To reduce a fraction, divide the top and bottom by the same number until you cannot any more, so the only common factor left is 1. This is called putting the fraction into simplest form.

What “reduce a fraction” means

  • A fraction is reduced (simplified) when the numerator and denominator are as small as possible but the value stays the same, for example 46=23\tfrac{4}{6}=\tfrac{2}{3}64​=32​.
  • Fractions like 23\tfrac{2}{3}32​ or 1128\tfrac{11}{28}2811​ are already reduced, because you cannot divide both numbers by a common factor bigger than 1.

Quick method: use the Greatest Common Factor (GCF)

Idea: Find the largest number that divides both the top and bottom, then divide by it once.

  1. List factors of the numerator (top number).
  2. List factors of the denominator (bottom number).
  3. Find the greatest common factor (GCF).
  4. Divide numerator and denominator by that GCF.

Example: Reduce 2050\tfrac{20}{50}5020​.

  • Factors of 20: 1, 2, 4, 5, 10, 20.
  • Factors of 50: 1, 2, 5, 10, 25, 50.
  • GCF is 10.
  • Divide top and bottom by 10: 20÷10=220\div 10=220÷10=2, 50÷10=550\div 10=550÷10=5, so 2050=25\tfrac{20}{50}=\tfrac{2}{5}5020​=52​.

You can think of it like “shrinking” the fraction in one step using the biggest possible number.

Step‑by‑step method: divide by any common factor

If the GCF is hard to see, you can reduce in smaller steps.

  1. Look for a small number (like 2, 3, 5) that divides both numerator and denominator.
  2. Divide both by that number.
  3. Repeat until there is no common factor greater than 1.

Example: Reduce 1664\tfrac{16}{64}6416​.

  • Both 16 and 64 are even → divide by 2: 1664=832\tfrac{16}{64}=\tfrac{8}{32}6416​=328​.
  • Still even → divide by 2: 832=416\tfrac{8}{32}=\tfrac{4}{16}328​=164​.
  • Still even → divide by 2: 416=28\tfrac{4}{16}=\tfrac{2}{8}164​=82​.
  • Still even → divide by 2: 28=14\tfrac{2}{8}=\tfrac{1}{4}82​=41​.
  • Now 1 and 4 have no common factor larger than 1, so 14\tfrac{1}{4}41​ is in simplest form.

This does the same as dividing by the GCF (which here is 16), just in several small steps.

Prime factorization trick

This is more systematic and helps you see all common factors.

  1. Break the numerator into prime factors.
  2. Break the denominator into prime factors.
  3. Cross out any prime factors that appear in both.
  4. Multiply what’s left on top and bottom; that new fraction is reduced.

Example: Reduce 1230\tfrac{12}{30}3012​.

  • 12=2×2×312=2\times 2\times 312=2×2×3.
  • 30=2×3×530=2\times 3\times 530=2×3×5.
  • Cancel common primes: cross out one 2 and one 3 from top and bottom.
  • Left with 25\tfrac{2}{5}52​, so 1230=25\tfrac{12}{30}=\tfrac{2}{5}3012​=52​.

This method makes it very clear which factors are shared.

Improper and mixed fractions

The reducing idea is the same; sometimes you just convert forms:

  • To reduce a mixed number, first turn it into an improper fraction using
    (whole×denominator)+numeratordenominator\tfrac{(\text{whole}\times \text{denominator})+\text{numerator}}{\text{denominator}}denominator(whole×denominator)+numerator​, then simplify.
  • To “finish” an improper fraction after simplifying, you can turn it back into a mixed number if you want.

Example: Reduce 2682\tfrac{6}{8}286​.

  • Convert: 268=(2×8)+68=2282\tfrac{6}{8}=\tfrac{(2\times 8)+6}{8}=\tfrac{22}{8}286​=8(2×8)+6​=822​.
  • Reduce 228\tfrac{22}{8}822​: GCF of 22 and 8 is 2 → 228=114\tfrac{22}{8}=\tfrac{11}{4}822​=411​.
  • Optionally: 114=234\tfrac{11}{4}=2\tfrac{3}{4}411​=243​.

Tiny checklist you can memorize

When you see a fraction and want to reduce it:

  • Check if both numbers are even → divide by 2.
  • Check divisibility by 3 (sum of digits is a multiple of 3).
  • Check for 5 (ends in 0 or 5).
  • Keep dividing top and bottom by any shared factor until no more work is possible.

If you want, send me a few fractions (like 18/24 or 45/60), and I can walk you through reducing them step by step.