True or False? If a number has been increased by 20% , to find the original number you decrease the new number by 20% .

False. If a number has been increased by 20% , you can not find the original number by decreasing the new number by 20% . You would divide by 1.2 .

If you are given the new number after a percentage increase or decrease, how do you find the original number? E.g. Find the original amount given that it was increased by 15% to 80.5.

Find the multiplier for the percentage change, e.g. 15% increase = 1.15. Divide the new number by the multiplier , e.g. 80.5 ÷ 1.15 = 70.

What is the multiplier when a number has been decreased by 45% ?

The multiplier for a 45% decrease is 0.55 . Subtract 45 from 100 and then divide by 100.

True or False? A number has been decreased by 10% . To find the original number, multiply the new number by 0.9 .

False. A number has been decreased by 10% . To find the original number, divide the new number by 0.9 . Do not multiply .

True or False? A number has been increased by 80% . To find the original number, divide the new number by 0.8 .

False. A number has been increased by 80% . To find the original number, divide the new number by 1.8 , not 0.8. You need to add 80 to 100 and then divide by 100 to find the multiplier.

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Percentages (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontIntroduction to Percentages
Define the term percentage.

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Cards in this collection (28)

Define the term percentage.
A percentage is a number of parts out of $100$ .
The words "per cent" mean "out of $100$ ", so $50 %$ means $\frac{50}{100}$ .
How do you convert between a decimal and a percentage?
Multiply by $100$ to turn a decimal into a percentage, and divide by $100$ to go back the other way.
So $0.7 = 70 %$ , and $4 % = 0.04$ .
Complete these conversions from a percentage to a decimal:
$25 % =______$
$2.5 % =______$
$0.25 % =______$
The completed conversions are:
$25 % = 0.25$
$2.5 % = 0.025$
$0.25 % = 0.0025$
Each time the percentage gets ten times smaller, so does the decimal.
Why is it easier to compare $\frac{1}{2}$ , $\frac{2}{5}$ and $\frac{3}{4}$ once they are written as percentages?
The three fractions have different denominators, but as percentages they can be lined up directly.
They become $50 %$ , $40 %$ and $75 %$ , so the order is clear at a glance.
How do you write $\frac{234}{650}$ as a percentage?
Divide the top by the bottom to get the decimal equivalent, then convert that decimal into a percentage.
Here $234 \div 650 = 0.36$ , which is $36 %$ .
True or False?
Writing a fraction as a percentage changes its value.
False.
Only the way it is written changes: $\frac{1}{4}$ and $25 %$ are the same amount, and a percentage is just another way of showing a fraction.
Without a calculator, how do you find $10 %$ and $1 %$ of an amount?
Divide by $10$ to find $10 %$ , and divide by $100$ to find $1 %$ .
These two are the building blocks used to reach most other percentages.
$10 %$ of $400$ is $40$ , and $1 %$ of $400$ is $4$ . Complete the working for $12 %$ of $400$ :
$12 % of 400 = 40 +______+______=______$
The completed working is:
$12 % of 400 = 40 + 4 + 4 = 48$
$12 %$ is built from one lot of $10 %$ and two lots of $1 %$ .
How do you use a multiplier to find $12 %$ of $650$ ?
The multiplier is the decimal equivalent of the percentage, so here it is $0.12$ .
Multiply the amount by it: $0.12 \times 650 = 78$ .
How do you find $150 %$ of an amount?
$100 %$ is the original amount, so $150 %$ is the original amount plus another $50 %$ of it.
For $60$ that gives $60 + 30 = 90$ .
To express one number as a percentage of another, which number goes on the bottom of the fraction?
The number you are comparing to goes on the bottom.
A £ $150$ deposit on a £ $1200$ trip is written $\frac{150}{1200}$ , which comes to $12.5 %$ .
True or False?
$35 %$ of $40$ gives the same answer as $40 %$ of $35$ .
True.
Both come to $14$ , because each one works out as $\frac{35 \times 40}{100}$ , and a multiplication can be done in either order.
Without a calculator, how do you increase $200$ by $21 %$ ?
Find $21 %$ of $200$ , which is $42$ , and then add it to the original amount.
That gives $200 + 42 = 242$ .
An item costing £ $500$ is discounted by $35 %$ . Without a calculator, how do you find the new price?
A discount is a decrease, so find $35 %$ of $500$ , which is $175$ , and then subtract it from the original price.
That gives $500 - 175 = 325$ , so the new price is £ $325$ .
Why does decreasing an amount by $35 %$ mean finding $65 %$ of it?
Taking $35 %$ away leaves the rest of the amount behind, and the whole amount is $100 %$ .
So what remains is $100 % - 35 % = 65 %$ .
Complete the working, which decreases $80$ by $15 %$ using a multiplier:
$______\times 80 =______$
The completed working is:
$0.85 \times 80 = 68$
Notice that the multiplier is multiplied by the original amount to apply the change.
True or False?
Increasing $30$ by $10 %$ gives the same answer as finding $110 %$ of $30$ .
True.
The original amount is $100 %$ of itself, so adding another $10 %$ on top makes $110 %$ , and both routes give $33$ .
How do you find the multiplier that was used for a percentage change?
Divide the amount after the change by the amount before it:
$m = \frac{amount after}{amount before}$
Going from $250$ to $310$ gives $\frac{310}{250} = 1.24$ .
What percentage changes do the multipliers $1.05$ and $0.75$ represent?
$1.05$ is an increase of $5 %$ , and $0.75$ is a decrease of $25 %$ .
Compare the multiplier with $1$ : how far above $1$ it sits gives the increase, and how far below gives the decrease.
Complete the formula for a percentage change:
$percentage change = \frac{after -______}{______} \times 100$
The completed formula is:
$percentage change = \frac{after - before}{before} \times 100$
The before value goes underneath, because a change is always measured against what you started with.
When a percentage change works out negative, what does that tell you?
A negative answer is a percentage decrease, so an answer of $- 28$ means a decrease of $28 %$ .
A positive answer is a percentage increase.
When finding a percentage profit or loss, which price plays the part of the "before" value?
The cost price, which is what the shop paid, is the "before" value, and the selling price is the "after".
A car bought for £ $8000$ and sold for £ $5600$ gives $\frac{5600}{8000} = 0.7$ , which is a loss of $30 %$ .
True or False?
A percentage increase can never be more than $100 %$ .
False.
An amount can more than double, and a change from $250$ to $600$ is an increase of $140 %$ .
True or False?
If a number has been increased by 20%, to find the original number you decrease the new number by 20%.
False.
If a number has been increased by 20%, you can not find the original number by decreasing the new number by 20%.
You would divide by 1.2.
If you are given the new number after a percentage increase or decrease, how do you find the original number?
E.g. Find the original amount given that it was increased by 15% to 80.5.
Find the multiplier for the percentage change, e.g. 15% increase = 1.15.
Divide the new number by the multiplier, e.g. 80.5 ÷ 1.15 = 70.
What is the multiplier when a number has been decreased by 45%?
The multiplier for a 45% decrease is 0.55.
Subtract 45 from 100 and then divide by 100.
True or False?
A number has been decreased by 10%.
To find the original number, multiply the new number by 0.9.
False.
A number has been decreased by 10%.
To find the original number, divide the new number by 0.9.
Do not multiply.
True or False?
A number has been increased by 80%.
To find the original number, divide the new number by 0.8.
False.
A number has been increased by 80%.
To find the original number, divide the new number by 1.8, not 0.8.
You need to add 80 to 100 and then divide by 100 to find the multiplier.

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