Add & Subtract Fractions | 5th Grade Math

Add & Subtract Fractions

Grade 5 Math – Notes & Formulae

Estimate Sums & Differences Using Benchmarks

  • Round fractions to benchmarks like 0, \(\frac{1}{2}\), or 1 to make calculation easier.
  • Example: Estimate \(\frac{5}{8} + \frac{1}{3}\):
    \(\frac{5}{8} \approx 1\), \(\frac{1}{3} \approx \frac{1}{2}\):
    Estimated sum: \(1 + \frac{1}{2} = \frac{3}{2}\) or 1.5.
Tip: Benchmarks help quickly check if your answer is reasonable!

Add Fractions With Unlike Denominators

  • Find the least common denominator (LCD).
  • Convert: Rewrite each fraction as an equivalent fraction with LCD.
  • Add numerators, keep denominator the same.
  • Example: \(\frac{1}{3} + \frac{1}{4}\)
    LCD is 12.
    \(\frac{1}{3} = \frac{4}{12}\), \(\frac{1}{4} = \frac{3}{12}\)
    Sum: \(\frac{4+3}{12} = \frac{7}{12}\)
  • Models: Use pictures/diagrams to show both fractions as parts of the same-sized whole.
Formula: \( \frac{a}{m} + \frac{b}{n} = \frac{a\cdot x}{lcd} + \frac{b\cdot y}{lcd} = \frac{a\cdot x + b\cdot y}{lcd} \)
where lcd = least common denominator, \( x = \frac{lcd}{m} \), \( y = \frac{lcd}{n} \)

Subtract Fractions With Unlike Denominators

  • Same steps as addition, but subtract numerators.
  • Example: \(\frac{5}{6} - \frac{1}{4}\)
    LCD is 12.
    \(\frac{5}{6} = \frac{10}{12}\), \(\frac{1}{4} = \frac{3}{12}\)
    Difference: \(\frac{10-3}{12} = \frac{7}{12}\)
  • Use area/length models for subtraction when visual support helps.
Formula: \( \frac{a}{m} - \frac{b}{n} = \frac{a\cdot x - b\cdot y}{lcd} \)

Word Problems & Adding 3 or More Fractions

  • Convert all fractions to the LCD, then add/subtract step by step.
  • For 3 or more fractions: Find a common denominator for all; add numerators.
  • Example: \(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}\)
    LCD = 12:
    \(\frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12} = 1\frac{1}{12}\)
  • In word problems, identify the action (add or subtract) and key information before solving.

Complete Sentences & Compare Sums/Differences

  • Fill missing numbers: Use inverse operations to find missing addends/minuends.
  • Example: \( \frac{a}{b} + \frac{?}{d} = \frac{c}{lcd} \) ⇒ Find ? that makes equation true.
  • To compare, subtract or use benchmarks/LCD; the bigger result is greater.

Quick Reference

  • Estimate answers with benchmarks.
  • Find LCD to add/subtract unlike denominators.
  • Add/subtract numerators, keep denominator the same.
  • Simplify fractions if possible.
  • For 3+ fractions, make all denominators match then combine.
  • Visual models help clarify addition/subtraction steps!
Tip: Always check for lowest terms and use estimation to spot errors.