Fun Fraction Patterns :: Teacher Resources and Classroom Games ... - Free Printable

Here are the solutions to the fraction pattern problems.

1. Add the missing fractions to complete the pattern:

a) The pattern increases by $\frac{1}{6}$ each time.
* $5 \frac{4}{6} + \frac{1}{6} = 5 \frac{5}{6}$
* $5 \frac{5}{6} + \frac{1}{6} = 6$ (since $\frac{6}{6}$ makes a whole)
* ...
* $4 \frac{5}{6} + \frac{1}{6} = 5$
* $5 + \frac{1}{6} = 5 \frac{1}{6}$

Missing numbers: $5 \frac{5}{6}, \quad 6, \quad 5, \quad 5 \frac{1}{6}$

b) The pattern increases by $5$ each time.
* $10 \frac{1}{2} + 5 = 15 \frac{1}{2}$
* $15 \frac{1}{2} + 5 = 20 \frac{1}{2}$
* ...
* $25 \frac{1}{2} + 5 = 30 \frac{1}{2}$
* $30 \frac{1}{2} + 5 = 35 \frac{1}{2}$

Missing numbers: $15 \frac{1}{2}, \quad 20 \frac{1}{2}, \quad 30 \frac{1}{2}, \quad 35 \frac{1}{2}$

c) The pattern decreases by $\frac{1}{3}$ each time.
* $8 \frac{2}{3} - \frac{1}{3} = 8 \frac{1}{3}$
* $8 \frac{1}{3} - \frac{1}{3} = 8$
* ...
* $9 \frac{1}{3} - \frac{1}{3} = 9$
* $9 - \frac{1}{3} = 8 \frac{2}{3}$
* $8 \frac{2}{3} - \frac{1}{3} = 8 \frac{1}{3}$
* $8 \frac{1}{3} - \frac{1}{3} = 8$

Missing numbers: $8 \frac{1}{3}, \quad 8, \quad 9, \quad 8 \frac{2}{3}, \quad 8 \frac{1}{3}, \quad 8$

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2. Fill in the missing fractions and write the rule:

Top Pattern:
The numbers go up by $\frac{2}{10}$ each step.
* $1 \frac{7}{10} + \frac{2}{10} = 1 \frac{9}{10}$
* $1 \frac{9}{10} + \frac{2}{10} = 2 \frac{1}{10}$
* $2 \frac{1}{10} + \frac{2}{10} = 2 \frac{3}{10}$
* $2 \frac{3}{10} + \frac{2}{10} = 2 \frac{5}{10}$ (which simplifies to $2 \frac{1}{2}$)
* $2 \frac{5}{10} + \frac{2}{10} = 2 \frac{7}{10}$

Rule: Increase by $\frac{2}{10}$ (or $\frac{1}{5}$).
Missing boxes: $1 \frac{9}{10}, \quad 2 \frac{1}{10}, \quad 2 \frac{5}{10}, \quad 2 \frac{7}{10}$

Bottom Pattern:
The numbers go up by $\frac{2}{6}$ each step.
* $4 \frac{2}{6} + \frac{2}{6} = 4 \frac{4}{6}$
* $4 \frac{4}{6} + \frac{2}{6} = 5$ (since $\frac{6}{6}$ is 1 whole)
* $5 + \frac{2}{6} = 5 \frac{2}{6}$
* $5 \frac{2}{6} + \frac{2}{6} = 5 \frac{4}{6}$
* $5 \frac{4}{6} + \frac{2}{6} = 6$

Rule: Increase by $\frac{2}{6}$ (or $\frac{1}{3}$).
Missing boxes: $4 \frac{4}{6}, \quad 5, \quad 5 \frac{2}{6}, \quad 5 \frac{4}{6}, \quad 6$

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3. Complete the fraction patterns:

a) Start at $1 \frac{3}{4}$ and increase by $\frac{1}{4}$ each time:
1. $1 \frac{3}{4} + \frac{1}{4} = 2$
2. $2 + \frac{1}{4} = 2 \frac{1}{4}$
3. $2 \frac{1}{4} + \frac{1}{4} = 2 \frac{2}{4}$ (or $2 \frac{1}{2}$)
4. $2 \frac{2}{4} + \frac{1}{4} = 2 \frac{3}{4}$
5. $2 \frac{3}{4} + \frac{1}{4} = 3$
6. $3 + \frac{1}{4} = 3 \frac{1}{4}$
7. $3 \frac{1}{4} + \frac{1}{4} = 3 \frac{2}{4}$ (or $3 \frac{1}{2}$)

b) Start at $5 \frac{4}{6}$ and decrease by $\frac{1}{6}$ each time:
1. $5 \frac{4}{6} - \frac{1}{6} = 5 \frac{3}{6}$ (or $5 \frac{1}{2}$)
2. $5 \frac{3}{6} - \frac{1}{6} = 5 \frac{2}{6}$ (or $5 \frac{1}{3}$)
3. $5 \frac{2}{6} - \frac{1}{6} = 5 \frac{1}{6}$
4. $5 \frac{1}{6} - \frac{1}{6} = 5$
5. $5 - \frac{1}{6} = 4 \frac{5}{6}$
6. $4 \frac{5}{6} - \frac{1}{6} = 4 \frac{4}{6}$ (or $4 \frac{2}{3}$)
7. $4 \frac{4}{6} - \frac{1}{6} = 4 \frac{3}{6}$ (or $4 \frac{1}{2}$)

Final Answer:
1a) $5 \frac{5}{6}, 6, 5, 5 \frac{1}{6}$
1b) $15 \frac{1}{2}, 20 \frac{1}{2}, 30 \frac{1}{2}, 35 \frac{1}{2}$
1c) $8 \frac{1}{3}, 8, 9, 8 \frac{2}{3}, 8 \frac{1}{3}, 8$

2 Top Rule: Increase by $\frac{2}{10}$
2 Top Boxes: $1 \frac{9}{10}, 2 \frac{1}{10}, 2 \frac{5}{10}, 2 \frac{7}{10}$
2 Bottom Rule: Increase by $\frac{2}{6}$
2 Bottom Boxes: $4 \frac{4}{6}, 5, 5 \frac{2}{6}, 5 \frac{4}{6}, 6$

3a) $2, 2 \frac{1}{4}, 2 \frac{2}{4}, 2 \frac{3}{4}, 3, 3 \frac{1}{4}, 3 \frac{2}{4}$
3b) $5 \frac{3}{6}, 5 \frac{2}{6}, 5 \frac{1}{6}, 5, 4 \frac{5}{6}, 4 \frac{4}{6}, 4 \frac{3}{6}$