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Percentages Toolkit (Cambridge (CIE) IGCSE Maths)

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    What number is a percentage out of?

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  • What number is a percentage out of?

    A percentage is out of 100.

  • True or False?

    To find a percentage of an amount, you can divide the percentage by 100 and multiply by the amount.

    True.

    To find a percentage of an amount, you divide the percentage by 100 and multiply by the amount.

    For example, 23% of 60 can be found by calculating 23 over 100 cross times 60.

  • How would you find one number as a percentage of another number?

    E.g. Find 12 as a percentage of 80.

    To find one number as a percentage of another number, divide the first number by the second number then multiply by 100.

    E.g. To find 12 as a percentage of 80, 12 over 80 cross times 100 equals 15 percent sign.

  • How would you find 25% of an amount without using a calculator?

    To find 25% of an amount without using a calculator is to divide the amount by 4 (by halving twice), as 25% is equivalent to a quarter.

    E.g. 25% of 60 can be calculated by 60 ÷ 4 = 15.

  • How would you find a percentage of an amount, where the percentage is greater than 100?

    E.g. 135% of 60

    To find a percentage of an amount where the percentage is greater than 100, use a multiplier which is equal to the percentage divided by 100.

    E.g. To find 135% of 60 calculate 1.35 × 60

    Without a calculator, find 35% of the amount, and add it on.

  • True or False?

    To increase an amount by 20%, you could multiply the amount by the multiplier 1.02.

    False.

    To increase an amount by 20%, you could multiply the amount by the multiplier 1.2. Multiplying an amount by 1.02 increases it by 2%.

  • How would you find the multiplier for decreasing an amount by 15%?

    To find the multiplier for decreasing an amount by 15%, you would subtract 15 from 100 and then divide by 100. The multiplier would be 0.85.

    A multiplier for a decreasing amount will always be less than 1.

  • True or False?

    To find the percentage change from 20 to 32 you can calculate fraction numerator 32 minus 20 over denominator 32 end fraction cross times 100.

    False.

    To find a percentage change, you need to divide by the original number,

    fraction numerator 32 minus 20 over denominator 20 end fraction cross times 100.

  • How do you find a percentage change?

    E.g. Find the percentage change for an amount that decreases from 80 to 60.

    You can find a percentage change by dividing the amount after by the amount before. This gives you the multiplier for the change.

    E.g. For an amount that is decreased from 80 to 60,

    the multiplier is 60 over 80 equals 0.75, which means that this is a decrease of 25%.

  • What is the equation used to calculate percentage profit or loss?

    The equation used to calculate percentage profit or loss is:

    fraction numerator Selling space price space minus space Cost space price over denominator Cost space price end fraction cross times 100

    If the result is positive, it is a percentage profit.
    If the result is negative, its is a percentage loss.

  • True or False?

    If a shopkeeper prices an item at 20% more than they originally bought it for, and then applies a 10% discount to the price, they would be selling the item for 10% more than it was originally bought for.

    False.

    They sell the item for 8% more than they originally bought it.

    To calculate a repeated percentage change, multiply all the percentage multipliers together to find the overall percentage multiplier.

    Percentage increase of 20% = 1.2, percentage decrease of 10% = 0.9.
    The overall percentage multiplier will be 1.2 × 0.9 = 1.08.
    This indicates an overall percentage increase of 8%.

  • True or False?

    If a number has been increased by 20%, to find the original number you decrease the new number by 20%.

    False.

    If a number has been increased by 20%, you can not find the original number by decreasing the new number by 20%.

    You would divide by 1.2.

  • If you are given the new number after a percentage increase or decrease, how do you find the original number?

    E.g. Find the original amount given that it was increased by 15% to 80.5.

    Find the multiplier for the percentage change, e.g. 15% increase = 1.15.

    Divide the new number by the multiplier, e.g. 80.5 ÷ 1.15 = 70.

  • What is the multiplier when a number has been decreased by 45%?

    The multiplier for a 45% decrease is 0.65.

    Subtract 45 from 100 and then divide by 100.

  • True or False?

    A number has been decreased by 10%.

    To find the original number, multiply the new number by 0.9.

    False.

    A number has been decreased by 10%.

    To find the original number, divide the new number by 0.9.
    Do not multiply.

  • True or False?

    A number has been increased by 80%.

    To find the original number, divide the new number by 0.8.

    False.

    A number has been increased by 80%.

    To find the original number, divide the new number by 1.8, not 0.8.
    You need to add 80 to 100 and then divide by 100 to find the multiplier.

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