Define reverse percentage .

A reverse percentage question gives you the value after a percentage increase or decrease and asks you to find the value before it. The change has already happened, so it is the starting amount that is unknown.

In a reverse percentage question, how do you get from the "after" amount to the "before" amount?

Divide the "after" amount by the percentage multiplier, which undoes the multiplication that produced it. For a decrease of 20% that means dividing by 0.8.

True or False? A price rose by 10% to £220, so the price before the rise was 90% of £220.

False. The 10% was worked out from the before price, so 10% of that price is not the same amount of money as 10% of £220. Taking 10% off £220 gives £198, whereas the correct answer is £200.

A population falls by 5% each year. If it is measured at the start of 2025 and again at the start of 2028, how many times has the change been applied?

Three times, once during each of the years 2025, 2026 and 2027. Count the gaps between the two dates rather than the dates themselves, or the power will come out one too large.

Define appreciation .

Appreciation is the value of something increasing by a percentage over a period of time. Paintings, collectible items and investment accounts are typical examples.

Define depreciation .

Depreciation is the value of something decreasing by a percentage over a period of time. Cars, laptops and mobile phones are typical examples.

True or False? Appreciation and depreciation questions are worked out by the same method.

True. Both are repeated percentage change applied to a value over time, and the only difference is whether that value is going up or down .

Define compound interest .

Compound interest is interest added to an amount of money at regular intervals , such as every year or every month. It applies to debt as well as to savings, increasing the amount owed just as it increases the amount saved.

When money earns compound interest at 4% per year, what percentage change is applied each year?

An increase of 4% , applied to whatever the account is worth at the start of that year. The interest rate is simply the percentage increase for one interest period.

Why does the amount of money added by compound interest grow every year, even though the interest rate stays the same?

The interest for each year is worked out on the whole balance, which by then includes the interest added in all the earlier years. So the same percentage is being taken of a larger and larger amount each time.

National 5MathsSQAFlashcardsNumerical SkillsPercentages

Percentages (SQA National 5 Maths): Flashcards

Exam code: X847 75

1/20

0Still learning

Know0

FrontReverse Percentages
Define reverse percentage.

Was this flashcard helpful?

Cards in this collection (20)

Define reverse percentage.
A reverse percentage question gives you the value after a percentage increase or decrease and asks you to find the value before it.
The change has already happened, so it is the starting amount that is unknown.
Complete the equation that a reverse percentage question is built on, using the words "before" and "after", where $p$ is the percentage multiplier.
$______\times p =______$
The completed equation is:
$before \times p = after$
Getting the order right is the whole point: the percentage change happens to the before amount, never to the after amount.
In a reverse percentage question, how do you get from the "after" amount to the "before" amount?
Divide the "after" amount by the percentage multiplier, which undoes the multiplication that produced it.
For a decrease of 20% that means dividing by 0.8.
True or False?
A price rose by 10% to £220, so the price before the rise was 90% of £220.
False.
The 10% was worked out from the before price, so 10% of that price is not the same amount of money as 10% of £220.
Taking 10% off £220 gives £198, whereas the correct answer is £200.
A salary is £33 170 this year, which is 7% more than it was last year. What was last year's salary?
The multiplier for a 7% increase is 1.07, so last year's salary multiplied by 1.07 gives £33 170.
Dividing instead, $33170 \div 1.07 = 31000$ , so last year's salary was £31 000.
Sale prices have been reduced by 10%, and a games console costs £441 in the sale. How can you find its original price by scaling from 1%?
The sale price is 90% of the original, so 90% is £441 and 1% is $441 \div 90 = 4.90$ pounds.
Multiplying that by 100 gives 100% of the original price, which is £490.
Define percentage multiplier.
A percentage multiplier is the decimal number you multiply by to carry out a percentage change in a single step.
An increase of 5% gives $100 % + 5 % = 105 %$ , so the multiplier is 1.05, while a decrease of 5% leaves 95% and a multiplier of 0.95.
How do you apply the same percentage change $n$ times in a row?
Raise the percentage multiplier to the power $n$ , then multiply the original quantity by it, so increasing 10 000 by 10% three times gives $10000 \times 1 . 1^{3} = 13310$ .
That is not the same as a single increase of 30%, which would give only 13 000.
True or False?
An increase of 10% followed by a decrease of 10% leaves an amount unchanged.
False.
The two multipliers give $1.1 \times 0.9 = 0.99$ , so the amount ends up 1% smaller than it started.
The decrease is taken off the larger, already increased amount, not off the original.
How do you work out a percentage change of one size followed by a percentage change of a different size?
Find the percentage multiplier for each change separately, then multiply the original quantity by them one after the other.
Decreasing 10 000 by 14% and then by 9% gives $10000 \times 0.86 \times 0.91 = 7826$ .
A collection of 3750 stamps grows by 7% in one year and then by 4% in the next. Complete the calculation of the new total.
$3750 \times______\times______= 4173$
The completed calculation is:
$3750 \times 1.07 \times 1.04 = 4173$
Each year needs its own multiplier, because the two percentages are different.
A population falls by 5% each year. If it is measured at the start of 2025 and again at the start of 2028, how many times has the change been applied?
Three times, once during each of the years 2025, 2026 and 2027.
Count the gaps between the two dates rather than the dates themselves, or the power will come out one too large.
Define appreciation.
Appreciation is the value of something increasing by a percentage over a period of time.
Paintings, collectible items and investment accounts are typical examples.
A painting bought for £425 000 rises in value by 6% each year. What is it worth four years later?
This is appreciation, so the value rises by 6% four times over.
Multiplying £425 000 by $1 . 06^{4}$ gives £536 552.708, which is about £537 000 to the nearest thousand pounds.
Define depreciation.
Depreciation is the value of something decreasing by a percentage over a period of time.
Cars, laptops and mobile phones are typical examples.
A car bought for £30 000 loses 12% of its value in the first year and then 8% in each of the next two years. What is it worth after three years?
This is depreciation, so the value falls three times, once by 12% and then twice by 8%.
Multiplying £30 000 by $0.88 \times 0 . 92^{2}$ gives £22 344.96.
True or False?
Appreciation and depreciation questions are worked out by the same method.
True.
Both are repeated percentage change applied to a value over time, and the only difference is whether that value is going up or down.
Define compound interest.
Compound interest is interest added to an amount of money at regular intervals, such as every year or every month.
It applies to debt as well as to savings, increasing the amount owed just as it increases the amount saved.
When money earns compound interest at 4% per year, what percentage change is applied each year?
An increase of 4%, applied to whatever the account is worth at the start of that year.
The interest rate is simply the percentage increase for one interest period.
Why does the amount of money added by compound interest grow every year, even though the interest rate stays the same?
The interest for each year is worked out on the whole balance, which by then includes the interest added in all the earlier years.
So the same percentage is being taken of a larger and larger amount each time.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:RoundingNext:Fractions

More Revision Notes you might like