Math Problem Statement

Uploaded worksheet with addition and subtraction of fractions, including mixed numbers and improper fractions.

Solution

It seems you've uploaded an image with fractions and operations for addition and subtraction. Let me analyze the content and provide solutions for the problems.


ADD THE FRACTIONS (Upper Section):

1. 15+35\frac{1}{5} + \frac{-3}{5}

  • Combine numerators: 1+(3)=21 + (-3) = -2.
  • Denominator remains the same: 55.
  • Result: 25\frac{-2}{5}.

2. 34+14\frac{3}{4} + \frac{-1}{4}

  • Combine numerators: 3+(1)=23 + (-1) = 2.
  • Denominator remains the same: 44.
  • Simplify: 24=12\frac{2}{4} = \frac{1}{2}.
  • Result: 12\frac{1}{2}.

3. 612+1112\frac{6}{12} + \frac{-11}{12}

  • Combine numerators: 6+(11)=56 + (-11) = -5.
  • Denominator remains the same: 1212.
  • Result: 512\frac{-5}{12}.

4. 18+58\frac{1}{8} + \frac{-5}{8}

  • Combine numerators: 1+(5)=41 + (-5) = -4.
  • Denominator remains the same: 88.
  • Simplify: 48=12\frac{-4}{8} = \frac{-1}{2}.
  • Result: 12\frac{-1}{2}.

5. 165+45\frac{-16}{5} + \frac{-4}{5}

  • Combine numerators: 16+(4)=20-16 + (-4) = -20.
  • Denominator remains the same: 55.
  • Simplify: 205=4\frac{-20}{5} = -4.
  • Result: 4-4.

6. 710+210\frac{-7}{10} + \frac{-2}{10}

  • Combine numerators: 7+(2)=9-7 + (-2) = -9.
  • Denominator remains the same: 1010.
  • Result: 910\frac{-9}{10}.

SUBTRACT THE FRACTIONS (Lower Section):

When rewriting subtraction as addition, you change the sign of the second fraction.

7. 2132232 \frac{1}{3} - 2 \frac{2}{3}

  • Rewrite as: 213+(223)2 \frac{1}{3} + (-2 \frac{2}{3}).
  • Convert to improper fractions:
    • 213=732 \frac{1}{3} = \frac{7}{3}.
    • 223=832 \frac{2}{3} = \frac{8}{3}.
  • Combine: 73+83=13\frac{7}{3} + \frac{-8}{3} = \frac{-1}{3}.
  • Result: 13\frac{-1}{3}.

8. 38(58)\frac{-3}{8} - \left(\frac{-5}{8}\right)

  • Rewrite as: 38+58\frac{-3}{8} + \frac{5}{8}.
  • Combine numerators: 3+5=2-3 + 5 = 2.
  • Denominator remains the same: 88.
  • Simplify: 28=14\frac{2}{8} = \frac{1}{4}.
  • Result: 14\frac{1}{4}.

9. 12312\frac{-1}{2} - 3 \frac{1}{2}

  • Rewrite as: 12+(312)\frac{-1}{2} + (-3 \frac{1}{2}).
  • Convert to improper fractions:
    • 312=723 \frac{1}{2} = \frac{7}{2}.
  • Combine: 12+72=82=4\frac{-1}{2} + \frac{-7}{2} = \frac{-8}{2} = -4.
  • Result: 4-4.

10. 54134\frac{5}{4} - \frac{13}{4}

  • Rewrite as: 54+134\frac{5}{4} + \frac{-13}{4}.
  • Combine numerators: 5+(13)=85 + (-13) = -8.
  • Denominator remains the same: 44.
  • Simplify: 84=2\frac{-8}{4} = -2.
  • Result: 2-2.

11. 4172174 \frac{1}{7} - 2 \frac{1}{7}

  • Rewrite as: 417+(217)4 \frac{1}{7} + (-2 \frac{1}{7}).
  • Convert to improper fractions:
    • 417=2974 \frac{1}{7} = \frac{29}{7}.
    • 217=1572 \frac{1}{7} = \frac{15}{7}.
  • Combine: 297+157=147=2\frac{29}{7} + \frac{-15}{7} = \frac{14}{7} = 2.
  • Result: 22.

12. 56126\frac{5}{6} - \frac{12}{6}

  • Rewrite as: 56+126\frac{5}{6} + \frac{-12}{6}.
  • Combine numerators: 5+(12)=75 + (-12) = -7.
  • Denominator remains the same: 66.
  • Result: 76\frac{-7}{6}.

Do you want more explanations or details about any step?

Related Questions:

  1. How do you simplify improper fractions into mixed numbers?
  2. Why do fractions need a common denominator for addition or subtraction?
  3. What are the steps to rewrite subtraction problems as addition?
  4. How can fractions with negative numerators be interpreted on a number line?
  5. How do you convert between mixed numbers and improper fractions?

Tip:

Always double-check your work by simplifying fractions to their lowest terms!

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Math Problem Analysis

Mathematical Concepts

Addition of Fractions
Subtraction of Fractions
Mixed Numbers
Improper Fractions
Simplification of Fractions

Formulas

a/b + c/b = (a + c)/b
a/b - c/b = (a - c)/b
Mixed number to improper fraction: whole * denominator + numerator

Theorems

Fractions with like denominators can be added or subtracted by combining numerators.
Rewriting subtraction as addition of the opposite sign.

Suitable Grade Level

Grades 5-7