Math Problem Statement

Addition and subtraction of fractions with the same denominator

Addition and subtraction of fractions with the same denominator, as seen in the image provided by the user.

Solution

Let's solve the fraction problems in the image, starting from the top:

1. 48+38\frac{4}{8} + \frac{3}{8}

  • Since the denominators are the same, we add the numerators: 4+38=78\frac{4 + 3}{8} = \frac{7}{8}

2. 710110\frac{7}{10} - \frac{1}{10}

  • Again, the denominators are the same, so we subtract the numerators: 7110=610\frac{7 - 1}{10} = \frac{6}{10} This fraction simplifies to: 610=35\frac{6}{10} = \frac{3}{5}

3. 748+948+448\frac{7}{48} + \frac{9}{48} + \frac{4}{48}

  • With the same denominator, we can add all numerators: 7+9+448=2048\frac{7 + 9 + 4}{48} = \frac{20}{48} This fraction simplifies to: 2048=512\frac{20}{48} = \frac{5}{12}

4. 4037337\frac{40}{37} - \frac{3}{37}

  • Subtract the numerators: 40337=3737=1\frac{40 - 3}{37} = \frac{37}{37} = 1

5. 1013+413\frac{10}{13} + \frac{4}{13}

  • Add the numerators: 10+413=1413\frac{10 + 4}{13} = \frac{14}{13} This is an improper fraction, and can be written as: 11131 \frac{1}{13}

6. 917+1117+1717\frac{9}{17} + \frac{11}{17} + \frac{17}{17}

  • Add the numerators: 9+11+1717=3717\frac{9 + 11 + 17}{17} = \frac{37}{17} This is an improper fraction, and can be written as: 23172 \frac{3}{17}

7. 23+4363\frac{2}{3} + \frac{4}{3} - \frac{6}{3}

  • Combine the numerators: 2+463=03=0\frac{2 + 4 - 6}{3} = \frac{0}{3} = 0

8. 7656\frac{7}{6} - \frac{5}{6}

  • Subtract the numerators: 756=26\frac{7 - 5}{6} = \frac{2}{6} This simplifies to: 26=13\frac{2}{6} = \frac{1}{3}

9. 713+913\frac{7}{13} + \frac{9}{13}

  • Add the numerators: 7+913=1613\frac{7 + 9}{13} = \frac{16}{13} This is an improper fraction, and can be written as: 13131 \frac{3}{13}

Would you like more details or explanations on any of the steps?

Here are 5 related questions to extend this topic:

  1. How do you add fractions with different denominators?
  2. How can you simplify an improper fraction?
  3. What is the process for converting a mixed number back to an improper fraction?
  4. Why is finding the least common denominator important when adding fractions?
  5. What are some tips for simplifying complex fractions?

Tip: When adding or subtracting fractions, always check if the resulting fraction can be simplified for a cleaner final answer!

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Math Problem Analysis

Mathematical Concepts

Addition of Fractions
Subtraction of Fractions
Fraction Simplification
Improper Fractions

Formulas

When adding fractions with the same denominator: \( \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} \)
When subtracting fractions with the same denominator: \( \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \)

Theorems

Fraction Arithmetic

Suitable Grade Level

Grades 5-7