Fractions and Mixed Numbers

Grade 5 Math – Notes & Formulae

Fractions Review

• A fraction shows parts of a whole: \(\frac{a}{b}\) where “a” is the numerator, “b” is the denominator.
• Example: \(\frac{3}{5}\) means 3 out of 5 equal pieces.
• A mixed number has a whole part and a fraction part, e.g. \(2\frac{1}{3}\).
• An improper fraction has numerator ≥ denominator, e.g. \(\frac{7}{3}\).

Equivalent Fractions

• Fractions that name the same amount.
• Rule: Multiply/divide numerator & denominator by the same number.
• Example: \(\frac{2}{3} = \frac{4}{6}\) (multiply by 2)

Write Fractions in Lowest Terms

• Reduce by dividing numerator & denominator by GCF (greatest common factor).
• Example: \(\frac{12}{18} \rightarrow \frac{2}{3}\) after dividing by 6.

Convert Improper Fractions & Mixed Numbers

• Improper to Mixed: Divide numerator by denominator, quotient = whole number, remainder = numerator.
• Example: \(\frac{17}{5} = 3\frac{2}{5}\)
• Mixed to Improper: Multiply whole × denominator + numerator: \(a\frac{b}{c} = \frac{a \times c + b}{c}\)
• Example: \(2\frac{3}{4} = \frac{2\times4+3}{4} = \frac{11}{4}\)

Least Common Denominator (LCD)

• The LCD is the LCM of denominators.
• Find LCD to add/subtract fractions with unlike denominators.
• Example: LCD of 6 & 8? Multiples: 6,12,18,24... 8,16,24... So LCD = 24.

Round Mixed Numbers

• If fraction less than ½, round down to whole.
• If fraction ½ or more, round up to next whole.
• Example: \(3\frac{4}{5} \approx 4\) (because \(\frac{4}{5} > \frac{1}{2}\))

Reciprocals

• The reciprocal of \(\frac{a}{b}\) is \(\frac{b}{a}\).
• Multiplying a number by its reciprocal equals 1: \(\frac{a}{b} \times \frac{b}{a} = 1\)
• Important for division in fractions, finding "one whole".

Quick Reference

• Fraction: \(\frac{\text{part}}{\text{whole}}\); mixed number: whole + fraction.
• Equivalent: Mult./divide by same value.
• Lowest terms: Divide numerator and denominator by GCF.
• Improper ↔ Mixed: Convert using division/multiplication.
• LCD: Use for adding/subtracting fractions.
• Reciprocal: Flip numerator/denominator!
• Round: Fraction <½ round down, ≥½ round up.