To subtract fractions with different denominators, follow these steps:
- Find the Least Common Denominator (LCD):
Identify the smallest number that both denominators can divide into evenly. This is often the least common multiple (LCM) of the denominators. For example, for denominators 4 and 3, the LCD is 12
- Rewrite Each Fraction with the LCD:
Convert each fraction to an equivalent fraction with the LCD as the new denominator. Multiply the numerator and denominator of each fraction by the number needed to get the LCD. For example, to convert 34\frac{3}{4}43 to a denominator of 12, multiply numerator and denominator by 3 to get 912\frac{9}{12}129
- Subtract the Numerators:
Once the fractions have the same denominator, subtract the numerators and keep the denominator the same. For example, 912−812=112\frac{9}{12}-\frac{8}{12}=\frac{1}{12}129−128=121
- Simplify the Resulting Fraction (if needed):
Reduce the fraction to its simplest form by dividing numerator and denominator by their greatest common divisor
Example:
Subtract 34−23\frac{3}{4}-\frac{2}{3}43−32:
- Find LCD of 4 and 3: 12
- Convert fractions: 34=912\frac{3}{4}=\frac{9}{12}43=129, 23=812\frac{2}{3}=\frac{8}{12}32=128
- Subtract numerators: 9−8=19-8=19−8=1
- Result: 112\frac{1}{12}121
Alternatively, you can use the cross-multiplication method:
- Multiply numerator of first fraction by denominator of second: 3×3=93\times 3=93×3=9
- Multiply numerator of second fraction by denominator of first: 2×4=82\times 4=82×4=8
- Subtract these results: 9−8=19-8=19−8=1
- Multiply denominators: 4×3=124\times 3=124×3=12
- Result: 112\frac{1}{12}121
Both methods yield the same answer. This process works for any fractions with different denominators
