Let’s solve each fraction addition problem step by step. We’ll find a common denominator, add the numerators, and simplify if needed.
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1. $\frac{1}{6} + \frac{5}{12}$
→ Common denominator of 6 and 12 is
12.
→ Convert $\frac{1}{6}$ to twelfths: $\frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
→ Now add: $\frac{2}{12} + \frac{5}{12} = \frac{7}{12}$
✔ Final: $\frac{7}{12}$
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2. $\frac{1}{8} + \frac{12}{24}$
→ Simplify $\frac{12}{24}$ first → it’s $\frac{1}{2}$
→ Now: $\frac{1}{8} + \frac{1}{2}$
→ Common denominator of 8 and 2 is
8
→ Convert $\frac{1}{2}$ to eighths: $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$
→ Add: $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$
✔ Final: $\frac{5}{8}$
*(Alternatively, without simplifying first: LCD of 8 and 24 is 24 → $\frac{3}{24} + \frac{12}{24} = \frac{15}{24} = \frac{5}{8}$ — same answer!)*
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3. $\frac{2}{3} + \frac{1}{15}$
→ LCD of 3 and 15 is
15
→ Convert $\frac{2}{3}$: $\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$
→ Add: $\frac{10}{15} + \frac{1}{15} = \frac{11}{15}$
✔ Final: $\frac{11}{15}$
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4. $\frac{3}{9} + \frac{7}{18}$
→ Simplify $\frac{3}{9}$ → $\frac{1}{3}$
→ Now: $\frac{1}{3} + \frac{7}{18}$
→ LCD of 3 and 18 is
18
→ Convert $\frac{1}{3}$: $\frac{1 \times 6}{3 \times 6} = \frac{6}{18}$
→ Add: $\frac{6}{18} + \frac{7}{18} = \frac{13}{18}$
✔ Final: $\frac{13}{18}$
*(Without simplifying: LCD of 9 and 18 is 18 → $\frac{6}{18} + \frac{7}{18} = \frac{13}{18}$ — same!)*
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5. $\frac{1}{6} + \frac{3}{12}$
→ Simplify $\frac{3}{12}$ → $\frac{1}{4}$? Wait — better to use LCD directly.
Actually, let’s do it cleanly:
LCD of 6 and 12 is
12
→ Convert $\frac{1}{6}$: $\frac{2}{12}$
→ $\frac{2}{12} + \frac{3}{12} = \frac{5}{12}$
✔ Final: $\frac{5}{12}$
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6. $\frac{2}{3} + \frac{2}{9}$
→ LCD of 3 and 9 is
9
→ Convert $\frac{2}{3}$: $\frac{6}{9}$
→ Add: $\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$
✔ Final: $\frac{8}{9}$
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7. $\frac{4}{5} + \frac{2}{15}$
→ LCD of 5 and 15 is
15
→ Convert $\frac{4}{5}$: $\frac{12}{15}$
→ Add: $\frac{12}{15} + \frac{2}{15} = \frac{14}{15}$
✔ Final: $\frac{14}{15}$
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8. $\frac{6}{8} + \frac{3}{16}$
→ Simplify $\frac{6}{8}$ → $\frac{3}{4}$ (optional)
But let’s use LCD of 8 and 16 →
16
→ Convert $\frac{6}{8}$: $\frac{12}{16}$
→ Add: $\frac{12}{16} + \frac{3}{16} = \frac{15}{16}$
✔ Final: $\frac{15}{16}$
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9. $\frac{1}{4} + \frac{3}{16}$
→ LCD of 4 and 16 is
16
→ Convert $\frac{1}{4}$: $\frac{4}{16}$
→ Add: $\frac{4}{16} + \frac{3}{16} = \frac{7}{16}$
✔ Final: $\frac{7}{16}$
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10. $\frac{1}{2} + \frac{2}{6}$
→ Simplify $\frac{2}{6}$ → $\frac{1}{3}$
→ Now: $\frac{1}{2} + \frac{1}{3}$
→ LCD of 2 and 3 is
6
→ Convert: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$
✔ Final: $\frac{5}{6}$
*(Without simplifying: LCD of 2 and 6 is 6 → $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ — same!)*
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Final Answer:
1. $\frac{7}{12}$
2. $\frac{5}{8}$
3. $\frac{11}{15}$
4. $\frac{13}{18}$
5. $\frac{5}{12}$
6. $\frac{8}{9}$
7. $\frac{14}{15}$
8. $\frac{15}{16}$
9. $\frac{7}{16}$
10. $\frac{5}{6}$
Parent Tip: Review the logic above to help your child master the concept of worksheet on adding and subtracting fractions.
