Percentages Flashcards

All 23 cards in this deck

What does 'percent' mean?

Number of parts per hundred.
e.g. $37\% = \frac{37}{100}$

How do you express one quantity as a percentage of another?

e.g. 15 as a percentage of 60

Divide the first by the second, then multiply by 100.
$\frac{15}{60}\times 100 = 25\%$

What decimal do you multiply by to find a percentage of a quantity?

e.g. 35% of an amount

The percentage divided by 100.
$35\% \to \times 0.35$

Without a calculator, how do you find 10%, 5% and 1% of an amount?

$10\%$: divide by 10; $5\%$: halve the 10%; $1\%$: divide by 100.

True or false? A percentage can never be more than 100%.

False. Percentages greater than 100% are fine — they mean more than the whole.
e.g. a percentage profit of 248.8%

What are the steps to find a percentage of a fraction of an amount?

e.g. 50% of the people said yes; 80% of those wanted a large screen

1. Write each percentage as a decimal: $0.5$ and $0.8$
2. Multiply the decimals: $0.5\times0.8=0.4$
3. Convert back: $40\%$ of all the people

What is the multiplier for increasing a quantity by a percentage?

e.g. increase by 15%

$1 + \frac{\text{percentage}}{100}$
$\times 1.15$

What is the multiplier for decreasing a quantity by a percentage?

e.g. decrease by 15%

$1 - \frac{\text{percentage}}{100}$
$\times 0.85$

What is the formula for percentage change?

$\dfrac{\text{new} - \text{original}}{\text{original}} \times 100$

What is the formula for percentage profit?

$\dfrac{\text{selling price} - \text{cost price}}{\text{cost price}} \times 100$

True or false? To work out a percentage change you divide the difference by the new value.

False. You divide the difference by the original value.

True or false? Increasing an amount by 30% and then decreasing the result by 30% returns it to the original amount.

False. $1.3 \times 0.7 = 0.91$, a 9% decrease overall.

What are the steps to find the overall percentage change after two successive changes?

e.g. an increase of 20% followed by a decrease of 50%

1. Write each multiplier: $1.2$ and $0.5$
2. Multiply them: $1.2\times0.5=0.6$
3. Compare with 1: $0.6$ is a 40% decrease overall

What single multiplier increases an amount by 140%?

$\times 2.4$
Since $1 + \frac{140}{100} = 2.4$

What is a reverse percentage problem?

One where you are given the value after a percentage change and must find the original value.

How do you find the original value before a percentage change?

e.g. after a 15% decrease the price is £46.75

Divide the new value by the multiplier.
$46.75 \div 0.85 = £55$

True or false? To find the price before 20% VAT was added, you subtract 20% of the total price.

False. You divide the total by $1.2$; the 20% was of the smaller pre-VAT price.

What are the steps to solve a reverse percentage problem?

e.g. after a 40% reduction a mattress costs £660

1. Write the multiplier for the change: $100-40=60\%$, so $0.6$
2. Divide the given value by it: $660 \div 0.6$
3. State the original: $£1100$

In a reverse percentage problem with two successive changes, how do you find the original value in one step?

e.g. a 20% profit then a 10% loss, ending at £162 000

Divide by the product of the two multipliers.
$162\,000 \div (1.2 \times 0.9) = 162\,000 \div 1.08 = £150\,000$

If a percentage increase adds a known amount of money, how do you find the original price?

e.g. a 20% increase adds £240

Divide the added amount by the decimal for that percentage.
$240 \div 0.2 = £1200$

True or false? Increasing a quantity by $100\%$ doubles it.

True. The multiplier is $1 + 1 = 2$, so the quantity is multiplied by 2.

What are the steps to compare two quantities using percentages?

e.g. 12 marks out of 40 in Test A and 21 marks out of 75 in Test B

1. Write each amount as a fraction of its own total: $\frac{12}{40}$ and $\frac{21}{75}$
2. Multiply each by 100: $30\%$ and $28\%$
3. Compare the percentages: Test A is the better result

True or false? Putting $25\%$ more cereal in a box for the same price is the same offer as reducing the price by $25\%$ for the same amount of cereal.

False. $125$ g for the old price of $100$ g is a reduction of $\frac{100}{125}=80\%$ of the price, i.e. only a $20\%$ price cut.