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
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:

10% of 220 = 22
20% would be 22 x 2 = 44
 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:

10% of 400=40
5% would be 40/2 = 20
2.5% would be 20/2=10  40+20+10 = 70 therefore 17.5% = ?70
 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:
 Year 1: 10% of 1200 = 120
New value: 1200  120 = ? 1080  Year 2: 10% of 1080 = ?108
New Value: 1080  108 = ?972  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:
 Year 1: 10% of 10,000 = ?1000
New Value: 10,000 + 1000 = ?11,000  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
Example 1: 5/10 = ?
 Fraction to Decimal: 5/10 = 0.5
 Mulitply by 100: 0.5 x 100 = 50
Answer: 50%
Example 2: 1/4 = ?
 Fraction to Decimal: 1/4 = 0.25
 Mulitply by 100: 0.25 x 100 = 25
Answer: 25%
Percentages to Fractions
Example 1: 75% = ?
 Divide 75 by 100: 75/100
 Simplify 75/100 = 3/4
Answer: 3/4
Example 2: 45% = ?
 Divide 45 by 100: 45/100
 Simplify 45/100 = 9/20
Answer: 9/20