True or False? A percentage cannot be greater than 100.

False. A percentage above 100 simply means more than the whole, so 350% is perfectly ordinary and converts to 3.5 as a decimal. Percentages below 1 are equally fine: 0.2% converts to 0.002.

Write 0.004 as a percentage.

The answer is 0.4%. Multiplying 0.004 by 100 gives 0.4, and the percentage sign is then attached. The answer is smaller than 1%, which is correct: 0.004 is only four thousandths of the whole.

True or False? Writing 12 as a percentage of 30 gives the same answer as writing 30 as a percentage of 12.

False. 12 out of 30 is 40%, but 30 out of 12 is 250%, so the two are nothing like each other. The quantity you are comparing to always goes on the bottom of the fraction, and swapping them changes the question.

What is the decimal multiplier for increasing an amount by 12%?

The multiplier is 1.12. Add the percentage to 100% to get 112%, then divide by 100 to turn that into a decimal. Multiplying by 1.12 finds the original amount and the increase together, in one step.

Define compound percentage change .

Compound percentage change is when several percentage increases or decreases are applied to a quantity one after the other. Each change acts on the result of the one before it, not on the original amount.

True or False? An amount that increases by 5% each year goes up by the same number of pounds each year.

False. Each 5% is taken from a larger amount than the year before, so the actual increase grows every year. Starting from £4000 the increases are £200, then £210, then £220.50, which is why repeated percentage change is not the same as adding a fixed amount.

National 5MathsSQAApplications of MathematicsFlashcardsNumeracy SkillsFractions & Percentages

Fractions & Percentages (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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FrontConverting between Fractions, Decimals & Percentages
Complete the two conversions:
To change a percentage into a decimal you $______$ by 100, and to change a decimal into a percentage you $______$ by 100.

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Cards in this collection (47)

Complete the two conversions:
To change a percentage into a decimal you $______$ by 100, and to change a decimal into a percentage you $______$ by 100.
The completed sentence is:
To change a percentage into a decimal you divide by 100, and to change a decimal into a percentage you multiply by 100.
So 6% is 0.06, and 1.32 is 132%.
How do you write a decimal as a fraction?
Write the digits over a power of 10, using one zero for each decimal place.
So 0.07 has two decimal places and becomes $\frac{7}{100}$ , while 0.513 has three and becomes $\frac{513}{1000}$ .
True or False?
37% and $\frac{37}{100}$ are the same number.
True.
Percent means out of 100, so writing the percentage over 100 is the whole of the conversion, with nothing else to do.
That is why a fraction whose denominator is already 100 needs no work either.
What are the two ways of changing a fraction into a decimal?
Either rewrite it as an equivalent fraction over a power of 10, so that $\frac{7}{20} = \frac{35}{100} = 0.35$ .
Or divide the numerator by the denominator, adding zeros after the decimal point as you need them, which turns $\frac{5}{8}$ into 0.625.
How do you change a fraction into a percentage?
If the denominator is already 100, the numerator is the percentage, so $\frac{17}{100} = 17 %$ .
Otherwise change the fraction into a decimal first, then multiply by 100: $\frac{4}{5} = 0.8$ , which gives 80%.
Complete these four familiar fractions as decimals:
$\frac{1}{2} =______, \frac{1}{4} =______, \frac{3}{4} =______and \frac{1}{5} =______$
The completed line is:
$\frac{1}{2} = 0.5, \frac{1}{4} = 0.25, \frac{3}{4} = 0.75 and \frac{1}{5} = 0.2$
Knowing this handful by heart saves time, and the same set gives 50%, 25%, 75% and 20% as percentages.
True or False?
A percentage cannot be greater than 100.
False.
A percentage above 100 simply means more than the whole, so 350% is perfectly ordinary and converts to 3.5 as a decimal.
Percentages below 1 are equally fine: 0.2% converts to 0.002.
Write 0.004 as a percentage.
The answer is 0.4%.
Multiplying 0.004 by 100 gives 0.4, and the percentage sign is then attached.
The answer is smaller than 1%, which is correct: 0.004 is only four thousandths of the whole.
On a calculator, what is the quickest way to find $\frac{11}{20}$ of 2000?
Multiply the fraction by the quantity in one step:
$\frac{11}{20} \times 2000 = 1100$
The word of is an instruction to multiply, which is what makes the single step valid.
True or False?
To find $\frac{3}{4}$ of an amount you divide by 3 and then multiply by 4.
False.
You divide by the denominator and multiply by the numerator, so it is divide by 4 and then multiply by 3.
Dividing by 3 first would give four thirds of the amount, which is more than you started with rather than less.
Complete the two shortcuts:
50% of an amount is found by dividing it by $______$ , and 20% by dividing it by $______$ instead.
The completed sentence is:
50% of an amount is found by dividing it by 2, and 20% by dividing it by 5 instead.
Each shortcut is just the equivalent fraction, since 50% is one half and 20% is one fifth.
How can you find 45% of 340 without a calculator?
Build it out of easier percentages: 10% of 340 is 34, so 40% is $4 \times 34 = 136$ , and 5% is half of 10%, which is 17.
Adding the two parts gives $136 + 17 = 153$ .
What is the decimal multiplier for finding 12% of an amount?
The multiplier is 0.12, found by dividing the percentage by 100.
You then multiply the quantity by it, so 12% of 650 is $0.12 \times 650 = 78$ .
How do you write 17 out of 25 as a percentage?
Write the first quantity as a fraction of the second, then multiply by 100:
$\frac{17}{25} \times 100 = 68$
So 17 is 68% of 25.
Without a calculator, why is it worth simplifying a fraction before turning it into a percentage?
Because the method divides 100% by the denominator, and an awkward denominator makes that division hard.
Writing 12 out of 30 as $\frac{12}{30}$ leaves you with $100 \div 30$ , but simplifying to $\frac{2}{5}$ gives $100 % \div 5 = 20 %$ , and $2 \times 20 % = 40 %$ .
True or False?
Writing 12 as a percentage of 30 gives the same answer as writing 30 as a percentage of 12.
False.
12 out of 30 is 40%, but 30 out of 12 is 250%, so the two are nothing like each other.
The quantity you are comparing to always goes on the bottom of the fraction, and swapping them changes the question.
True or False?
$\frac{3}{5}$ and 55% cannot be compared, because one is a fraction and the other is a percentage.
False.
They compare perfectly well once both are written in the same form, either both as percentages or both as fractions over the same denominator.
Here $\frac{3}{5}$ is 60%, which is larger than 55%.
How do you write 14% as a fraction with denominator 90, so it can be set beside $\frac{13}{90}$ ?
Find 14% of the denominator, and use the result as the numerator.
$0.14 \times 90 = 12.6, so 14 % = \frac{12.6}{90}$
A numerator does not have to be a whole number for this to work.
Without a calculator, when is it easier to convert the percentage rather than the fraction?
When 100 does not divide neatly by the denominator of the fraction.
Turning $\frac{13}{90}$ into a percentage means working out $100 \div 90$ , which is unpleasant, whereas rewriting the percentage over 90 leaves two numerators that can be read off against each other.
Greg scored 28 out of 40 in Physics and 72% in Chemistry. In which subject did he do better?
Chemistry, by two percentage points.
$\frac{28}{40}$ simplifies to $\frac{7}{10}$ , which is 70%, and 72% is larger than 70%.
Simplifying first is what makes this one easy: tenths convert to percentages at a glance.
A calculator is allowed. Complete the comparison of $\frac{3}{8}$ with 40%:
$\frac{3}{8} \times 100 =______%, which is______than 40 %$
The completed comparison is:
$\frac{3}{8} \times 100 = 37.5 %, which is less than 40 %$
With a calculator this route is almost always the quicker of the two.
Define mixed number.
A mixed number is a number written with a whole number part and a fraction part side by side.
For example $3 \frac{3}{4}$ means three whole ones and three quarters, and it is another way of writing 3.75.
How do you change $5 \frac{2}{7}$ into an improper fraction?
Work out how many sevenths the whole number is worth, then add the sevenths you already have.
One whole is 7 sevenths, so 5 wholes are $5 \times 7 = 35$ sevenths, and 35 sevenths plus 2 sevenths gives $\frac{37}{7}$ .
Define improper fraction.
An improper fraction is a fraction whose numerator is bigger than its denominator, also called a top-heavy fraction.
For example $\frac{15}{4}$ means fifteen quarters, which is more than one whole.
How do you change $\frac{22}{3}$ into a mixed number?
Divide the numerator by the denominator and keep the remainder, since $22 \div 3 = 7$ remainder 1.
The whole number part is the 7, and the remainder goes back over the original denominator, giving $7 \frac{1}{3}$ .
True or False?
$\frac{15}{4}$ and $3 \frac{3}{4}$ are the same number.
True.
Any number greater than 1 can be written either as an improper fraction or as a mixed number, and the two forms are worth exactly the same.
Three wholes are 12 quarters, and 12 quarters plus 3 quarters is 15 quarters.
Complete the conversion into a mixed number:
$\frac{17}{5} =______\frac{______}{5}$
The completed conversion is:
$\frac{17}{5} = 3 \frac{2}{5}$
The denominator never changes: only the numerator is split into whole fifths and a remainder.
John has $5 \frac{3}{4}$ litres of water and each cup holds $\frac{1}{4}$ of a litre. How many cups can he fill?
He can fill 23 cups.
The question is really asking how many quarters there are in $5 \frac{3}{4}$ , so rewrite it as the improper fraction $\frac{23}{4}$ .
This is what improper fractions are for: they count the parts directly, where a mixed number hides them inside the whole numbers.
How do you add two fractions that already have the same denominator?
Add the numerators and leave the denominator alone, so that $\frac{3}{7} + \frac{2}{7} = \frac{5}{7}$ .
Subtraction works in exactly the same way, and the denominator is what tells you what size of piece you are counting.
True or False?
$\frac{3}{5} + \frac{1}{4} = \frac{4}{9}$
False.
Denominators are never added, because fifths and quarters are different sizes of piece and cannot simply be counted together.
Rewrite both over a common denominator first: $\frac{12}{20} + \frac{5}{20} = \frac{17}{20}$ .
What is the quickest reliable common denominator for $\frac{2}{7}$ and $\frac{1}{6}$ ?
Multiply the two denominators together to get 42, which is always a common multiple of both.
Any common multiple will do, so a smaller one is fine when you can spot it, but the product never fails.
True or False?
To work out $\frac{1}{6} + \frac{5}{12}$ , only one of the two fractions has to be rewritten.
True.
12 is already a multiple of 6, so 12 can be the common denominator and the second fraction is left exactly as it is.
Only $\frac{1}{6}$ changes, becoming $\frac{2}{12}$ , and the sum is $\frac{7}{12}$ .
How do you subtract a fraction from a whole number, such as $2 - \frac{1}{2}$ ?
Rewrite the whole number as a fraction using the same denominator as the fraction you are subtracting.
Here 2 becomes $\frac{4}{2}$ , and the subtraction is then the ordinary same-denominator case: $\frac{4}{2} - \frac{1}{2} = \frac{3}{2}$ .
Complete the addition:
$\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{______}{15} = \frac{______}{15}$
The completed addition is:
$\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}$
Each fraction was multiplied top and bottom by the other denominator, which is why $\frac{1}{3}$ became $\frac{5}{15}$ .
There are two cakes. George eats $\frac{3}{4}$ of a cake and Sophie eats $\frac{2}{3}$ of a cake. How much cake is left?
There is $\frac{7}{12}$ of a cake left.
Together they eat $\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$ of a cake.
Writing the 2 cakes as $\frac{24}{12}$ then gives $\frac{24}{12} - \frac{17}{12} = \frac{7}{12}$ .
What is the decimal multiplier for increasing an amount by 12%?
The multiplier is 1.12.
Add the percentage to 100% to get 112%, then divide by 100 to turn that into a decimal.
Multiplying by 1.12 finds the original amount and the increase together, in one step.
True or False?
A decimal multiplier of 0.94 decreases an amount.
True.
Any multiplier below 1 makes an amount smaller, and 0.94 comes from $100 % - 6 % = 94 %$ .
This is the quickest check on your own working: a multiplier above 1 must be an increase, and one below 1 must be a decrease.
Complete the working to increase £250 by 20%:
$\pounds 250 \times______= \pounds______$
The completed working is:
$\pounds 250 \times 1.2 = \pounds 300$
Note that 120% written as a decimal is 1.2, not 1.20 or 12, which is where this most often goes wrong.
A sunflower grew from 8.40 cm to 11.34 cm. What was the percentage increase?
The increase was 35%.
The sunflower grew by $11.34 - 8.40 = 2.94$ cm.
Putting that over the starting height gives $\frac{2.94}{8.40} \times 100 = 35$ .
True or False?
To find a percentage change you divide the difference by the new amount.
False.
The difference is always divided by the original amount, because a percentage change measures the change against where it started.
A fall from £400 to £340 is a £60 drop, and $\frac{60}{400} \times 100 = 15$ , so it is a 15% decrease and not $60 \div 340$ .
A race took Maisie 350 minutes last year, and this year she took 8% less time. How long did she take?
She took 322 minutes.
An 8% decrease has multiplier 0.92, so $350 \times 0.92 = 322$ .
The answer is sensibly a little under 350, which is the check worth making before writing it down.
Define compound percentage change.
Compound percentage change is when several percentage increases or decreases are applied to a quantity one after the other.
Each change acts on the result of the one before it, not on the original amount.
£4000 increases by 5% each year for 3 years. How do you find the final amount in one calculation?
Raise the multiplier to the power of the number of changes, then multiply by the original amount:
$\pounds 4000 \times 1 . 05^{3} = \pounds 4630.50$
The power counts the changes, so three years of growth means an index of 3.
True or False?
An amount that increases by 5% each year goes up by the same number of pounds each year.
False.
Each 5% is taken from a larger amount than the year before, so the actual increase grows every year.
Starting from £4000 the increases are £200, then £210, then £220.50, which is why repeated percentage change is not the same as adding a fixed amount.
A vole population is 8000 at the start of 2025 and falls by 5% each year. What is it at the start of 2028?
The population is 6859 voles.
From the start of 2025 to the start of 2028 is three years, so the multiplier 0.95 is raised to the power 3.
$8000 \times 0 . 95^{3} = 6859$
How do you handle a compound change when the percentage is different each time?
Work out each multiplier separately, then multiply the original amount by all of them in turn.
To decrease 10000 by 14% and then by a further 9%, the multipliers are 0.86 and 0.91, giving $10000 \times 0.86 \times 0.91 = 7826$ .
A collection of 3750 stamps grows by 7% and then by a further 4%. Complete the working:
$3750 \times 1.07 \times______=______$
The completed working is:
$3750 \times 1.07 \times 1.04 = 4173$
The order of the two multipliers makes no difference to the final answer, since multiplication can be done in any order.

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