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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The word percent meansout of 100.

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So, 40% means 40 out of 100.

We can also writethis as a fraction.

40100

%We use this sign to show percentages.

Can you think of any other words with cent in them?

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.

Sometimes, you can work out

percentages easily. At other times, you

may have to estimate.

There are 100 squares in this grid.

50% are Red27% are Yellow23% are Green

Can you estimate the percentage of each shape that is red?

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To change apercentage into a decimal,

divide it by 100.

To change adecimal 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

As long as you remember thatpercent 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.

2310023% =

4910049% = 60

10060% = 35=

Remember that some fractions can be simplified!

Changing fractions to percentages isa little more complicated...

First, change thefraction into a decimal...

(Divide the denominatorby the numerator)

Then, change the decimal into a percentage...

(Multiply it by 100)

57100

78

= 0.57 = 57%

= 0.875 = 87.5%

(0.57 x 100 = 57)

(0.875 x 100 = 87.5)

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Percentage 1% 10% 20% 25% 50% 75% 100%

Fraction 1100

10100

20100

25100

50100

75100

100100

Simplified Fraction

1100

110

15

14

12

34

11

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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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:

2510025% =

25100 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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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 thenmultiply 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 = 10030% of 500 = 15040% 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 =

Sometimes, amountswill 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 = 15150 + 15 = 165

b) If 10% are taken away• Work out 10% of 150• Subtract this from the amount

150 ÷ 10 = 15150 - 15 = 135

When should we

ADD SUBTRACTSUBTRACTSUBTRACTshould we

add or subtract?

GainHike

IncreaseGo up

RiseSurge

DeclineDecrease

DiscountDrop

SaleReduce

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 thanNoah’s, so her tower is 65cm tall.

Percentages are also used when we are dealing

with different types of measurements.

Here are some examples: