Let's solve each of these problems step by step. The task is to
add two proper fractions and, where needed,
simplify the result.
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Key Rules:
- If the denominators are the same, add the numerators and keep the denominator.
- Simplify the resulting fraction if possible (reduce to lowest terms).
- If the sum is an improper fraction (numerator ≥ denominator), convert to a mixed number — but in this case, since all are proper fractions being added, the results will either be proper or improper, but we'll simplify as needed.
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Let’s go through each problem:
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1.
$\frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}$
→ Add numerators: $3+1=4$, denominator stays 6 → $\frac{4}{6}$ → Simplify: divide numerator and denominator by 2 → $\frac{2}{3}$
2.
$\frac{6}{9} + \frac{1}{9} = \frac{7}{9}$
→ $6+1=7$, denominator 9 → $\frac{7}{9}$ (already simplified)
3.
$\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$
→ $1+1=2$ → $\frac{2}{3}$
4.
$\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$
→ $2+1=3$ → $\frac{3}{5}$
5.
$\frac{6}{8} + \frac{1}{8} = \frac{7}{8}$
→ $6+1=7$ → $\frac{7}{8}$
6.
$\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$
→ $1+1=2$ → $\frac{2}{5}$
7.
$\frac{7}{9} + \frac{1}{9} = \frac{8}{9}$
→ $7+1=8$ → $\frac{8}{9}$
8.
$\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$
→ $2+3=5$ → $\frac{5}{7}$
9.
$\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$
→ $2+3=5$ → $\frac{5}{6}$
10.
$\frac{2}{6} + \frac{2}{6} = \frac{4}{6} = \frac{2}{3}$
→ $2+2=4$ → $\frac{4}{6}$ → Simplify: divide by 2 → $\frac{2}{3}$
11.
$\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$
→ $4+1=5$ → $\frac{5}{6}$
12.
$\frac{4}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4}$
→ $4+2=6$ → $\frac{6}{8}$ → Simplify: divide by 2 → $\frac{3}{4}$
13.
$\frac{3}{9} + \frac{3}{9} = \frac{6}{9} = \frac{2}{3}$
→ $3+3=6$ → $\frac{6}{9}$ → Simplify: divide by 3 → $\frac{2}{3}$
14.
$\frac{2}{8} + \frac{4}{8} = \frac{6}{8} = \frac{3}{4}$
→ $2+4=6$ → $\frac{6}{8}$ → Simplify → $\frac{3}{4}$
15.
$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
→ $2+1=3$ → $\frac{3}{4}$
16.
$\frac{3}{7} + \frac{1}{7} = \frac{4}{7}$
→ $3+1=4$ → $\frac{4}{7}$
17.
$\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$
→ $2+2=4$ → $\frac{4}{5}$
18.
$\frac{2}{7} + \frac{1}{7} = \frac{3}{7}$
→ $2+1=3$ → $\frac{3}{7}$
19.
$\frac{2}{8} + \frac{5}{8} = \frac{7}{8}$
→ $2+5=7$ → $\frac{7}{8}$
20.
$\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$
→ $1+1=2$ → $\frac{2}{4}$ → Simplify → $\frac{1}{2}$
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | $\frac{2}{3}$ |
| 2 | $\frac{7}{9}$ |
| 3 | $\frac{2}{3}$ |
| 4 | $\frac{3}{5}$ |
| 5 | $\frac{7}{8}$ |
| 6 | $\frac{2}{5}$ |
| 7 | $\frac{8}{9}$ |
| 8 | $\frac{5}{7}$ |
| 9 | $\frac{5}{6}$ |
| 10 | $\frac{2}{3}$ |
| 11 | $\frac{5}{6}$ |
| 12 | $\frac{3}{4}$ |
| 13 | $\frac{2}{3}$ |
| 14 | $\frac{3}{4}$ |
| 15 | $\frac{3}{4}$ |
| 16 | $\frac{4}{7}$ |
| 17 | $\frac{4}{5}$ |
| 18 | $\frac{3}{7}$ |
| 19 | $\frac{7}{8}$ |
| 20 | $\frac{1}{2}$ |
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✔ All answers are simplified to lowest terms.
Let me know if you'd like this formatted for printing or need explanations for any specific ones!
Parent Tip: Review the logic above to help your child master the concept of worksheet adding fractions.
