Teach Me Maths

Adding and Subtracting Fractions

Question 11 mark

Work out \frac{3}{8}+\frac{1}{8}

Hint

The denominators are the same, so add the numerators only.

Worked solution

Work out \frac{3}{8}+\frac{1}{8}

  1. The denominators are both 8, so add the numerators: 3+1=4.
  2. \frac{4}{8}=\frac{1}{2}.
  3. Answer: \frac{1}{2}.

Question 22 marks

Work out \frac{1}{4}+\frac{3}{8}

Hint

Change the quarters into eighths first.

Worked solution

Work out \frac{1}{4}+\frac{3}{8}

  1. \frac{1}{4}=\frac{2}{8}.
  2. \frac{2}{8}+\frac{3}{8}=\frac{5}{8}.
  3. Answer: \frac{5}{8}.

Question 32 marks

Work out \frac{3}{5}-\frac{1}{4}

Hint

Write both fractions with a common denominator of 20.

Worked solution

Work out \frac{3}{5}-\frac{1}{4}

  1. \frac{3}{5}=\frac{12}{20} and \frac{1}{4}=\frac{5}{20}.
  2. \frac{12}{20}-\frac{5}{20}=\frac{7}{20}.
  3. Answer: \frac{7}{20}.

Question 42 marks

Ella eats \frac{1}{3} of a pizza.

Finn eats \frac{2}{5} of the same pizza.

What fraction of the pizza do they eat altogether?

Hint

Add the two fractions using a common denominator of 15.

Worked solution

Ella eats \frac{1}{3} of a pizza.

Finn eats \frac{2}{5} of the same pizza.

What fraction of the pizza do they eat altogether?

  1. Altogether they eat \frac{1}{3}+\frac{2}{5} of the pizza.
  2. \frac{1}{3}=\frac{5}{15} and \frac{2}{5}=\frac{6}{15}.
  3. \frac{5}{15}+\frac{6}{15}=\frac{11}{15}.
  4. Answer: \frac{11}{15}.

Question 52 marks

Work out 1\frac{1}{2}+2\frac{1}{3}

Hint

Add the whole numbers, then add the fractions using sixths.

Worked solution

Work out 1\frac{1}{2}+2\frac{1}{3}

  1. Add the whole numbers: 1+2=3.
  2. Add the fractions: \frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}.
  3. Answer: 3\frac{5}{6}.

Question 62 marks

Work out \frac{5}{6}+\frac{3}{4}

Hint

Write both fractions with a common denominator of 12.

Worked solution

Work out \frac{5}{6}+\frac{3}{4}

  1. \frac{5}{6}=\frac{10}{12} and \frac{3}{4}=\frac{9}{12}.
  2. \frac{10}{12}+\frac{9}{12}=\frac{19}{12}.
  3. \frac{19}{12}=1\frac{7}{12}.
  4. Answer: 1\frac{7}{12} (or \frac{19}{12}).

Question 72 marks

A piece of ribbon is 2 metres long.

Jess cuts off \frac{5}{8} of a metre.

How much ribbon is left? Give your answer in metres.

Hint

Write 2 metres as eighths of a metre.

Worked solution

A piece of ribbon is 2 metres long.

Jess cuts off \frac{5}{8} of a metre.

How much ribbon is left? Give your answer in metres.

  1. 2=\frac{16}{8}.
  2. \frac{16}{8}-\frac{5}{8}=\frac{11}{8}.
  3. \frac{11}{8}=1\frac{3}{8}.
  4. Answer: 1\frac{3}{8} metres.

Question 82 marks

Work out 5\frac{7}{9}-2\frac{1}{3}

Hint

Subtract the whole numbers, then subtract the fractions using ninths.

Worked solution

Work out 5\frac{7}{9}-2\frac{1}{3}

  1. Whole numbers: 5-2=3.
  2. Fractions: \frac{1}{3}=\frac{3}{9}, so \frac{7}{9}-\frac{3}{9}=\frac{4}{9}.
  3. Answer: 3\frac{4}{9}.

Question 92 marks

Work out 2\frac{3}{4}+1\frac{2}{3}

Give your answer as a mixed number.

Hint

Add the whole numbers, then add the fractions using twelfths.

Worked solution

Work out 2\frac{3}{4}+1\frac{2}{3}

Give your answer as a mixed number.

  1. Whole numbers: 2+1=3.
  2. Fractions: \frac{3}{4}+\frac{2}{3}=\frac{9}{12}+\frac{8}{12}=\frac{17}{12}.
  3. \frac{17}{12}=1\frac{5}{12}, so the total is 3+1\frac{5}{12}=4\frac{5}{12}.
  4. Answer: 4\frac{5}{12}.

Question 102 marks

Work out the missing fraction.

\frac{2}{5}+\square=\frac{13}{15}

Hint

The missing fraction is the difference between \frac{13}{15} and \frac{2}{5}.

Worked solution

Work out the missing fraction.

\frac{2}{5}+\square=\frac{13}{15}

  1. Missing fraction =\frac{13}{15}-\frac{2}{5}.
  2. \frac{2}{5}=\frac{6}{15}, so \frac{13}{15}-\frac{6}{15}=\frac{7}{15}.
  3. Check: \frac{6}{15}+\frac{7}{15}=\frac{13}{15}.
  4. Answer: \frac{7}{15}.

Question 113 marks

Work out 5\frac{1}{6}-2\frac{3}{4}

Give your answer as a mixed number.

(a)

Write down the whole number part of your answer.

1 mark

(b)

Write down the fraction part of your answer.

2 marks

Hint

\frac{1}{6} is smaller than \frac{3}{4}, so change both mixed numbers to improper fractions first.

Worked solution

Work out 5\frac{1}{6}-2\frac{3}{4}

Give your answer as a mixed number.

Part (a)

Write down the whole number part of your answer.

  1. 5\frac{1}{6}=\frac{31}{6}=\frac{62}{12} and 2\frac{3}{4}=\frac{11}{4}=\frac{33}{12}.
  2. \frac{62}{12}-\frac{33}{12}=\frac{29}{12}.
  3. \frac{29}{12}=2\frac{5}{12}, because 2\times12=24 and 29-24=5.
  4. The whole number part is 2.

Part (b)

Write down the fraction part of your answer.

  1. From part (a), the answer is 2\frac{5}{12}.
  2. The fraction part is \frac{5}{12}.

Question 123 marks

Amara's garden is split into three parts.

\frac{3}{8} of the garden is grass.

\frac{1}{3} of the garden is vegetables.

The rest of the garden is flowers.

What fraction of the garden is flowers?

Hint

Add the two fractions you know, then take the total away from 1 whole garden.

Worked solution

Amara's garden is split into three parts.

\frac{3}{8} of the garden is grass.

\frac{1}{3} of the garden is vegetables.

The rest of the garden is flowers.

What fraction of the garden is flowers?

  1. Grass and vegetables: \frac{3}{8}+\frac{1}{3}=\frac{9}{24}+\frac{8}{24}=\frac{17}{24}.
  2. The whole garden is \frac{24}{24}.
  3. Flowers: \frac{24}{24}-\frac{17}{24}=\frac{7}{24}.
  4. Answer: \frac{7}{24}.

Question 132 marks

Dev goes for a run in three parts.

The parts are \frac{3}{4} km, \frac{2}{3} km and \frac{1}{2} km.

Work out the total distance Dev runs.

Hint

Write all three fractions as twelfths.

Worked solution

Dev goes for a run in three parts.

The parts are \frac{3}{4} km, \frac{2}{3} km and \frac{1}{2} km.

Work out the total distance Dev runs.

  1. \frac{3}{4}=\frac{9}{12}, \frac{2}{3}=\frac{8}{12} and \frac{1}{2}=\frac{6}{12}.
  2. \frac{9}{12}+\frac{8}{12}+\frac{6}{12}=\frac{23}{12}.
  3. \frac{23}{12}=1\frac{11}{12}.
  4. Answer: 1\frac{11}{12} km.

Question 143 marks

The diagram shows a rectangle.

Work out the perimeter of the rectangle.

Hint

The perimeter is the total distance around all four sides.

Worked solution

The diagram shows a rectangle.

Work out the perimeter of the rectangle.

  1. Two sides are 2\frac{1}{2} cm and two sides are 1\frac{3}{4} cm.
  2. One long side and one short side: 2\frac{2}{4}+1\frac{3}{4}=3\frac{5}{4}=4\frac{1}{4} cm.
  3. Perimeter =2\times4\frac{1}{4}=8\frac{2}{4}=8\frac{1}{2} cm.
  4. Answer: 8\frac{1}{2} cm.

Question 153 marks

Leah works out 1\frac{3}{4}+2\frac{2}{5}

Here is her working.

1\frac{3}{4}+2\frac{2}{5}=3\frac{5}{9}

Her answer is wrong.

(a)

What mistake did Leah make?

1 mark

(b)

Work out the correct answer.

2 marks

Hint

Fractions can only be added once their denominators are the same.

Worked solution

Leah works out 1\frac{3}{4}+2\frac{2}{5}

Here is her working.

1\frac{3}{4}+2\frac{2}{5}=3\frac{5}{9}

Her answer is wrong.

Part (a)

What mistake did Leah make?

  1. She added the whole numbers wrongly.
  2. She should have multiplied the fractions.
  3. She added the numerators and added the denominators.
  4. She forgot to simplify her answer.
  1. Leah added the numerators, 3+2=5, and added the denominators, 4+5=9.
  2. Fractions need a common denominator before they can be added.

Part (b)

Work out the correct answer.

  1. Whole numbers: 1+2=3.
  2. Fractions: \frac{3}{4}+\frac{2}{5}=\frac{15}{20}+\frac{8}{20}=\frac{23}{20}=1\frac{3}{20}.
  3. 3+1\frac{3}{20}=4\frac{3}{20}.
  4. Answer: 4\frac{3}{20}.

Question 16Challenge3 marks

Work out the missing number.

\square+1\frac{5}{6}=3\frac{1}{4}

Give your answer as a mixed number.

Hint

The missing number is 3\frac{1}{4} take away 1\frac{5}{6}.

Worked solution

Work out the missing number.

\square+1\frac{5}{6}=3\frac{1}{4}

Give your answer as a mixed number.

  1. Missing number =3\frac{1}{4}-1\frac{5}{6}.
  2. 3\frac{1}{4}=\frac{13}{4}=\frac{39}{12} and 1\frac{5}{6}=\frac{11}{6}=\frac{22}{12}.
  3. \frac{39}{12}-\frac{22}{12}=\frac{17}{12}=1\frac{5}{12}.
  4. Check: 1\frac{5}{12}+1\frac{10}{12}=2\frac{15}{12}=3\frac{3}{12}=3\frac{1}{4}.
  5. Answer: 1\frac{5}{12}.

Question 17Challenge4 marks

A, B, C and D are four points on a straight cycle path, in that order.

The diagram shows some of the distances between them.

(a)

Work out the distance from C to D.

2 marks

(b)

Work out the distance from B to C.

2 marks

Hint

The distance from A to D is made up of the distance from A to C and the distance from C to D.

Worked solution

A, B, C and D are four points on a straight cycle path, in that order.

The diagram shows some of the distances between them.

Part (a)

Work out the distance from C to D.

  1. C to D = A to D - A to C =6\frac{1}{4}-4\frac{1}{2}.
  2. 4\frac{1}{2}=4\frac{2}{4}. Since \frac{1}{4} is less than \frac{2}{4}, write 6\frac{1}{4} as 5\frac{5}{4}.
  3. 5\frac{5}{4}-4\frac{2}{4}=1\frac{3}{4}.
  4. Answer: 1\frac{3}{4} km.

Part (b)

Work out the distance from B to C.

  1. B to C = B to D - C to D =3\frac{2}{3}-1\frac{3}{4}.
  2. 3\frac{2}{3}=\frac{11}{3}=\frac{44}{12} and 1\frac{3}{4}=\frac{7}{4}=\frac{21}{12}.
  3. \frac{44}{12}-\frac{21}{12}=\frac{23}{12}=1\frac{11}{12}.
  4. Answer: 1\frac{11}{12} km.

Question 18Challenge4 marks

Mo does his homework on three days.

Monday: \frac{5}{6} of an hour

Tuesday: \frac{1}{4} of an hour

Wednesday: 1\frac{1}{2} hours

(a)

Work out the total time Mo spends on his homework. Give your answer in hours.

2 marks

(b)

Mo planned to spend 3 hours on homework over the three days.

How many more minutes does he need to spend?

2 marks

Hint

Use twelfths of an hour. There are 60 minutes in an hour.

Worked solution

Mo does his homework on three days.

Monday: \frac{5}{6} of an hour

Tuesday: \frac{1}{4} of an hour

Wednesday: 1\frac{1}{2} hours

Part (a)

Work out the total time Mo spends on his homework. Give your answer in hours.

  1. \frac{5}{6}=\frac{10}{12}, \frac{1}{4}=\frac{3}{12} and 1\frac{1}{2}=1\frac{6}{12}.
  2. \frac{10}{12}+\frac{3}{12}+1\frac{6}{12}=1\frac{19}{12}=2\frac{7}{12}.
  3. Answer: 2\frac{7}{12} hours.

Part (b)

Mo planned to spend 3 hours on homework over the three days.

How many more minutes does he need to spend?

  1. 3-2\frac{7}{12}=\frac{5}{12} of an hour.
  2. \frac{1}{12} of an hour is 60\div12=5 minutes.
  3. So \frac{5}{12} of an hour is 5\times5=25 minutes.
  4. Answer: 25 minutes.

Question 19Challenge4 marks

Priya is painting a room.

She needs 1\frac{3}{4} litres of paint for the walls and \frac{7}{8} of a litre of paint for the ceiling.

She has one tin of paint. The tin holds 2\frac{1}{2} litres.

(a)

How much paint does Priya need altogether?

2 marks

(b)

Is one tin of paint enough?

2 marks

Hint

Write all the amounts in eighths of a litre.

Worked solution

Priya is painting a room.

She needs 1\frac{3}{4} litres of paint for the walls and \frac{7}{8} of a litre of paint for the ceiling.

She has one tin of paint. The tin holds 2\frac{1}{2} litres.

Part (a)

How much paint does Priya need altogether?

  1. 1\frac{3}{4}=1\frac{6}{8}.
  2. 1\frac{6}{8}+\frac{7}{8}=1\frac{13}{8}=2\frac{5}{8}.
  3. Answer: 2\frac{5}{8} litres.

Part (b)

Is one tin of paint enough?

  1. Yes. She will have \frac{1}{8} of a litre left over.
  2. Yes. She will have \frac{3}{8} of a litre left over.
  3. No. She needs \frac{1}{8} of a litre more.
  4. No. She needs \frac{3}{8} of a litre more.
  1. 2\frac{1}{2}=2\frac{4}{8}.
  2. She needs 2\frac{5}{8} litres, which is more than 2\frac{4}{8} litres, so one tin is not enough.
  3. 2\frac{5}{8}-2\frac{4}{8}=\frac{1}{8}, so she needs \frac{1}{8} of a litre more.

Question 20Challenge3 marks

Freya has a jug of water.

She pours \frac{2}{5} of a litre of water out of the jug.

She then adds \frac{3}{4} of a litre of water to the jug.

There are now 1\frac{1}{2} litres of water in the jug.

How much water was in the jug at the start?

Hint

Work backwards: undo the last thing Freya did first.

Worked solution

Freya has a jug of water.

She pours \frac{2}{5} of a litre of water out of the jug.

She then adds \frac{3}{4} of a litre of water to the jug.

There are now 1\frac{1}{2} litres of water in the jug.

How much water was in the jug at the start?

  1. Before she added \frac{3}{4} of a litre: 1\frac{1}{2}-\frac{3}{4}=\frac{6}{4}-\frac{3}{4}=\frac{3}{4} of a litre.
  2. Before she poured out \frac{2}{5} of a litre: \frac{3}{4}+\frac{2}{5}=\frac{15}{20}+\frac{8}{20}=\frac{23}{20} litres.
  3. \frac{23}{20}=1\frac{3}{20}.
  4. Answer: 1\frac{3}{20} litres.

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