Math worksheet for practicing adding fractions with unlike denominators, including simplification.
A worksheet titled "Adding Fractions with Unlike Denominators, Requires Simplifying" showing a step-by-step example and multiple practice problems for adding fractions.
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Step-by-step solution for: Fractions unlike denominator adding worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Fractions unlike denominator adding worksheet
Absolutely! Let’s solve each problem step by step. The goal is to add fractions with unlike denominators and then simplify the result.
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1. Find the Least Common Denominator (LCD) — the smallest number both denominators divide into.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the numerators, keeping the denominator the same.
4. Simplify the resulting fraction (if possible) by dividing numerator and denominator by their GCF (Greatest Common Factor).
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Let’s go problem by problem:
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- LCD of 12 and 6 = 12
- $\frac{4}{6} = \frac{8}{12}$
- Add: $\frac{2}{12} + \frac{8}{12} = \frac{10}{12}$
- Simplify: $\frac{10}{12} = \frac{5}{6}$
✔ Answer: $\frac{5}{6}$
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- LCD of 8 and 4 = 8
- $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{4}{8} + \frac{2}{8} = \frac{6}{8}$
- Simplify: $\frac{6}{8} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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- LCD of 5 and 10 = 10
- $\frac{3}{5} = \frac{6}{10}$
- Add: $\frac{6}{10} + \frac{2}{10} = \frac{8}{10}$
- Simplify: $\frac{8}{10} = \frac{4}{5}$
✔ Answer: $\frac{4}{5}$
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- LCD of 3 and 9 = 9
- $\frac{1}{3} = \frac{3}{9}$
- Add: $\frac{3}{9} + \frac{3}{9} = \frac{6}{9}$
- Simplify: $\frac{6}{9} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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- LCD of 10 and 5 = 10
- $\frac{2}{5} = \frac{4}{10}$
- Add: $\frac{2}{10} + \frac{4}{10} = \frac{6}{10}$
- Simplify: $\frac{6}{10} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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- LCD of 6 and 12 = 12
- $\frac{3}{6} = \frac{6}{12}$
- Add: $\frac{6}{12} + \frac{2}{12} = \frac{8}{12}$
- Simplify: $\frac{8}{12} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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- LCD of 2 and 10 = 10
- $\frac{1}{2} = \frac{5}{10}$
- Add: $\frac{5}{10} + \frac{1}{10} = \frac{6}{10}$
- Simplify: $\frac{6}{10} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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- LCD of 6 and 3 = 6
- $\frac{1}{3} = \frac{2}{6}$
- Add: $\frac{1}{6} + \frac{2}{6} = \frac{3}{6}$
- Simplify: $\frac{3}{6} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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- LCD of 6 and 12 = 12
- $\frac{1}{6} = \frac{2}{12}$
- Add: $\frac{2}{12} + \frac{4}{12} = \frac{6}{12}$
- Simplify: $\frac{6}{12} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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- LCD of 4 and 8 = 8
- $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{2}{8} + \frac{2}{8} = \frac{4}{8}$
- Simplify: $\frac{4}{8} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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- LCD of 5 and 10 = 10
- $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{2}{10} + \frac{2}{10} = \frac{4}{10}$
- Simplify: $\frac{4}{10} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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- LCD of 14 and 7 = 14
- $\frac{1}{7} = \frac{2}{14}$
- Add: $\frac{4}{14} + \frac{2}{14} = \frac{6}{14}$
- Simplify: $\frac{6}{14} = \frac{3}{7}$
✔ Answer: $\frac{3}{7}$
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- LCD of 4, 3, and 12 = 12
- $\frac{1}{4} = \frac{3}{12}$, $\frac{1}{3} = \frac{4}{12}$, $\frac{3}{12} = \frac{3}{12}$
- Add: $\frac{3}{12} + \frac{4}{12} + \frac{3}{12} = \frac{10}{12}$
- Simplify: $\frac{10}{12} = \frac{5}{6}$
✔ Answer: $\frac{5}{6}$
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- LCD of 2, 10, and 5 = 10
- $\frac{1}{2} = \frac{5}{10}$, $\frac{1}{10} = \frac{1}{10}$, $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{5}{10} + \frac{1}{10} + \frac{2}{10} = \frac{8}{10}$
- Simplify: $\frac{8}{10} = \frac{4}{5}$
✔ Answer: $\frac{4}{5}$
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- LCD of 14 and 7 = 14
- $\frac{2}{7} = \frac{4}{14}$, $\frac{1}{7} = \frac{2}{14}$, $\frac{1}{14} = \frac{1}{14}$
- Add: $\frac{1}{14} + \frac{4}{14} + \frac{2}{14} = \frac{7}{14}$
- Simplify: $\frac{7}{14} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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- LCD of 8 and 2 = 8
- $\frac{1}{2} = \frac{4}{8}$, $\frac{1}{8} = \frac{1}{8}$, $\frac{1}{8} = \frac{1}{8}$
- Add: $\frac{1}{8} + \frac{4}{8} + \frac{1}{8} = \frac{6}{8}$
- Simplify: $\frac{6}{8} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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## 🎉 Final Answers Summary:
a. $\frac{5}{6}$
b. $\frac{3}{4}$
c. $\frac{4}{5}$
d. $\frac{2}{3}$
e. $\frac{3}{5}$
f. $\frac{2}{3}$
g. $\frac{3}{5}$
h. $\frac{1}{2}$
i. $\frac{1}{2}$
j. $\frac{1}{2}$
k. $\frac{2}{5}$
l. $\frac{3}{7}$
m. $\frac{5}{6}$
n. $\frac{4}{5}$
o. $\frac{1}{2}$
p. $\frac{3}{4}$
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Let me know if you’d like this in a printable format or need help explaining any step further! 😊
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✔ General Steps:
1. Find the Least Common Denominator (LCD) — the smallest number both denominators divide into.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the numerators, keeping the denominator the same.
4. Simplify the resulting fraction (if possible) by dividing numerator and denominator by their GCF (Greatest Common Factor).
---
Let’s go problem by problem:
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a. $\frac{2}{12} + \frac{4}{6}$
- LCD of 12 and 6 = 12
- $\frac{4}{6} = \frac{8}{12}$
- Add: $\frac{2}{12} + \frac{8}{12} = \frac{10}{12}$
- Simplify: $\frac{10}{12} = \frac{5}{6}$
✔ Answer: $\frac{5}{6}$
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b. $\frac{4}{8} + \frac{1}{4}$
- LCD of 8 and 4 = 8
- $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{4}{8} + \frac{2}{8} = \frac{6}{8}$
- Simplify: $\frac{6}{8} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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c. $\frac{3}{5} + \frac{2}{10}$
- LCD of 5 and 10 = 10
- $\frac{3}{5} = \frac{6}{10}$
- Add: $\frac{6}{10} + \frac{2}{10} = \frac{8}{10}$
- Simplify: $\frac{8}{10} = \frac{4}{5}$
✔ Answer: $\frac{4}{5}$
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d. $\frac{1}{3} + \frac{3}{9}$
- LCD of 3 and 9 = 9
- $\frac{1}{3} = \frac{3}{9}$
- Add: $\frac{3}{9} + \frac{3}{9} = \frac{6}{9}$
- Simplify: $\frac{6}{9} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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e. $\frac{2}{10} + \frac{2}{5}$
- LCD of 10 and 5 = 10
- $\frac{2}{5} = \frac{4}{10}$
- Add: $\frac{2}{10} + \frac{4}{10} = \frac{6}{10}$
- Simplify: $\frac{6}{10} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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f. $\frac{3}{6} + \frac{2}{12}$
- LCD of 6 and 12 = 12
- $\frac{3}{6} = \frac{6}{12}$
- Add: $\frac{6}{12} + \frac{2}{12} = \frac{8}{12}$
- Simplify: $\frac{8}{12} = \frac{2}{3}$
✔ Answer: $\frac{2}{3}$
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g. $\frac{1}{2} + \frac{1}{10}$
- LCD of 2 and 10 = 10
- $\frac{1}{2} = \frac{5}{10}$
- Add: $\frac{5}{10} + \frac{1}{10} = \frac{6}{10}$
- Simplify: $\frac{6}{10} = \frac{3}{5}$
✔ Answer: $\frac{3}{5}$
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h. $\frac{1}{6} + \frac{1}{3}$
- LCD of 6 and 3 = 6
- $\frac{1}{3} = \frac{2}{6}$
- Add: $\frac{1}{6} + \frac{2}{6} = \frac{3}{6}$
- Simplify: $\frac{3}{6} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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i. $\frac{1}{6} + \frac{4}{12}$
- LCD of 6 and 12 = 12
- $\frac{1}{6} = \frac{2}{12}$
- Add: $\frac{2}{12} + \frac{4}{12} = \frac{6}{12}$
- Simplify: $\frac{6}{12} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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j. $\frac{1}{4} + \frac{2}{8}$
- LCD of 4 and 8 = 8
- $\frac{1}{4} = \frac{2}{8}$
- Add: $\frac{2}{8} + \frac{2}{8} = \frac{4}{8}$
- Simplify: $\frac{4}{8} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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k. $\frac{1}{5} + \frac{2}{10}$
- LCD of 5 and 10 = 10
- $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{2}{10} + \frac{2}{10} = \frac{4}{10}$
- Simplify: $\frac{4}{10} = \frac{2}{5}$
✔ Answer: $\frac{2}{5}$
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l. $\frac{4}{14} + \frac{1}{7}$
- LCD of 14 and 7 = 14
- $\frac{1}{7} = \frac{2}{14}$
- Add: $\frac{4}{14} + \frac{2}{14} = \frac{6}{14}$
- Simplify: $\frac{6}{14} = \frac{3}{7}$
✔ Answer: $\frac{3}{7}$
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m. $\frac{1}{4} + \frac{1}{3} + \frac{3}{12}$
- LCD of 4, 3, and 12 = 12
- $\frac{1}{4} = \frac{3}{12}$, $\frac{1}{3} = \frac{4}{12}$, $\frac{3}{12} = \frac{3}{12}$
- Add: $\frac{3}{12} + \frac{4}{12} + \frac{3}{12} = \frac{10}{12}$
- Simplify: $\frac{10}{12} = \frac{5}{6}$
✔ Answer: $\frac{5}{6}$
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n. $\frac{1}{2} + \frac{1}{10} + \frac{1}{5}$
- LCD of 2, 10, and 5 = 10
- $\frac{1}{2} = \frac{5}{10}$, $\frac{1}{10} = \frac{1}{10}$, $\frac{1}{5} = \frac{2}{10}$
- Add: $\frac{5}{10} + \frac{1}{10} + \frac{2}{10} = \frac{8}{10}$
- Simplify: $\frac{8}{10} = \frac{4}{5}$
✔ Answer: $\frac{4}{5}$
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o. $\frac{1}{14} + \frac{2}{7} + \frac{1}{7}$
- LCD of 14 and 7 = 14
- $\frac{2}{7} = \frac{4}{14}$, $\frac{1}{7} = \frac{2}{14}$, $\frac{1}{14} = \frac{1}{14}$
- Add: $\frac{1}{14} + \frac{4}{14} + \frac{2}{14} = \frac{7}{14}$
- Simplify: $\frac{7}{14} = \frac{1}{2}$
✔ Answer: $\frac{1}{2}$
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p. $\frac{1}{8} + \frac{1}{2} + \frac{1}{8}$
- LCD of 8 and 2 = 8
- $\frac{1}{2} = \frac{4}{8}$, $\frac{1}{8} = \frac{1}{8}$, $\frac{1}{8} = \frac{1}{8}$
- Add: $\frac{1}{8} + \frac{4}{8} + \frac{1}{8} = \frac{6}{8}$
- Simplify: $\frac{6}{8} = \frac{3}{4}$
✔ Answer: $\frac{3}{4}$
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## 🎉 Final Answers Summary:
a. $\frac{5}{6}$
b. $\frac{3}{4}$
c. $\frac{4}{5}$
d. $\frac{2}{3}$
e. $\frac{3}{5}$
f. $\frac{2}{3}$
g. $\frac{3}{5}$
h. $\frac{1}{2}$
i. $\frac{1}{2}$
j. $\frac{1}{2}$
k. $\frac{2}{5}$
l. $\frac{3}{7}$
m. $\frac{5}{6}$
n. $\frac{4}{5}$
o. $\frac{1}{2}$
p. $\frac{3}{4}$
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Let me know if you’d like this in a printable format or need help explaining any step further! 😊
Parent Tip: Review the logic above to help your child master the concept of super teacher worksheet adding fractions with unlike denominators.
