Percentages Flashcards

All 35 cards in this deck

What does 'percentage' mean?

Number of parts per hundred.

If 73% of tickets sold were adult tickets, what percentage were not adult tickets?

27%.
The whole is 100%, so $100 - 73 = 27$.

True or false? A percentage can be greater than 100%.

True.
It just means more than the whole, e.g. 150% of 40 is 60.

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

e.g. 60% of 70

The percentage divided by 100.
$60\% \to 0.6$, so $0.6 \times 70 = 42$.

True or false? 0.3 as a multiplier means 30%, and 1.3 means 130%.

True.
So 1.3 increases an amount by 30%, not by 3%.

What percentage is the same as the whole of something?

100%.

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

Divide by 10.
e.g. 10% of 80 is 8.

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

Divide by 100.
e.g. 1% of 800 is 8.

Without a calculator, how do you find 50% and 25% of an amount?

50% is dividing by 2; 25% is dividing by 4.
e.g. 50% of 240 is 120.

What are the steps to find a percentage of an amount using 10% and 1% building blocks?

e.g. 23% of 400

1. Find 10%: $400 \div 10 = 40$
2. Find 1%: $400 \div 100 = 4$
3. Combine: $2 \times 40 + 3 \times 4 = 92$

How do you find a percentage over 100% of an amount?

e.g. 150% of 60

Multiply by the percentage $\div 100$.
$1.5 \times 60 = 90$.

True or false? Finding 20% of 80 means working out $80 - 20$.

False.
It means $0.2 \times 80 = 16$.

What multiplier increases an amount by a percentage?

e.g. increase by 20%

$1 + \dfrac{\text{percentage}}{100}$.
For 20% the multiplier is 1.2.

What multiplier decreases an amount by a percentage?

e.g. decrease by 3%

$1 - \dfrac{\text{percentage}}{100}$.
For 3% the multiplier is 0.97.

True or false? To increase an amount by 3% you multiply by 1.3.

False.
You multiply by 1.03; 1.3 is an increase of 30%.

What single multiplier adds VAT at 20% to a price?

1.2 (i.e. finding 120% of the price).

In a multi-step problem with a 10% discount then VAT at 20%, what do you do with the two multipliers?

e.g. price $P$

Multiply by both in turn: $P \times 0.9 \times 1.2$.

True or false? Increasing an amount by 10% and then decreasing the result by 10% gives you back the original amount.

False.
The multipliers give $1.1 \times 0.9 = 0.99$, so you end with 99% of the original.

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

e.g. 18 as a percentage of 56

$\dfrac{\text{part}}{\text{whole}} \times 100$.
$\dfrac{18}{56} \times 100 = 32\%$ (to the nearest whole number).

What is the formula for percentage change?

$\dfrac{\text{change}}{\text{original}} \times 100$.

True or false? In a percentage change calculation you divide the change by the new value.

False.
You divide the change by the original value.

What are the steps to work out a percentage profit?

e.g. bought for £10, sold for £12

1. Find the profit: $12 - 10 = 2$
2. Divide by the cost price: $2 \div 10 = 0.2$
3. Multiply by 100: 20% profit

How do you find a percentage loss?

e.g. bought for £80, sold for £56

$\dfrac{\text{loss}}{\text{cost price}} \times 100$.
$\dfrac{24}{80} \times 100 = 30\%$ loss.

If new value $\div$ original value $= 3.6$, what is the percentage increase?

260%.
$3.6 \times 100 = 360\%$, then subtract 100%.

What is a reverse percentage problem?

Finding the original value when you are given the amount after a percentage increase or decrease.

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

e.g. after a 30% reduction the price is £280

Divide by the decrease multiplier.
$280 \div 0.7 = £400$.

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

e.g. after a 9% increase the population is 165 680

Divide by the increase multiplier.
$165\,680 \div 1.09 = 152\,000$.

True or false? To find the price before a 30% discount you add 30% back onto the sale price.

False.
You divide the sale price by 0.7, because the 30% was taken off the original, not the sale price.

What are the steps to solve a reverse percentage problem using the multiplier method?

e.g. after a 15% decrease a car is worth £13 600

1. Write the multiplier: $100 - 15 = 85\%$, so 0.85
2. Divide the new amount by it: $13\,600 \div 0.85$
3. State the original: £16 000

A 20% increase adds £240 to a price. How do you find the original price?

Divide the increase by the decimal for 20%: $240 \div 0.2 = £1200$.

In a reverse percentage, what does the sale price of a book represent as a percentage after a 30% reduction?

70% of the original price.

What are the steps to compare two quantities using percentages?

e.g. is 45 out of 60 better than 18 out of 25?

1. Write the first as a percentage: $45 \div 60 \times 100 = 75\%$
2. Write the second as a percentage: $18 \div 25 \times 100 = 72\%$
3. Compare: $75\% > 72\%$, so 45 out of 60 is better.

True or false? The item with the bigger profit in pounds always has the bigger percentage profit.

False. The percentage profit also depends on the cost price, so a smaller cash profit on a cheap item can be a bigger percentage.

What are the steps to decide which of two offers is cheaper?

e.g. 12 lessons at £24 each — Offer 1: first lesson free; Offer 2: 5% off every lesson

1. Total cost of Offer 1: $24 \times 11 = £264$
2. Total cost of Offer 2: $24 \times 0.95 \times 12 = £273.60$
3. Compare and state which: Offer 1 is cheaper.

True or false? An offer of '25% off' always saves you more money than an offer of '£5 off'.

False. It depends on the original price — you must work out the actual saving for each offer before comparing.