% of . . .
1. 800 = _____ 2. 255 = _____ 3. 2.23 = _____
4. 32.5 = _____
5. 2,500 = _____
6. 48.89 = _____
7. 199.9 = _____
8. 2,527 = _____
You try . . .
% part “is”
100 whole “of”
=
Miscellaneous . . .
1. 20% of 90 2. 20% of 420
3. 5% of 440 4. 5% of 82
5. 15% of 80 6. 15% of 1,000
7. 1% of 325.5
8. 1% of 8
9. 50% of 70
10. 50% of $6.24
11. 25% of 20 12. 25% of $4.40
We can use the above formula to solve ANY type of percentage problem. WHY??? Because, using this formula allows us to find the missing percentage, find the missing part, or find the missing _________________________.
We place _________ in the correct position, according to what we need to find.
How do we set the proportion up??? Like this . . .
5 out of 85 is what percent? =
Find 25% of 75: =
20 is 10% of what number? =
The Percent proportion formula . . .
Solving for the percent . . .
Solving for the part . . .
Solving for the whole . . .
% part “is”
100 whole “of”
=
Real-Life Scenarios: 1) Collin scored an 88% on the test. If there were 40 total
questions, how many did Collin answer correctly?
2) Jane scored a 94% on the test. If she answered 47 questions correctly, how many total questions were on the test?
3) On the Unit 8 Test, Holly got 40 questions correct out of 45 total questions. What was her percentage score?
4) Hannah made $40 from babysitting. She spends $8 at the dollar store. What percent of her babysitting money did she spend?
5) Henry earned $45 mowing lawns. This is 25% of his total savings. What is his total savings?
6) Callie spent 30% of her savings on an iPod. If the i-Pod was $120, how much did she have in savings to begin with?
Fill in the missing spaces in the below charts by using the mental math strategies
from your notes (do not use a calculator):
Math-7 Practice/homework“mental percentages”
DATE: ______/_______/_______NAME:____________________________________________________________________________
50 8.4 280 4,080
10%
5%
15%
20%
25%
42.6 160 240.8 90
10%
5%
15%
20%
25%
Miscellaneous . . .
1. 20% of 25 2. 10% of 1,248
3. 5% of 6 4. 10% of 22.8
5. 15% of 822
6. 1% of 2.7 7. 25% of 20 8. 50% of 500
Use the Percent Proportion Formula to answer the following (some do not work out
evenly– round to the nearest tenth unless otherwise specified) :
Math-7 Practice/homework“Percent Proportions”
DATE: ______/_______/_______NAME:____________________________________________________________________________
1) Bridget scored a 95% on the test. If there were 40 questions, how many did she answer correctly?
2) Zack scored a 92% on the test. If he answered 23 questions correctly, how many total questions were on the test?
3) Linda got 33 questions correct out of 40 total questions on the test. What is her percentage score (round to the nearest whole percent)?
4) Nate had $50 in his piggy bank. He took $22 out in order to buy some headphones. What percent of his original total did he take out?
5) Sandy withdrew 34% of her savings. If she withdrew $120, how much was in her savings to begin with?
6) Kelly spent 60% of her paycheck at Target. If her paycheck was $300, how much did she spend?
= =
