Work out (1)/(5) + (2)/(5). Give your answer as a fraction.

Check the denominators: (1)/(5) + (2)/(5) Add the numerators: (1+2)/(5) = (3)/(5) State the exact answer: (3)/(5) Answer: (3)/(5)

Work out (3)/(4) - (1)/(4). Give your answer in its simplest form.

Check the denominators: (3)/(4) - (1)/(4) Subtract the numerators: (3-1)/(4) = (2)/(4) Simplify: (2)/(4) = (1)/(2) Answer: (1)/(2)

Work out (1)/(2) × (1)/(3).

Recall the multiplication rule: (a)/(b) × (c)/(d) = (ac)/(bd) Multiply tops and bottoms: (1 × 1)/(2 × 3) = (1)/(6) State the exact answer: (1)/(6) Answer: (1)/(6)

Treat pi like a unit: 2π + 5π Add the multipliers: 2 + 5 = 7 State the exact answer: 2π + 5π = 7π Answer: 7π

Treat pi like a unit: 10π - 4π Subtract the multipliers: 10 - 4 = 6 State the exact answer: 10π - 4π = 6π Answer: 6π

Exact calculation Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Exact calculation questions. See exactly how to solve problems on adding fractions, same denominator, subtracting fractions, simplifying.

adding fractionssame denominatorsubtracting fractionssimplifyingmultiplying fractionsmultiples of pi

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Work out

\frac{1}{5} + \frac{2}{5}

. Give your answer as a fraction.

Worked solution

Check the denominators
$\frac{1}{5} + \frac{2}{5}$
Both fractions are in fifths, so they can be added straight away.
Add the numerators
$\frac{1+2}{5} = \frac{3}{5}$
When the denominators match, add the tops and keep the bottom the same.
State the exact answer
$\frac{3}{5}$
Three fifths is already in its simplest form — an exact answer, not a rounded decimal.

Answer

\frac{3}{5}

Question 2

1 markeasy

Work out

\frac{3}{4} - \frac{1}{4}

. Give your answer in its simplest form.

Worked solution

Check the denominators
$\frac{3}{4} - \frac{1}{4}$
Both fractions are in quarters, so they can be subtracted straight away.
Subtract the numerators
$\frac{3-1}{4} = \frac{2}{4}$
Take the tops away and keep the bottom the same.
Simplify
$\frac{2}{4} = \frac{1}{2}$
Divide top and bottom by $2$ to give the simplest form, one half.

Answer

\frac{1}{2}

Question 3

1 markeasy

Work out

\frac{1}{2} \times \frac{1}{3}

Worked solution

Recall the multiplication rule
$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$
To multiply fractions, multiply the tops together and the bottoms together.
Multiply tops and bottoms
$\frac{1 \times 1}{2 \times 3} = \frac{1}{6}$
$1$ times $1$ is $1$ , and $2$ times $3$ is $6$ .
State the exact answer
$\frac{1}{6}$
A half of a third is one sixth — already in simplest form.

Answer

\frac{1}{6}

Question 4

1 markeasy

Simplify

2\pi + 5\pi

Worked solution

Treat pi like a unit
$2\pi + 5\pi$
Multiples of pi collect together just like terms in algebra: $2$ lots of pi plus $5$ lots of pi.
Add the multipliers
$2 + 5 = 7$
Add the numbers in front of pi.
State the exact answer
$2\pi + 5\pi = 7\pi$
Seven lots of pi, written $7\pi$ — an exact value, unlike any decimal for pi.

Answer

7\pi

Question 5

1 markeasy

Simplify

10\pi - 4\pi

Worked solution

Treat pi like a unit
$10\pi - 4\pi$
Ten lots of pi minus four lots of pi — collect the terms.
Subtract the multipliers
$10 - 4 = 6$
Subtract the numbers in front of pi.
State the exact answer
$10\pi - 4\pi = 6\pi$
Six lots of pi, written $6\pi$ .

Answer

6\pi

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