GCSE FDP equivalence Practice Questions

Turn the fraction into a division

A fraction bar just means 'divide the top number by the bottom number'.

Work out the division

Dividing gives $0.5$. This is one of the conversions worth learning by heart.

State the answer

So $\frac{1}{2} = 0.5$ exactly.

Turn the fraction into a division

A fraction bar just means 'divide the top number by the bottom number'.

Work out the division

Dividing gives $0.3$. This is one of the conversions worth learning by heart.

State the answer

So $\frac{3}{10} = 0.3$ exactly.

Percent means 'out of $100$'

To change a fraction into a percentage, multiply it by $100$.

Multiply the fraction by $100$

Working out the multiplication gives $75$.

Attach the percent sign

Writing the percent sign shows this is a number out of $100$.

Check with a benchmark

The fraction is bigger than a half ($0.5$), and the percentage is on the matching side of $50\%$.

Why multiplying by $100$ works

One whole is $100\%$, so a fraction of a whole is that same fraction of $100\%$.

State the percentage

So $\frac{3}{4} = 75\%$.

State what must be shown

We must prove the fraction equals the percentage exactly.

Change the fraction to a decimal

Scaling $5/8$ to $625/1000$ shows the decimal is $0.625$.

Multiply the decimal by $100$

Multiplying by $100$ turns the decimal into a percentage.

Attach the percent sign

So the percentage is $62.5\%$.

Conclude

The fraction and the percentage are exactly equal, as required.

Check the two forms match

Both sides describe exactly the same amount, just written differently.

Sense check

Equal values sit at the same point on a number line, which these do.

Reflect on the method

Turning both sides into one common form is the reliable way to prove an equivalence.

Restate the conclusion

The statement is shown to be true.

Check the two forms match

Both sides describe exactly the same amount, just written differently.

Percent means 'out of $100$'

A percentage is a number out of $100$, so write it as a fraction over $100$.

Clear the decimal from the fraction

Multiply top and bottom by $10$ so there is no decimal left in the fraction.

Find the highest common factor

The biggest number dividing both $875$ and $1000$ is $125$.

Divide top and bottom by the HCF

Dividing top and bottom by the same number simplifies without changing the value.

Check by converting back

Turning the fraction back into a percentage returns the value we started with.

Check the size makes sense

The percentage is bigger than a half ($0.5$) of the whole, which the fraction agrees with.

Write it as a decimal too

The same amount as a decimal is the percentage divided by $100$.

Why over $100$

Because 'per cent' literally means 'per hundred', every percentage starts life over $100$.

Watch a common slip

The denominator is $100$, not $10$; per cent means per hundred.

Cancel in stages if it helps

You can cancel with smaller factors step by step instead of finding the HCF at once.

Say it in words

Reading the fraction aloud keeps its meaning clear.

Real-world use

Sale signs and statistics often need turning from a percentage into a fraction.

Exam tip: simplest form

Always cancel fully; the simplest form is usually where the mark sits.

Double-check the cancelling

Confirm the top and bottom share no further common factor.

State the simplest form

So $87.5\% = \frac{7}{8}$ in its simplest form.