Adding Fractions with unlike denominators exercise - Free Printable
Educational worksheet: Adding Fractions with unlike denominators exercise. Download and print for classroom or home learning activities.
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Step-by-step solution for: Adding Fractions with unlike denominators exercise
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Show Answer Key & Explanations
Step-by-step solution for: Adding Fractions with unlike denominators exercise
Of course! I'll solve each fraction addition problem step-by-step, following the instructions provided in the worksheet.
The steps are:
1. Write out the multiples of each denominator.
2. Find the Lowest Common Multiple (LCM).
3. Write the equivalent fractions with the LCM as the denominator for both fractions.
4. Solve the equation.
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Problem 1: $\frac{1}{2} + \frac{2}{3}$
* Step 1: Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 3: 3, 6, 9, 12, 15...
* Step 2: LCM of 2 and 3 is 6.
* Step 3: Convert to equivalent fractions with denominator 6.
* $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
* $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
* Step 4: Add the numerators: $\frac{3}{6} + \frac{4}{6} = \frac{7}{6}$
* This can also be written as a mixed number: $1\frac{1}{6}$
Answer: $\frac{7}{6}$ or $1\frac{1}{6}$
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Problem 2: $\frac{3}{4} + \frac{1}{8}$
* Step 1: Multiples of 4: 4, 8, 12, 16...
Multiples of 8: 8, 16, 24...
* Step 2: LCM of 4 and 8 is 8.
* Step 3: Convert to equivalent fractions with denominator 8.
* $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
* $\frac{1}{8}$ stays the same.
* Step 4: Add the numerators: $\frac{6}{8} + \frac{1}{8} = \frac{7}{8}$
Answer: $\frac{7}{8}$
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Problem 3: $\frac{4}{9} + \frac{1}{3}$
* Step 1: Multiples of 9: 9, 18, 27...
Multiples of 3: 3, 6, 9, 12, 15...
* Step 2: LCM of 9 and 3 is 9.
* Step 3: Convert to equivalent fractions with denominator 9.
* $\frac{4}{9}$ stays the same.
* $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$
* Step 4: Add the numerators: $\frac{4}{9} + \frac{3}{9} = \frac{7}{9}$
Answer: $\frac{7}{9}$
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Problem 4: $\frac{3}{5} + \frac{1}{2}$
* Step 1: Multiples of 5: 5, 10, 15, 20...
Multiples of 2: 2, 4, 6, 8, 10, 12...
* Step 2: LCM of 5 and 2 is 10.
* Step 3: Convert to equivalent fractions with denominator 10.
* $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
* $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$
* Step 4: Add the numerators: $\frac{6}{10} + \frac{5}{10} = \frac{11}{10}$
* This can also be written as a mixed number: $1\frac{1}{10}$
Answer: $\frac{11}{10}$ or $1\frac{1}{10}$
---
Problem 5: $\frac{1}{6} + \frac{2}{3}$
* Step 1: Multiples of 6: 6, 12, 18...
Multiples of 3: 3, 6, 9, 12...
* Step 2: LCM of 6 and 3 is 6.
* Step 3: Convert to equivalent fractions with denominator 6.
* $\frac{1}{6}$ stays the same.
* $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
* Step 4: Add the numerators: $\frac{1}{6} + \frac{4}{6} = \frac{5}{6}$
Answer: $\frac{5}{6}$
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Problem 6: $\frac{1}{4} + \frac{1}{6}$
* Step 1: Multiples of 4: 4, 8, 12, 16...
Multiples of 6: 6, 12, 18...
* Step 2: LCM of 4 and 6 is 12.
* Step 3: Convert to equivalent fractions with denominator 12.
* $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
* $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
* Step 4: Add the numerators: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$
Answer: $\frac{5}{12}$
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Problem 7: $\frac{1}{4} + \frac{1}{2}$
* Step 1: Multiples of 4: 4, 8, 12...
Multiples of 2: 2, 4, 6, 8...
* Step 2: LCM of 4 and 2 is 4.
* Step 3: Convert to equivalent fractions with denominator 4.
* $\frac{1}{4}$ stays the same.
* $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
* Step 4: Add the numerators: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$
Answer: $\frac{3}{4}$
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Problem 8: $\frac{3}{12} + \frac{1}{4}$
* Step 1: Multiples of 12: 12, 24, 36...
Multiples of 4: 4, 8, 12, 16...
* Step 2: LCM of 12 and 4 is 12.
* Step 3: Convert to equivalent fractions with denominator 12.
* $\frac{3}{12}$ stays the same.
* $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
* Step 4: Add the numerators: $\frac{3}{12} + \frac{3}{12} = \frac{6}{12}$
* Simplify the fraction: $\frac{6}{12} = \frac{1}{2}$
Answer: $\frac{6}{12}$ or simplified, $\frac{1}{2}$
---
Here are all the final answers:
1. $\frac{1}{2} + \frac{2}{3} = \boxed{\frac{7}{6}}$ (or $1\frac{1}{6}$)
2. $\frac{3}{4} + \frac{1}{8} = \boxed{\frac{7}{8}}$
3. $\frac{4}{9} + \frac{1}{3} = \boxed{\frac{7}{9}}$
4. $\frac{3}{5} + \frac{1}{2} = \boxed{\frac{11}{10}}$ (or $1\frac{1}{10}$)
5. $\frac{1}{6} + \frac{2}{3} = \boxed{\frac{5}{6}}$
6. $\frac{1}{4} + \frac{1}{6} = \boxed{\frac{5}{12}}$
7. $\frac{1}{4} + \frac{1}{2} = \boxed{\frac{3}{4}}$
8. $\frac{3}{12} + \frac{1}{4} = \boxed{\frac{1}{2}}$
The steps are:
1. Write out the multiples of each denominator.
2. Find the Lowest Common Multiple (LCM).
3. Write the equivalent fractions with the LCM as the denominator for both fractions.
4. Solve the equation.
---
Problem 1: $\frac{1}{2} + \frac{2}{3}$
* Step 1: Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 3: 3, 6, 9, 12, 15...
* Step 2: LCM of 2 and 3 is 6.
* Step 3: Convert to equivalent fractions with denominator 6.
* $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
* $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
* Step 4: Add the numerators: $\frac{3}{6} + \frac{4}{6} = \frac{7}{6}$
* This can also be written as a mixed number: $1\frac{1}{6}$
Answer: $\frac{7}{6}$ or $1\frac{1}{6}$
---
Problem 2: $\frac{3}{4} + \frac{1}{8}$
* Step 1: Multiples of 4: 4, 8, 12, 16...
Multiples of 8: 8, 16, 24...
* Step 2: LCM of 4 and 8 is 8.
* Step 3: Convert to equivalent fractions with denominator 8.
* $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
* $\frac{1}{8}$ stays the same.
* Step 4: Add the numerators: $\frac{6}{8} + \frac{1}{8} = \frac{7}{8}$
Answer: $\frac{7}{8}$
---
Problem 3: $\frac{4}{9} + \frac{1}{3}$
* Step 1: Multiples of 9: 9, 18, 27...
Multiples of 3: 3, 6, 9, 12, 15...
* Step 2: LCM of 9 and 3 is 9.
* Step 3: Convert to equivalent fractions with denominator 9.
* $\frac{4}{9}$ stays the same.
* $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$
* Step 4: Add the numerators: $\frac{4}{9} + \frac{3}{9} = \frac{7}{9}$
Answer: $\frac{7}{9}$
---
Problem 4: $\frac{3}{5} + \frac{1}{2}$
* Step 1: Multiples of 5: 5, 10, 15, 20...
Multiples of 2: 2, 4, 6, 8, 10, 12...
* Step 2: LCM of 5 and 2 is 10.
* Step 3: Convert to equivalent fractions with denominator 10.
* $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
* $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$
* Step 4: Add the numerators: $\frac{6}{10} + \frac{5}{10} = \frac{11}{10}$
* This can also be written as a mixed number: $1\frac{1}{10}$
Answer: $\frac{11}{10}$ or $1\frac{1}{10}$
---
Problem 5: $\frac{1}{6} + \frac{2}{3}$
* Step 1: Multiples of 6: 6, 12, 18...
Multiples of 3: 3, 6, 9, 12...
* Step 2: LCM of 6 and 3 is 6.
* Step 3: Convert to equivalent fractions with denominator 6.
* $\frac{1}{6}$ stays the same.
* $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
* Step 4: Add the numerators: $\frac{1}{6} + \frac{4}{6} = \frac{5}{6}$
Answer: $\frac{5}{6}$
---
Problem 6: $\frac{1}{4} + \frac{1}{6}$
* Step 1: Multiples of 4: 4, 8, 12, 16...
Multiples of 6: 6, 12, 18...
* Step 2: LCM of 4 and 6 is 12.
* Step 3: Convert to equivalent fractions with denominator 12.
* $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
* $\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
* Step 4: Add the numerators: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$
Answer: $\frac{5}{12}$
---
Problem 7: $\frac{1}{4} + \frac{1}{2}$
* Step 1: Multiples of 4: 4, 8, 12...
Multiples of 2: 2, 4, 6, 8...
* Step 2: LCM of 4 and 2 is 4.
* Step 3: Convert to equivalent fractions with denominator 4.
* $\frac{1}{4}$ stays the same.
* $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
* Step 4: Add the numerators: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$
Answer: $\frac{3}{4}$
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Problem 8: $\frac{3}{12} + \frac{1}{4}$
* Step 1: Multiples of 12: 12, 24, 36...
Multiples of 4: 4, 8, 12, 16...
* Step 2: LCM of 12 and 4 is 12.
* Step 3: Convert to equivalent fractions with denominator 12.
* $\frac{3}{12}$ stays the same.
* $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
* Step 4: Add the numerators: $\frac{3}{12} + \frac{3}{12} = \frac{6}{12}$
* Simplify the fraction: $\frac{6}{12} = \frac{1}{2}$
Answer: $\frac{6}{12}$ or simplified, $\frac{1}{2}$
---
Here are all the final answers:
1. $\frac{1}{2} + \frac{2}{3} = \boxed{\frac{7}{6}}$ (or $1\frac{1}{6}$)
2. $\frac{3}{4} + \frac{1}{8} = \boxed{\frac{7}{8}}$
3. $\frac{4}{9} + \frac{1}{3} = \boxed{\frac{7}{9}}$
4. $\frac{3}{5} + \frac{1}{2} = \boxed{\frac{11}{10}}$ (or $1\frac{1}{10}$)
5. $\frac{1}{6} + \frac{2}{3} = \boxed{\frac{5}{6}}$
6. $\frac{1}{4} + \frac{1}{6} = \boxed{\frac{5}{12}}$
7. $\frac{1}{4} + \frac{1}{2} = \boxed{\frac{3}{4}}$
8. $\frac{3}{12} + \frac{1}{4} = \boxed{\frac{1}{2}}$
Parent Tip: Review the logic above to help your child master the concept of adding fractions different denominators worksheet.
