The document introduces percentages and provides examples and explanations of key percentage concepts such as: - Percent means out of 100 - Methods for converting between percentages, fractions, and decimals - Finding a percentage of a number by changing the percentage to a fraction and multiplying - Understanding when to add or subtract percentages depending on if an amount is increasing or decreasing - Using percentages in contexts involving money such as calculating discounts, tax, or price increases.

1. Hello there!
We are the Percentages Penguins and our colony of 100 penguins
is here to help you discover the wonderful world of percentages!
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2. The word percent means
out of 100.
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So, 40% means 40 out of 100.
We can also write
this as a fraction.
40
100
%We use this sign to
show percentages.
Can you think of any other
words with cent in them?

3. Aargh!
My phone’s
battery is
only 10%
charged!
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Buy today and get 25% off
the price of your next order!
I scored 80% on
the Science test!
Percentages can be used in lots of
different ways. Here are some examples.
Can you think of any more?
There is a
30% chance
of rain today.
45% of the penguins in
our colony are female.

4. Sometimes, you
can work out
percentages easily.
At other times, you
may have to
estimate.
There are 100
squares in this grid.
50% are Red
27% are Yellow
23% are Green
Can you estimate the percentage
of each shape that is red?
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5. To change a
percentage into a decimal,
divide it by 100.
To change a
decimal into a percentage,
multiply it by 100.
23% = 0.23
(23 ÷ 100 = 0.23)
5% = 0.05
(5 ÷ 100 = 0.05)
0.35 = 35%
(0.35 x 100 = 35)
0.03 = 3%
(0.03 x 100 = 3)
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÷ 100 x 100

6. As long as you remember that
percent means out of 100,
changing percentages into fractions is easy!
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There are 100 squares in this grid.
Twenty-three of them are orange.
23
100
23% =
49
100
49% =
60
100
60% =
3
5
=
Remember that some fractions can be simplified!

7. Changing fractions to percentages is
a little more complicated...
First, change the
fraction into a decimal...
(Divide the denominator
by the numerator)
Then, change the decimal
into a percentage...
(Multiply it by 100)
57
100
7
8
= 0.57 = 57%
= 0.875 = 87.5%
(0.57 x 100 = 57)
(0.875 x 100 = 87.5)
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8. Percentage 1% 10% 20% 25% 50% 75% 100%
Fraction
1
100
10
100
20
100
25
100
50
100
75
100
100
100
Simplified
Fraction
1
100
1
10
1
5
1
4
1
2
3
4
1
1
Decimal 0.01 0.1 0.2 0.25 0.5 0.75 1.0
It is helpful if you can
remember these percentages
and their matching fractions
and decimals.
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9. To find a percentage of an amount, change the
percentage into a fraction and then multiply them.
Question:
What is 25% of 200?
1) Change the percentage into a fraction:
2) Multiply the fraction and the amount:
25
100
25% =
25
100
x 200 = 50
To multiply an amount by a fraction...
Divide it by the denominator
(the bottom part of the fraction)
and multiply it by the numerator
(the top part of the fraction).
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10. There are
some quicker
methods to
help you find
different
percentages
of amounts:
To find 50% of a number,
divide it by 2...
50% of 40 = 20
To find 25% of a number,
divide it by 4...
25% of 40 = 10
To find 75% of a number,
find 25% and then
multiply that by 3...
75% of 40 = 30
To find 1% of a number,
divide it by 100...
1% of 300 = 3
To find 10% of a number,
divide it by 10...
10% of 500 = 50
If the percentage is a
multiple of 10, use the
method above to help you.
20% of 500 = 100
30% of 500 = 150
40% of 500 = 200
Could you combine any
of these methods to find
11% of a number...
or 85% of a number?
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If your calculator has a % button,
you can use that to find percentages!
Question:
What is 36% of 950?
Press the following keys to find the answer...
Remember that ‘of’ means multiply.
Your answer should be 342.
If your calculator doesn’t have a % button, change the
percentage to a decimal and then multiply that by the amount.
3 6 % x 9 5 0 =

12. Sometimes, amounts
will increase (go up)
or decrease (go down)
by a percentage.
Question:
There are 150 bricks in a construction
set. How many bricks will there be if:
a) 10% are added?
b) 10% are taken away?
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a) If 10% are added
• Work out 10% of 150
• Add this to the original amount
150 ÷ 10 = 15
150 + 15 = 165
b) If 10% are taken away
• Work out 10% of 150
• Subtract this from the amount
150 ÷ 10 = 15
150 - 15 = 135
When
should we
ADD SUBTRACTSUBTRACTSUBTRACT
should we
add or
subtract?
Gain
Hike
Increase
Go up
Rise
Surge
Decline
Decrease
Discount
Drop
Sale
Reduce

13. People often use
percentages
when they are
dealing with
money.
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Question:
A car costs $1,200. If the price
increases by 10%, what is the
new price?
• Work out 10% of $1,200
• Add this to the price
$1,200 ÷ 10 = $120
$1,200 + $120 = $1,320
Question:
A pair of shoes cost $45 last week.
Today, there is a 10% discount.
What is the new price?
• Work out 10% of $45
• Subtract this from the price
$45 ÷ 10 = $4.50
$45 - $4.50 = $40.50

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Question:
A field has an area of 50m2.
If 80% of the field is used by a herd of
cows, what area is left for the sheep?
If 80% of the field is used by cows, 20% of it can be used by the sheep.
10% of 50m2 is 5m2, so 20% is 10m2.
Question:
Ava and Noah are building towers.
Noah’s tower is 50cm tall and
Ava’s tower is 30% taller.
How tall is Ava’s tower?
10% of 50cm is 5cm.
30% of 50cm is 15cm.
Ava’s tower is 15cm taller than
Noah’s, so her tower is 65cm tall.
Percentages are
also used when
we are dealing
with different types
of measurements.
Here are some
examples: