Compare Fractions

Grade 5 Math – Notes & Formulae

Graph & Compare Fractions on Number Lines

• Draw (or imagine) a number line from 0 to 1 (or beyond for larger fractions).
• Divide into equal parts: Denominator = number of parts.
• Count from 0 for numerator’s position.
• Fractions further to the right are greater.
• Example: Compare \(\frac{3}{4}\) and \(\frac{2}{3}\); place both on the same line. The one closer to 1 is larger.

Compare Fractions Using Benchmarks

• Benchmarks are familiar reference values like 0, \(\frac{1}{2}\), and 1.
• Compare each fraction to \(\frac{1}{2}\) or 1 to see which is closer or bigger/smaller.
• Example: \(\frac{5}{8} > \frac{1}{2}\) since \(5>4\) for denominator 8.
  \(\frac{3}{8} < \frac{1}{2}\).

Compare Fractions & Mixed Numbers

• If denominators are the same, compare numerators.
• If denominators differ, find common denominator (usually LCD) or cross-multiply.
• Cross-multiply: For \(\frac{a}{b}\) vs. \(\frac{c}{d}\), compare \(ad\) and \(bc\):
  If \(a \times d > c \times b\), then \(\frac{a}{b} > \frac{c}{d}\)
• Convert mixed numbers to improper if needed.
• Example: Compare \(\frac{3}{5}\) and \(\frac{2}{3}\): \(3\times3=9\), \(5\times2=10\), so \(9 < 10\) → \(\frac{3}{5} < \frac{2}{3}\)
• For mixed numbers, compare whole parts first.

Put Fractions in Order

• Find common denominators (LCD), rewrite each fraction, then compare numerators.
• Alternatively, convert each to decimal (divide numerator by denominator) for fast ordering.
• Order from least to greatest or vice versa as needed.
• Example: \(\frac{1}{4}, \frac{3}{8}, \frac{2}{5}\) → LCD is 40:
  \(\frac{10}{40}, \frac{15}{40}, \frac{16}{40}\) → Order: \(\frac{1}{4} < \frac{3}{8} < \frac{2}{5}\)

Quick Reference

• On a number line, further right = bigger fraction.
• Use benchmarks like 0, \(\frac{1}{2}\), 1.
• Cross-multiply to compare when denominators are different.
• Use LCD to make denominators match for comparing and ordering.
• With mixed numbers, compare whole part first, then fraction.
• Decimals are a handy comparison tool for tricky fractions!