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Adding and Subtracting Fractions

Learn to add and subtract fractions with same and different denominators

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Adding and Subtracting Fractions

Same Denominator

When fractions have the same denominator, simply add or subtract the numerators:

27+37=2+37=57\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}

59−29=5−29=39=13\frac{5}{9} - \frac{2}{9} = \frac{5 - 2}{9} = \frac{3}{9} = \frac{1}{3}

Different Denominators

Steps:

  1. Find a common denominator (usually the LCM)
  2. Convert each fraction to an equivalent fraction
  3. Add or subtract the numerators
  4. Simplify if possible

Example: 14+16\frac{1}{4} + \frac{1}{6}

LCM of 4 and 6 is 12: 14=312,16=212\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}

312+212=512\frac{3}{12} + \frac{2}{12} = \frac{5}{12}

Mixed Numbers

Convert to improper fractions first, then add/subtract: 213+112=73+322\frac{1}{3} + 1\frac{1}{2} = \frac{7}{3} + \frac{3}{2}

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: 38+28\frac{3}{8} + \frac{2}{8}

💡 Show Solution

Solution:

Same denominator - add the numerators: 38+28=3+28=58\frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8}

Answer: 58\frac{5}{8}

2Problem 2easy

❓ Question:

Calculate: 38+28\frac{3}{8} + \frac{2}{8}

💡 Show Solution

Solution:

Same denominator - add the numerators: 38+28=3+28=58\frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8}

Answer: 58\frac{5}{8}

3Problem 3medium

❓ Question:

Calculate: 23+14\frac{2}{3} + \frac{1}{4}

💡 Show Solution

Solution:

Find common denominator (LCM of 3 and 4 is 12):

23=812\frac{2}{3} = \frac{8}{12}

14=312\frac{1}{4} = \frac{3}{12}

Add: 812+312=1112\frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Answer: 1112\frac{11}{12}

4Problem 4medium

❓ Question:

Calculate: 23+14\frac{2}{3} + \frac{1}{4}

💡 Show Solution

Solution:

Find common denominator (LCM of 3 and 4 is 12):

23=812\frac{2}{3} = \frac{8}{12}

14=312\frac{1}{4} = \frac{3}{12}

Add: 812+312=1112\frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Answer: 1112\frac{11}{12}

5Problem 5hard

❓ Question:

Sarah ran 2342\frac{3}{4} miles on Monday and 1561\frac{5}{6} miles on Tuesday. How many total miles did she run?

💡 Show Solution

Solution:

Convert to improper fractions: 234=114,156=1162\frac{3}{4} = \frac{11}{4}, \quad 1\frac{5}{6} = \frac{11}{6}

Find common denominator (LCM of 4 and 6 is 12): 114=3312,116=2212\frac{11}{4} = \frac{33}{12}, \quad \frac{11}{6} = \frac{22}{12}

Add: 3312+2212=5512=4712\frac{33}{12} + \frac{22}{12} = \frac{55}{12} = 4\frac{7}{12}

Answer: 47124\frac{7}{12} miles

6Problem 6hard

❓ Question:

Sarah ran 2342\frac{3}{4} miles on Monday and 1561\frac{5}{6} miles on Tuesday. How many total miles did she run?

💡 Show Solution

Solution:

Convert to improper fractions: 234=114,156=1162\frac{3}{4} = \frac{11}{4}, \quad 1\frac{5}{6} = \frac{11}{6}

Find common denominator (LCM of 4 and 6 is 12): 114=3312,116=2212\frac{11}{4} = \frac{33}{12}, \quad \frac{11}{6} = \frac{22}{12}

Add: 3312+2212=5512=4712\frac{33}{12} + \frac{22}{12} = \frac{55}{12} = 4\frac{7}{12}

Answer: 47124\frac{7}{12} miles

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Understanding FractionsWorking with DecimalsDividing FractionsDecimal Operations

❓ Frequently Asked Questions

What is Adding and Subtracting Fractions?▾
Learn to add and subtract fractions with same and different denominators
How can I study Adding and Subtracting Fractions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Adding and Subtracting Fractions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Adding and Subtracting Fractions on Study Mondo are free to access. No account is needed.
What course covers Adding and Subtracting Fractions?▾
Adding and Subtracting Fractions is part of the Grade 6 Math course on Study Mondo, specifically in the Fractions and Decimals section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Adding and Subtracting Fractions?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.