KS2 Summer Fractions Addition and Subtraction Board Game - Free Printable
Educational worksheet: KS2 Summer Fractions Addition and Subtraction Board Game. Download and print for classroom or home learning activities.
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Step-by-step solution for: KS2 Summer Fractions Addition and Subtraction Board Game
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Show Answer Key & Explanations
Step-by-step solution for: KS2 Summer Fractions Addition and Subtraction Board Game
To solve the problems on the board game, we need to add or subtract the fractions in each square. Here is the step-by-step solution for every problem shown on the board.
1. $\frac{2}{8} + \frac{1}{3}$
* First, simplify $\frac{2}{8}$ to $\frac{1}{4}$.
* Find a common denominator for 4 and 3, which is 12.
* Convert fractions: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add them: $\frac{3}{12} + \frac{4}{12} = \mathbf{\frac{7}{12}}$
2. $1\frac{3}{9} - \frac{2}{5}$
* Simplify the mixed number fraction: $\frac{3}{9} = \frac{1}{3}$, so it becomes $1\frac{1}{3}$.
* Convert to improper fractions: $1\frac{1}{3} = \frac{4}{3}$.
* Find a common denominator for 3 and 5, which is 15.
* Convert fractions: $\frac{4}{3} = \frac{20}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
* Subtract: $\frac{20}{15} - \frac{6}{15} = \frac{14}{15}$.
* Answer: $\mathbf{\frac{14}{15}}$
3. $\frac{2}{3} + \frac{6}{9}$
* Simplify $\frac{6}{9}$ by dividing top and bottom by 3: $\frac{6}{9} = \frac{2}{3}$.
* Add the fractions: $\frac{2}{3} + \frac{2}{3} = \frac{4}{3}$.
* Convert to a mixed number: $\mathbf{1\frac{1}{3}}$
4. $1\frac{9}{10} - \frac{2}{3}$
* Convert mixed number to improper fraction: $1\frac{9}{10} = \frac{19}{10}$.
* Common denominator for 10 and 3 is 30.
* Convert fractions: $\frac{19}{10} = \frac{57}{30}$ and $\frac{2}{3} = \frac{20}{30}$.
* Subtract: $\frac{57}{30} - \frac{20}{30} = \frac{37}{30}$.
* Convert to mixed number: $\mathbf{1\frac{7}{30}}$
5. $\frac{1}{2} + \frac{2}{3}$
* Common denominator for 2 and 3 is 6.
* Convert fractions: $\frac{1}{2} = \frac{3}{6}$ and $\frac{2}{3} = \frac{4}{6}$.
* Add them: $\frac{3}{6} + \frac{4}{6} = \mathbf{\frac{7}{6}}$ (or $1\frac{1}{6}$)
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6. $\frac{2}{10} + \frac{3}{5}$
* Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
* Add: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$.
* Answer: $\mathbf{\frac{4}{5}}$
7. $\frac{7}{12}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{\frac{7}{12}}$
8. $1\frac{3}{8}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{1\frac{3}{8}}$
9. $\frac{7}{24}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{\frac{7}{24}}$
10. $1\frac{1}{12}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{1\frac{1}{12}}$
11. $1\frac{1}{8} - \frac{5}{6}$
* Convert mixed number to improper fraction: $1\frac{1}{8} = \frac{9}{8}$.
* Common denominator for 8 and 6 is 24.
* Convert fractions: $\frac{9}{8} = \frac{27}{24}$ and $\frac{5}{6} = \frac{20}{24}$.
* Subtract: $\frac{27}{24} - \frac{20}{24} = \mathbf{\frac{7}{24}}$
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12. $\frac{8}{9} - \frac{1}{3}$
* Convert $\frac{1}{3}$ to ninths: $\frac{1}{3} = \frac{3}{9}$.
* Subtract: $\frac{8}{9} - \frac{3}{9} = \mathbf{\frac{5}{9}}$
13. $1\frac{2}{9} - \frac{3}{5}$
* Improper fraction: $1\frac{2}{9} = \frac{11}{9}$.
* Common denominator (45): $\frac{11}{9} = \frac{55}{45}$ and $\frac{3}{5} = \frac{27}{45}$.
* Subtract: $\frac{55}{45} - \frac{27}{45} = \frac{28}{45}$.
* Answer: $\mathbf{\frac{28}{45}}$
14. $\frac{3}{4} - \frac{1}{9}$
* Common denominator (36): $\frac{3}{4} = \frac{27}{36}$ and $\frac{1}{9} = \frac{4}{36}$.
* Subtract: $\frac{27}{36} - \frac{4}{36} = \mathbf{\frac{23}{36}}$
15. $1\frac{9}{10} - \frac{3}{5}$
* Note that $\frac{3}{5} = \frac{6}{10}$.
* Subtract: $1\frac{9}{10} - \frac{6}{10} = 1\frac{3}{10}$.
* Answer: $\mathbf{1\frac{3}{10}}$
16. $\frac{1}{2} - \frac{1}{3}$
* Common denominator (6): $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$.
* Subtract: $\frac{3}{6} - \frac{2}{6} = \mathbf{\frac{1}{6}}$
17. $\frac{7}{10} - \frac{1}{5}$
* Note that $\frac{1}{5} = \frac{2}{10}$.
* Subtract: $\frac{7}{10} - \frac{2}{10} = \mathbf{\frac{5}{10}}$ which simplifies to $\mathbf{\frac{1}{2}}$
18. $1\frac{5}{8} - \frac{2}{5}$
* Improper fraction: $1\frac{5}{8} = \frac{13}{8}$.
* Common denominator (40): $\frac{13}{8} = \frac{65}{40}$ and $\frac{2}{5} = \frac{16}{40}$.
* Subtract: $\frac{65}{40} - \frac{16}{40} = \frac{49}{40}$.
* Mixed number: $\mathbf{1\frac{9}{40}}$
19. $1\frac{1}{10} - \frac{1}{5}$
* Note that $\frac{1}{5} = \frac{2}{10}$.
* Improper fraction: $1\frac{1}{10} = \frac{11}{10}$.
* Subtract: $\frac{11}{10} - \frac{2}{10} = \frac{9}{10}$.
* Answer: $\mathbf{\frac{9}{10}}$
20. $\frac{1}{2} - \frac{2}{9}$
* Common denominator (18): $\frac{1}{2} = \frac{9}{18}$ and $\frac{2}{9} = \frac{4}{18}$.
* Subtract: $\frac{9}{18} - \frac{4}{18} = \mathbf{\frac{5}{18}}$
21. $1\frac{1}{10} - \frac{1}{3}$
* Improper fraction: $1\frac{1}{10} = \frac{11}{10}$.
* Common denominator (30): $\frac{11}{10} = \frac{33}{30}$ and $\frac{1}{3} = \frac{10}{30}$.
* Subtract: $\frac{33}{30} - \frac{10}{30} = \frac{23}{30}$.
* Answer: $\mathbf{\frac{23}{30}}$
22. $\frac{2}{5} - \frac{1}{2}$
* Common denominator (10): $\frac{2}{5} = \frac{4}{10}$ and $\frac{1}{2} = \frac{5}{10}$.
* Subtract: $\frac{4}{10} - \frac{5}{10} = -\frac{1}{10}$.
* *Note: In elementary games, this might be an error in the problem design, or the answer is simply negative.*
* Answer: $\mathbf{-\frac{1}{10}}$
23. $1\frac{2}{5} - \frac{3}{4}$
* Improper fraction: $1\frac{2}{5} = \frac{7}{5}$.
* Common denominator (20): $\frac{7}{5} = \frac{28}{20}$ and $\frac{3}{4} = \frac{15}{20}$.
* Subtract: $\frac{28}{20} - \frac{15}{20} = \frac{13}{20}$.
* Answer: $\mathbf{\frac{13}{20}}$
24. $1\frac{2}{3} - \frac{3}{5}$
* Improper fraction: $1\frac{2}{3} = \frac{5}{3}$.
* Common denominator (15): $\frac{5}{3} = \frac{25}{15}$ and $\frac{3}{5} = \frac{9}{15}$.
* Subtract: $\frac{25}{15} - \frac{9}{15} = \frac{16}{15}$.
* Mixed number: $\mathbf{1\frac{1}{15}}$
25. $1\frac{1}{2} - \frac{2}{9}$
* Improper fraction: $1\frac{1}{2} = \frac{3}{2}$.
* Common denominator (18): $\frac{3}{2} = \frac{27}{18}$ and $\frac{2}{9} = \frac{4}{18}$.
* Subtract: $\frac{27}{18} - \frac{4}{18} = \frac{23}{18}$.
* Mixed number: $\mathbf{1\frac{5}{18}}$
Final Answer:
Here are the solutions for the visible squares:
Main Board:
1. $\frac{7}{12}$
2. $\frac{14}{15}$
3. $1\frac{1}{3}$
4. $1\frac{7}{30}$
5. $\frac{7}{6}$ (or $1\frac{1}{6}$)
6. $\frac{4}{5}$
7. $\frac{7}{12}$
8. $1\frac{3}{8}$
9. $\frac{7}{24}$
10. $1\frac{1}{12}$
11. $\frac{7}{24}$
Side Board:
12. $\frac{5}{9}$
13. $\frac{28}{45}$
14. $\frac{23}{36}$
15. $1\frac{3}{10}$
16. $\frac{1}{6}$
17. $\frac{1}{2}$
18. $1\frac{9}{40}$
19. $\frac{9}{10}$
20. $\frac{5}{18}$
21. $\frac{23}{30}$
22. $-\frac{1}{10}$
23. $\frac{13}{20}$
24. $1\frac{1}{15}$
25. $1\frac{5}{18}$
Row 1
1. $\frac{2}{8} + \frac{1}{3}$
* First, simplify $\frac{2}{8}$ to $\frac{1}{4}$.
* Find a common denominator for 4 and 3, which is 12.
* Convert fractions: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
* Add them: $\frac{3}{12} + \frac{4}{12} = \mathbf{\frac{7}{12}}$
2. $1\frac{3}{9} - \frac{2}{5}$
* Simplify the mixed number fraction: $\frac{3}{9} = \frac{1}{3}$, so it becomes $1\frac{1}{3}$.
* Convert to improper fractions: $1\frac{1}{3} = \frac{4}{3}$.
* Find a common denominator for 3 and 5, which is 15.
* Convert fractions: $\frac{4}{3} = \frac{20}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
* Subtract: $\frac{20}{15} - \frac{6}{15} = \frac{14}{15}$.
* Answer: $\mathbf{\frac{14}{15}}$
3. $\frac{2}{3} + \frac{6}{9}$
* Simplify $\frac{6}{9}$ by dividing top and bottom by 3: $\frac{6}{9} = \frac{2}{3}$.
* Add the fractions: $\frac{2}{3} + \frac{2}{3} = \frac{4}{3}$.
* Convert to a mixed number: $\mathbf{1\frac{1}{3}}$
4. $1\frac{9}{10} - \frac{2}{3}$
* Convert mixed number to improper fraction: $1\frac{9}{10} = \frac{19}{10}$.
* Common denominator for 10 and 3 is 30.
* Convert fractions: $\frac{19}{10} = \frac{57}{30}$ and $\frac{2}{3} = \frac{20}{30}$.
* Subtract: $\frac{57}{30} - \frac{20}{30} = \frac{37}{30}$.
* Convert to mixed number: $\mathbf{1\frac{7}{30}}$
5. $\frac{1}{2} + \frac{2}{3}$
* Common denominator for 2 and 3 is 6.
* Convert fractions: $\frac{1}{2} = \frac{3}{6}$ and $\frac{2}{3} = \frac{4}{6}$.
* Add them: $\frac{3}{6} + \frac{4}{6} = \mathbf{\frac{7}{6}}$ (or $1\frac{1}{6}$)
---
Row 2
6. $\frac{2}{10} + \frac{3}{5}$
* Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
* Add: $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$.
* Answer: $\mathbf{\frac{4}{5}}$
7. $\frac{7}{12}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{\frac{7}{12}}$
8. $1\frac{3}{8}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{1\frac{3}{8}}$
9. $\frac{7}{24}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{\frac{7}{24}}$
10. $1\frac{1}{12}$
* This square already has the answer written on the shell.
* Answer: $\mathbf{1\frac{1}{12}}$
11. $1\frac{1}{8} - \frac{5}{6}$
* Convert mixed number to improper fraction: $1\frac{1}{8} = \frac{9}{8}$.
* Common denominator for 8 and 6 is 24.
* Convert fractions: $\frac{9}{8} = \frac{27}{24}$ and $\frac{5}{6} = \frac{20}{24}$.
* Subtract: $\frac{27}{24} - \frac{20}{24} = \mathbf{\frac{7}{24}}$
---
Right Side Board Problems
12. $\frac{8}{9} - \frac{1}{3}$
* Convert $\frac{1}{3}$ to ninths: $\frac{1}{3} = \frac{3}{9}$.
* Subtract: $\frac{8}{9} - \frac{3}{9} = \mathbf{\frac{5}{9}}$
13. $1\frac{2}{9} - \frac{3}{5}$
* Improper fraction: $1\frac{2}{9} = \frac{11}{9}$.
* Common denominator (45): $\frac{11}{9} = \frac{55}{45}$ and $\frac{3}{5} = \frac{27}{45}$.
* Subtract: $\frac{55}{45} - \frac{27}{45} = \frac{28}{45}$.
* Answer: $\mathbf{\frac{28}{45}}$
14. $\frac{3}{4} - \frac{1}{9}$
* Common denominator (36): $\frac{3}{4} = \frac{27}{36}$ and $\frac{1}{9} = \frac{4}{36}$.
* Subtract: $\frac{27}{36} - \frac{4}{36} = \mathbf{\frac{23}{36}}$
15. $1\frac{9}{10} - \frac{3}{5}$
* Note that $\frac{3}{5} = \frac{6}{10}$.
* Subtract: $1\frac{9}{10} - \frac{6}{10} = 1\frac{3}{10}$.
* Answer: $\mathbf{1\frac{3}{10}}$
16. $\frac{1}{2} - \frac{1}{3}$
* Common denominator (6): $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$.
* Subtract: $\frac{3}{6} - \frac{2}{6} = \mathbf{\frac{1}{6}}$
17. $\frac{7}{10} - \frac{1}{5}$
* Note that $\frac{1}{5} = \frac{2}{10}$.
* Subtract: $\frac{7}{10} - \frac{2}{10} = \mathbf{\frac{5}{10}}$ which simplifies to $\mathbf{\frac{1}{2}}$
18. $1\frac{5}{8} - \frac{2}{5}$
* Improper fraction: $1\frac{5}{8} = \frac{13}{8}$.
* Common denominator (40): $\frac{13}{8} = \frac{65}{40}$ and $\frac{2}{5} = \frac{16}{40}$.
* Subtract: $\frac{65}{40} - \frac{16}{40} = \frac{49}{40}$.
* Mixed number: $\mathbf{1\frac{9}{40}}$
19. $1\frac{1}{10} - \frac{1}{5}$
* Note that $\frac{1}{5} = \frac{2}{10}$.
* Improper fraction: $1\frac{1}{10} = \frac{11}{10}$.
* Subtract: $\frac{11}{10} - \frac{2}{10} = \frac{9}{10}$.
* Answer: $\mathbf{\frac{9}{10}}$
20. $\frac{1}{2} - \frac{2}{9}$
* Common denominator (18): $\frac{1}{2} = \frac{9}{18}$ and $\frac{2}{9} = \frac{4}{18}$.
* Subtract: $\frac{9}{18} - \frac{4}{18} = \mathbf{\frac{5}{18}}$
21. $1\frac{1}{10} - \frac{1}{3}$
* Improper fraction: $1\frac{1}{10} = \frac{11}{10}$.
* Common denominator (30): $\frac{11}{10} = \frac{33}{30}$ and $\frac{1}{3} = \frac{10}{30}$.
* Subtract: $\frac{33}{30} - \frac{10}{30} = \frac{23}{30}$.
* Answer: $\mathbf{\frac{23}{30}}$
22. $\frac{2}{5} - \frac{1}{2}$
* Common denominator (10): $\frac{2}{5} = \frac{4}{10}$ and $\frac{1}{2} = \frac{5}{10}$.
* Subtract: $\frac{4}{10} - \frac{5}{10} = -\frac{1}{10}$.
* *Note: In elementary games, this might be an error in the problem design, or the answer is simply negative.*
* Answer: $\mathbf{-\frac{1}{10}}$
23. $1\frac{2}{5} - \frac{3}{4}$
* Improper fraction: $1\frac{2}{5} = \frac{7}{5}$.
* Common denominator (20): $\frac{7}{5} = \frac{28}{20}$ and $\frac{3}{4} = \frac{15}{20}$.
* Subtract: $\frac{28}{20} - \frac{15}{20} = \frac{13}{20}$.
* Answer: $\mathbf{\frac{13}{20}}$
24. $1\frac{2}{3} - \frac{3}{5}$
* Improper fraction: $1\frac{2}{3} = \frac{5}{3}$.
* Common denominator (15): $\frac{5}{3} = \frac{25}{15}$ and $\frac{3}{5} = \frac{9}{15}$.
* Subtract: $\frac{25}{15} - \frac{9}{15} = \frac{16}{15}$.
* Mixed number: $\mathbf{1\frac{1}{15}}$
25. $1\frac{1}{2} - \frac{2}{9}$
* Improper fraction: $1\frac{1}{2} = \frac{3}{2}$.
* Common denominator (18): $\frac{3}{2} = \frac{27}{18}$ and $\frac{2}{9} = \frac{4}{18}$.
* Subtract: $\frac{27}{18} - \frac{4}{18} = \frac{23}{18}$.
* Mixed number: $\mathbf{1\frac{5}{18}}$
Final Answer:
Here are the solutions for the visible squares:
Main Board:
1. $\frac{7}{12}$
2. $\frac{14}{15}$
3. $1\frac{1}{3}$
4. $1\frac{7}{30}$
5. $\frac{7}{6}$ (or $1\frac{1}{6}$)
6. $\frac{4}{5}$
7. $\frac{7}{12}$
8. $1\frac{3}{8}$
9. $\frac{7}{24}$
10. $1\frac{1}{12}$
11. $\frac{7}{24}$
Side Board:
12. $\frac{5}{9}$
13. $\frac{28}{45}$
14. $\frac{23}{36}$
15. $1\frac{3}{10}$
16. $\frac{1}{6}$
17. $\frac{1}{2}$
18. $1\frac{9}{40}$
19. $\frac{9}{10}$
20. $\frac{5}{18}$
21. $\frac{23}{30}$
22. $-\frac{1}{10}$
23. $\frac{13}{20}$
24. $1\frac{1}{15}$
25. $1\frac{5}{18}$
Parent Tip: Review the logic above to help your child master the concept of add and subtract fractions activity.
