Once you have grasped how to calculate fractions of amounts and percentages of amounts you can then apply this to solving problems
The most basic of these problems will be where you have to increase or decrease an amount by a given fraction or percentage
e.g If a box of cereal weighs 450g one week and then the next week it is on sale 1
with extra free, how much will it now weigh?
5
You calculate the fraction of the amount FIRST
1 of 450g = 450g ÷ 5 = 90g
5 Next we need to ADD this to the original amount as the extra weight has been added
This gives us 450g + 90g
540g
1
e.g2 If a pair of trainers originally costs £80 but are then available in a sale which has '30% off all trainers', how much do the trainers now cost?
First step: Calculate 30% of £80
find 10% of £80 by dividing £80 by 10
£80 ÷ 10 = £8
30% = 10% + 10% + 10%
So 30% of £80 = £8 + £8 + £8 = £24
Last step: Subtract this amount from the original amount as this is a decrease in price!
£80 ­ £24 = £56
Answer = £56
2
The next step is to calculate the Fractional or percentage increase/decrease where you have to work out what the fraction or percentage was instead of being given it. To calculate the fractional or percentage increase or decrease of an amount you can use the following formula:
Fractional change = difference in amounts
original amount
Once you have the fractional change you can use this to work out the percentage change!!
e.g1 If a box of 6 eggs cost £1.50 and then increase in price to £1.95, what is the percentage increase?
Using the above formula:
difference in amounts = 45p
original amount = 150p Need to convert the units to make them all the same!!
= 45 = 9 = 3
150 30 10
We convert the fraction to a percentage!
3 = 30%
10
So the price increased by 30%
3
e.g 2
If a shirt originally costs £60 but you are able to buy it for £45 in a sale, what was the percentage discount that you got?
Using the formula again:
difference in amounts = £15
original price = £60
This gives us a FRACTION of 15 = 3 = 1
60 12 4
1 = 25% so this was a 25% decrease in the price
4
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