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Percentages

Percent means out of 100; the symbol for percentage is %. The percentage of a whole birthday cake is 100%.

100%50%

Half the cake would
be 50% or 50/100
Remember!
Percent means out
of 100. We can
simplify 50/100 to 1/2.

Look at the boxes below to help you understand percentages.

This box has no shade = 100%.Shaded part: 50/100 = 1/2.

100%

50%

50%

Shaded part: 25/100 = 1/4 Shaded part: 12.5/100 = 1/8

25%	25%
25%	25%

12.5%	12.5%
12.5%	12.5%
12.5%	12.5%
12.5%	12.5%

Percentage of an Item

Q.1 What is 25% of an item that costs ?300?

We know 100% of the item is ?300 so 25% of the item would be 25/100 x ?300.

We are going to look at two different methods to calculate the result.

Method 1 Step1: Write the percentage as a fraction. Step 2: Cancel out the zeros. Step 3: Multiply 25 by 3. Answer = ?75

Method 2 10% of 300 = 30 20% would be 30 x 2 =60 5% would be 30/2= 15 25% would be: (60 + 15 = 75) Answer= ?75

Q.2 The value of an item is worth ?220 within a year it increases by 20%.
What is the new value of the item?

Answer:

1. 10% of 220 = 22
   20% would be 22 x 2 = 44
   
   
2. The value has increased by ?44
   so the new value will be the original price plus the 20% increase.
   ?220 + ?44 = ?266

Q.3 An item worth ?400 decreases by 17.5%.
What is the new value of the item?

Answer:

1. 10% of 400=40
   5% would be 40/2 = 20
   2.5% would be 20/2=10


2. 40+20+10 = 70 therefore 17.5% = ?70


3. The new value after the decrease would be: ?400 - ?70 = ?330

Q4. An item is valued at ?1200. What would the value be in 3 years time, if it decreases by 10% each year?

Answer:

1. Year 1: 10% of 1200 = 120
   New value: 1200 - 120 = ? 1080


2. Year 2: 10% of 1080 = ?108
   New Value: 1080 - 108 = ?972


3. Year 3: 10% of 972 = ?97.20
   New Value: 972 - 97.20 = ?874.80

In 3 years time the value of the item would be worth ?874.80.

Q4.A painting is valued at ?10,000. What would it be worth in 2 years time, if it increases by 10% each year?

Answer:

1. Year 1: 10% of 10,000 = ?1000
   New Value: 10,000 + 1000 = ?11,000


2. Year 2: 10% of ?11,000 = ?1100
   New Value: 11,000 + 1100 = ?12,100
   

In 2 years time the painting would be worth ?12,100.

Profit and Loss in Percentages

Example 1

John bought a car for ?12,500 five years a go. He sells the car to Mary for ?9,000.

Loss made: 12500 - 9000 = ?3,500

To find the loss made in percentage we would use the loss formula.

Answer= 28%

Example2

Sara sold her saphire ring to a jewellery shop for ?1,450. She bought the ring 6 years ago for ?850.

Profit made: 1450 - 850 = ?600

To find the profit made in percentage we would use the profit formula.

Answer= 71%

Fractions to Percentages

Percentages to Fractions

Now try the Exercises!

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