Add & Subtract Mixed Numbers

Grade 5 Math – Complete Notes & Formulae

Estimate Sums & Differences

• Round each mixed number to nearest whole (ignore fraction part for quick estimate).
• Example: \(3\frac{3}{4} + 2\frac{1}{5} \approx 4 + 2 = 6\)
• Benchmarks: Use 0, \(\frac{1}{2}\), or 1 for fraction part to get closer estimates.

Add Mixed Numbers (Unlike Denominators)

• Add whole numbers together.
• Find the least common denominator (LCD) for the fractions. Rewrite both fractions using LCD.
• Add the fractions. If the result is improper (\(>\) 1), regroup by adding 1 to the whole number part.
• Simplify if needed.
• Example: \(2\frac{1}{3} + 3\frac{1}{4}:\)
  Whole: \(2 + 3 = 5\), LCD = 12.
  \(\frac{1}{3} = \frac{4}{12}\), \(\frac{1}{4} = \frac{3}{12}\)
  \(\frac{4}{12} + \frac{3}{12} = \frac{7}{12}\)
  Final: \(5\frac{7}{12}\)

Subtract Mixed Numbers (Unlike Denominators)

• Find LCD and rewrite both fractions.
• If the top fraction is too small, borrow 1 from the whole number.
• Subtract fractions, then subtract whole numbers.
• Combine and simplify.
• Example: \(5\frac{2}{5} - 2\frac{3}{4}\)
  LCD = 20.
  \(\frac{2}{5} = \frac{8}{20}\), \(\frac{3}{4} = \frac{15}{20}\)
  Not enough, so borrow 1 from 5 (\(4\)), \(\frac{8}{20} + \frac{20}{20} = \frac{28}{20}\)
  \(\frac{28}{20} - \frac{15}{20} = \frac{13}{20}\)
  \(4 - 2 = 2\), answer: \(2\frac{13}{20}\)

With or Without Regrouping

• Without regrouping: Fraction sum/difference ≤ 1, no need to adjust whole number.
• With regrouping: Fraction sum > 1, or need to borrow for subtraction. Adjust whole parts accordingly.
• Example: \(1\frac{3}{5} + 2\frac{4}{5} = 3\frac{7}{5} = 4\frac{2}{5}\) (since \(\frac{7}{5} = 1\frac{2}{5}\))

Word Problems & Recipes

• Identify action (add/subtract). Convert all mixed numbers to improper, find LCD, solve, then simplify as mixed number if needed.
• For multi-step: solve each operation in order, simplify after each.
• Example: A recipe calls for \(2\frac{3}{4}\) cups + \(1\frac{2}{3}\) cups.
  Improper: \(\frac{11}{4}\) + \(\frac{5}{3}\). LCD 12: \(\frac{33}{12} + \frac{20}{12} = \frac{53}{12} = 4\frac{5}{12}\)

Complete Sentences & Compare Sums/Differences

• Solve for missing values using inverse operations (subtract/add as needed).
• To compare, solve both mixed number calculations first, then compare results (whole part first, fractions next).

Quick Reference

• Estimate by rounding mixed numbers to whole numbers.
• Always find LCD for fractional parts before combining.
• Add/subtract whole number and fraction parts separately.
• Regroup (borrow) if the top fraction is smaller when subtracting.
• Simplify and convert answers to mixed numbers as needed.
• Check for reasonableness after solving.