Grade 7 percentages_amount_before_change.ppt

Percentage

1. © T Madas
Finding
the amount
before a
Percentage
Change

2. © T Madas
The value of a painting went up by 25% and is now
valued at £400.
What was its value before the increase?
The answer IS NOT £400 less 25%,
WHY?
If you increase £300 by 25% you
get
i.e. £300
£375
Why doesn’t a decrease by 25% get balanced by an
increase of 25%?
How do we solve a problem like this?

3. © T Madas
Value
Before
400
x 1.25
£320
400
÷ 1.25
The value of a painting went up by 25% and is now
valued at £400.
What was its value before the increase?

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An item costs £282 after V.A.T at 17.5%.
What is its price before V.A.T?
This formal equation set up
shows why this method works
but it is not strictly required
b1.175´ 282= Û
1.175b282=
b=
282
1.175
Û
Û
240b=
b
£240
x 1.175
÷ 1.175
£282

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An item costs £93.50 after a 15% discount.
What did it cost before the discount?
b0.85´ 93.5= Û
0.85b93.5=
b=
93.5
0.85
Û
Û
110b=
b
£110
x 0.85
÷ 0.85
£93.50

6. © T Madas
Find the number which was increased by 12%
to give 420.
b1.12´ 420= Û
1.12b420=
b=
420
1.12
Û
Û
375b=
b
375
x 1.12
÷ 1.12
420

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Find the number which was decreased by 17%
to give 415.
b0.83´ 415= Û
0.83b415=
b=
415
0.83
Û
Û
500b=
b
500
x 0.83
÷ 0.83
415

8. © T Madas
Finding the amount before
a percentage increase or
decrease:
Take the final amount and
divide it by the appropriate
percentage multiplier
Find the number that was
increased by 30% to give 520
520 ÷ 1.3 = 400
Find the number that was
decreased by 30% to give 420
420 ÷ 0.7 = 600
Finding the amount after
a percentage increase or
decrease:
Take the original amount
and multiply it, by the
appropriate percentage
multiplier
Increase 500 by 15%
500 x 1.15 = 575
Decrease 700 by 11%
700 x 0.89 = 623
Percentage Multiplier SummaryPercentage Multiplier Summary

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Practice
on finding
the amount
before a
Percentage
Change
using a
calculator

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What number was increased by 10% to give 121? 110
Amounts Before Percentage Changes
What number was increased by 15% to give 184? 160
What number was increased by 12% to give 252? 225
What number was increased by 27% to give 406.4? 320
What number was decreased by 10% to give 468? 520
What number was decreased by 25% to give 273? 364
What number was decreased by 40% to give 252? 420
What number was decreased by 11% to give 534? 600

11. © T Madas
What number was increased by 12% to give 140? 125
What number was decreased by 12% to give 484? 550
What number was increased by 17.5% to give 282? 240
What number was decreased by 17.5% to give 660? 800
What number was increased by 5.5% to give 147.7? 140
What number was decreased by 5.5% to give 1701? 1800
What number was increased by 1% to give 343.4? 340
What number was decreased by 1% to give 742.5? 750
Amounts Before Percentage Changes

12. © T Madas
110% of a number is 121. What is the number? 110
115% of a number is 184. What is the number? 160
112% of a number is 252. What is the number? 225
127% of a number is 406.4. What is the number? 320
90% of a number is 468. What is the number? 520
75% of a number is 273. What is the number? 364
60% of a number is 252. What is the number? 420
89% of a number is 534. What is the number? 600
Amounts Before Percentage Changes

13. © T Madas
112% of a number is 140. What is the number? 125
88% of a number is 484. What is the number? 550
117.5% of a number is 282. What is the number? 240
87.5% of a number is 700. What is the number? 800
105.5% of a number is 147.7. What is the number? 140
94.5% of a number is 1701. What is the number? 1800
101% of a number is 343.4. What is the number? 340
99% of a number is 742.5. What is the number? 750
Amounts Before Percentage Changes

14. © T Madas
Test
on finding
the amount
before a
Percentage
Change
using a
calculator

15. © T Madas
What number was increased by 10% to give 121? 110
Amounts Before Percentage Changes
What number was increased by 15% to give 184? 160
What number was increased by 12% to give 252? 225
What number was increased by 27% to give 406.4? 320
What number was decreased by 10% to give 468? 520
What number was decreased by 25% to give 273? 364
What number was decreased by 40% to give 252? 420
What number was decreased by 11% to give 534? 600

16. © T Madas
What number was increased by 12% to give 140? 125
What number was decreased by 12% to give 484? 550
What number was increased by 17.5% to give 282? 240
What number was decreased by 17.5% to give 660? 800
What number was increased by 5.5% to give 147.7? 140
What number was decreased by 5.5% to give 1701? 1800
What number was increased by 1% to give 343.4? 340
What number was decreased by 1% to give 742.5? 750
Amounts Before Percentage Changes

17. © T Madas
110% of a number is 121. What is the number? 110
115% of a number is 184. What is the number? 160
112% of a number is 252. What is the number? 225
127% of a number is 406.4. What is the number? 320
90% of a number is 468. What is the number? 520
75% of a number is 273. What is the number? 364
60% of a number is 252. What is the number? 420
89% of a number is 534. What is the number? 600
Amounts Before Percentage Changes

18. © T Madas
112% of a number is 140. What is the number? 125
88% of a number is 484. What is the number? 550
117.5% of a number is 282. What is the number? 240
87.5% of a number is 700. What is the number? 800
105.5% of a number is 147.7. What is the number? 140
94.5% of a number is 1701. What is the number? 1800
101% of a number is 343.4. What is the number? 340
99% of a number is 742.5. What is the number? 750
Amounts Before Percentage Changes

19. © T Madas