Cover work · Fractions: Four Operations

Non-calculator

Work through each section on your own. There is a worked example to remind you of the method, then questions to answer. Show your working. If you finish, try the Challenge.

① Add & subtract

Reminder — worked example
Work out $\dfrac{5}{6} - \dfrac{2}{3}$.
Common denominator 6: $\dfrac{5}{6} = \dfrac{5}{6}$ and $\dfrac{2}{3} = \dfrac{4}{6}$.
$\dfrac{5}{6} - \dfrac{4}{6} = \dfrac{1}{6}$.
Now try these:
  1. 1Work out $\dfrac{7}{10} + \dfrac{1}{2}$.
  2. 2Work out $\dfrac{7}{12} - \dfrac{1}{4}$.
  3. 3Work out $\dfrac{3}{8} - \dfrac{1}{4}$.
  4. 4Work out $\dfrac{3}{8} + \dfrac{1}{2}$.
  5. 5Work out $\dfrac{1}{2} - \dfrac{1}{4}$.
  6. 6Work out $\dfrac{5}{6} - \dfrac{1}{8}$.
  7. 7Work out $\dfrac{1}{2} + \dfrac{9}{10}$.
  8. 8Work out $\dfrac{9}{10} + \dfrac{2}{5}$.
  9. 9Work out $\dfrac{2}{5} + \dfrac{7}{10}$.
  10. 10Work out $\dfrac{1}{4} + \dfrac{1}{10}$.
  11. 11Work out $\dfrac{1}{2} - \dfrac{3}{8}$.
  12. 12Work out $\dfrac{3}{4} - \dfrac{1}{2}$.

② Mixed numbers (add/subtract)

Reminder — worked example
Work out $2\tfrac{3}{5} + 4\tfrac{1}{3}$.
Write as improper fractions: $2\tfrac{3}{5} = \dfrac{13}{5}$, $4\tfrac{1}{3} = \dfrac{13}{3}$.
Common denominator 15: $\dfrac{39}{15} + \dfrac{65}{15} = \dfrac{104}{15}$.
So the answer is $\dfrac{104}{15} = 6\tfrac{14}{15}$.
Now try these:
  1. 1Work out $3\tfrac{1}{2} + 3\tfrac{1}{4}$.
  2. 2Work out $1\tfrac{1}{2} + 4\tfrac{2}{5}$.
  3. 3Work out $1\tfrac{3}{8} + 1\tfrac{1}{2}$.
  4. 4Work out $1\tfrac{4}{5} + 4\tfrac{1}{4}$.
  5. 5Work out $1\tfrac{1}{3} + 2\tfrac{4}{5}$.
  6. 6Work out $2\tfrac{1}{5} + 2\tfrac{2}{3}$.
  7. 7Work out $3\tfrac{1}{3} + 1\tfrac{3}{4}$.
  8. 8Work out $2\tfrac{1}{6} + 1\tfrac{1}{5}$.
  9. 9Work out $3\tfrac{1}{3} + 1\tfrac{7}{8}$.
  10. 10Work out $4\tfrac{1}{5} + 4\tfrac{1}{2}$.
  11. 11Work out $4\tfrac{1}{4} + 2\tfrac{1}{2}$.
  12. 12Work out $2\tfrac{3}{5} + 3\tfrac{1}{4}$.

③ Multiply

Reminder — worked example
Work out $3\tfrac{4}{5} \times \dfrac{5}{6}$.
Write the mixed number as an improper fraction: $3\tfrac{4}{5} = \dfrac{19}{5}$.
Multiply numerators and denominators: $3\tfrac{4}{5} \times \dfrac{5}{6} = \dfrac{19 \times 5}{5 \times 6} = \dfrac{95}{30} = \dfrac{19}{6}$.
Now try these:
  1. 1Work out $2\tfrac{1}{2} \times \dfrac{4}{3}$.
  2. 2Work out $2\tfrac{2}{3} \times \dfrac{5}{2}$.
  3. 3Work out $3\tfrac{4}{5} \times \dfrac{1}{6}$.
  4. 4Work out $\dfrac{2}{3} \times \dfrac{3}{5}$.
  5. 5Work out $3\tfrac{2}{3} \times \dfrac{3}{2}$.
  6. 6Work out $\dfrac{2}{3} \times \dfrac{1}{5}$.
  7. 7Work out $\dfrac{1}{5} \times \dfrac{3}{5}$.
  8. 8Work out $1\tfrac{2}{3} \times \dfrac{5}{3}$.
  9. 9Work out $\dfrac{2}{3} \times \dfrac{1}{4}$.
  10. 10Work out $\dfrac{2}{5} \times \dfrac{1}{5}$.
  11. 11Work out $3\tfrac{4}{5} \times \dfrac{5}{6}$.
  12. 12Work out $\dfrac{2}{5} \times \dfrac{3}{5}$.

★ Challenge — finished early?

Find three different fractions that add up to exactly 1. How many ways can you find?

Teacher solutions · Fractions: Four Operations

Full worked solutions

For the cover teacher: students work independently. Read out a section's worked example if they're stuck. Full solutions below; the Challenge is open-ended (no single answer).

① Add & subtract

1. Work out $\dfrac{7}{10} + \dfrac{1}{2}$. $\dfrac{7}{10} + \dfrac{5}{10} = \dfrac{12}{10} = \dfrac{6}{5}$. = $\dfrac{6}{5}$
2. Work out $\dfrac{7}{12} - \dfrac{1}{4}$. $\dfrac{7}{12} - \dfrac{3}{12} = \dfrac{4}{12} = \dfrac{1}{3}$. = $\dfrac{1}{3}$
3. Work out $\dfrac{3}{8} - \dfrac{1}{4}$. $\dfrac{3}{8} - \dfrac{2}{8} = \dfrac{1}{8}$. = $\dfrac{1}{8}$
4. Work out $\dfrac{3}{8} + \dfrac{1}{2}$. $\dfrac{3}{8} + \dfrac{4}{8} = \dfrac{7}{8}$. = $\dfrac{7}{8}$
5. Work out $\dfrac{1}{2} - \dfrac{1}{4}$. $\dfrac{2}{4} - \dfrac{1}{4} = \dfrac{1}{4}$. = $\dfrac{1}{4}$
6. Work out $\dfrac{5}{6} - \dfrac{1}{8}$. $\dfrac{20}{24} - \dfrac{3}{24} = \dfrac{17}{24}$. = $\dfrac{17}{24}$
7. Work out $\dfrac{1}{2} + \dfrac{9}{10}$. $\dfrac{5}{10} + \dfrac{9}{10} = \dfrac{14}{10} = \dfrac{7}{5}$. = $\dfrac{7}{5}$
8. Work out $\dfrac{9}{10} + \dfrac{2}{5}$. $\dfrac{9}{10} + \dfrac{4}{10} = \dfrac{13}{10}$. = $\dfrac{13}{10}$
9. Work out $\dfrac{2}{5} + \dfrac{7}{10}$. $\dfrac{4}{10} + \dfrac{7}{10} = \dfrac{11}{10}$. = $\dfrac{11}{10}$
10. Work out $\dfrac{1}{4} + \dfrac{1}{10}$. $\dfrac{5}{20} + \dfrac{2}{20} = \dfrac{7}{20}$. = $\dfrac{7}{20}$
11. Work out $\dfrac{1}{2} - \dfrac{3}{8}$. $\dfrac{4}{8} - \dfrac{3}{8} = \dfrac{1}{8}$. = $\dfrac{1}{8}$
12. Work out $\dfrac{3}{4} - \dfrac{1}{2}$. $\dfrac{3}{4} - \dfrac{2}{4} = \dfrac{1}{4}$. = $\dfrac{1}{4}$

② Mixed numbers (add/subtract)

1. Work out $3\tfrac{1}{2} + 3\tfrac{1}{4}$. So the answer is $\dfrac{27}{4} = 6\tfrac{3}{4}$. = $\dfrac{27}{4}$
2. Work out $1\tfrac{1}{2} + 4\tfrac{2}{5}$. So the answer is $\dfrac{59}{10} = 5\tfrac{9}{10}$. = $\dfrac{59}{10}$
3. Work out $1\tfrac{3}{8} + 1\tfrac{1}{2}$. So the answer is $\dfrac{23}{8} = 2\tfrac{7}{8}$. = $\dfrac{23}{8}$
4. Work out $1\tfrac{4}{5} + 4\tfrac{1}{4}$. So the answer is $\dfrac{121}{20} = 6\tfrac{1}{20}$. = $\dfrac{121}{20}$
5. Work out $1\tfrac{1}{3} + 2\tfrac{4}{5}$. So the answer is $\dfrac{62}{15} = 4\tfrac{2}{15}$. = $\dfrac{62}{15}$
6. Work out $2\tfrac{1}{5} + 2\tfrac{2}{3}$. So the answer is $\dfrac{73}{15} = 4\tfrac{13}{15}$. = $\dfrac{73}{15}$
7. Work out $3\tfrac{1}{3} + 1\tfrac{3}{4}$. So the answer is $\dfrac{61}{12} = 5\tfrac{1}{12}$. = $\dfrac{61}{12}$
8. Work out $2\tfrac{1}{6} + 1\tfrac{1}{5}$. So the answer is $\dfrac{101}{30} = 3\tfrac{11}{30}$. = $\dfrac{101}{30}$
9. Work out $3\tfrac{1}{3} + 1\tfrac{7}{8}$. So the answer is $\dfrac{125}{24} = 5\tfrac{5}{24}$. = $\dfrac{125}{24}$
10. Work out $4\tfrac{1}{5} + 4\tfrac{1}{2}$. So the answer is $\dfrac{87}{10} = 8\tfrac{7}{10}$. = $\dfrac{87}{10}$
11. Work out $4\tfrac{1}{4} + 2\tfrac{1}{2}$. So the answer is $\dfrac{27}{4} = 6\tfrac{3}{4}$. = $\dfrac{27}{4}$
12. Work out $2\tfrac{3}{5} + 3\tfrac{1}{4}$. So the answer is $\dfrac{117}{20} = 5\tfrac{17}{20}$. = $\dfrac{117}{20}$

③ Multiply

1. Work out $2\tfrac{1}{2} \times \dfrac{4}{3}$. Multiply numerators and denominators: $2\tfrac{1}{2} \times \dfrac{4}{3} = \dfrac{5 \times 4}{2 \times 3} = \dfrac{20}{6} = \dfrac{10}{3}$. = $\dfrac{10}{3}$
2. Work out $2\tfrac{2}{3} \times \dfrac{5}{2}$. Multiply numerators and denominators: $2\tfrac{2}{3} \times \dfrac{5}{2} = \dfrac{8 \times 5}{3 \times 2} = \dfrac{40}{6} = \dfrac{20}{3}$. = $\dfrac{20}{3}$
3. Work out $3\tfrac{4}{5} \times \dfrac{1}{6}$. Multiply numerators and denominators: $3\tfrac{4}{5} \times \dfrac{1}{6} = \dfrac{19 \times 1}{5 \times 6} = \dfrac{19}{30}$. = $\dfrac{19}{30}$
4. Work out $\dfrac{2}{3} \times \dfrac{3}{5}$. Multiply numerators and denominators: $\dfrac{2}{3} \times \dfrac{3}{5} = \dfrac{2 \times 3}{3 \times 5} = \dfrac{6}{15} = \dfrac{2}{5}$. = $\dfrac{2}{5}$
5. Work out $3\tfrac{2}{3} \times \dfrac{3}{2}$. Multiply numerators and denominators: $3\tfrac{2}{3} \times \dfrac{3}{2} = \dfrac{11 \times 3}{3 \times 2} = \dfrac{33}{6} = \dfrac{11}{2}$. = $\dfrac{11}{2}$
6. Work out $\dfrac{2}{3} \times \dfrac{1}{5}$. Multiply numerators and denominators: $\dfrac{2}{3} \times \dfrac{1}{5} = \dfrac{2 \times 1}{3 \times 5} = \dfrac{2}{15}$. = $\dfrac{2}{15}$
7. Work out $\dfrac{1}{5} \times \dfrac{3}{5}$. Multiply numerators and denominators: $\dfrac{1}{5} \times \dfrac{3}{5} = \dfrac{1 \times 3}{5 \times 5} = \dfrac{3}{25}$. = $\dfrac{3}{25}$
8. Work out $1\tfrac{2}{3} \times \dfrac{5}{3}$. Multiply numerators and denominators: $1\tfrac{2}{3} \times \dfrac{5}{3} = \dfrac{5 \times 5}{3 \times 3} = \dfrac{25}{9}$. = $\dfrac{25}{9}$
9. Work out $\dfrac{2}{3} \times \dfrac{1}{4}$. Multiply numerators and denominators: $\dfrac{2}{3} \times \dfrac{1}{4} = \dfrac{2 \times 1}{3 \times 4} = \dfrac{2}{12} = \dfrac{1}{6}$. = $\dfrac{1}{6}$
10. Work out $\dfrac{2}{5} \times \dfrac{1}{5}$. Multiply numerators and denominators: $\dfrac{2}{5} \times \dfrac{1}{5} = \dfrac{2 \times 1}{5 \times 5} = \dfrac{2}{25}$. = $\dfrac{2}{25}$
11. Work out $3\tfrac{4}{5} \times \dfrac{5}{6}$. Multiply numerators and denominators: $3\tfrac{4}{5} \times \dfrac{5}{6} = \dfrac{19 \times 5}{5 \times 6} = \dfrac{95}{30} = \dfrac{19}{6}$. = $\dfrac{19}{6}$
12. Work out $\dfrac{2}{5} \times \dfrac{3}{5}$. Multiply numerators and denominators: $\dfrac{2}{5} \times \dfrac{3}{5} = \dfrac{2 \times 3}{5 \times 5} = \dfrac{6}{25}$. = $\dfrac{6}{25}$

★ Challenge

Find three different fractions that add up to exactly 1. How many ways can you find? (open — accept any correct, well-explained answer)
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