Subtracting Fractions with Unlike Denominators Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Compute 1112−38−16\frac{11}{12} - \frac{3}{8} - \frac{1}{6}.

Solution

  1. 1
    Find the LCD of 12,8,612, 8, 6: LCD=24\text{LCD} = 24.
  2. 2
    Convert: 1112=2224\frac{11}{12} = \frac{22}{24}, 38=924\frac{3}{8} = \frac{9}{24}, 16=424\frac{1}{6} = \frac{4}{24}.
  3. 3
    Subtract in order: 2224−924−424=22−9−424=924\frac{22}{24} - \frac{9}{24} - \frac{4}{24} = \frac{22 - 9 - 4}{24} = \frac{9}{24}.
  4. 4
    Simplify: gcd⁡(9,24)=3\gcd(9, 24) = 3, so 924=38\frac{9}{24} = \frac{3}{8}.

Answer

38\frac{3}{8}
When subtracting three or more unlike fractions, find a single LCD for all of them, convert each, then combine all numerators in one step. Simplify the result by dividing by the GCD.

About Subtracting Fractions with Unlike Denominators

Subtracting fractions with different denominators by first rewriting them with a common denominator, then subtracting numerators.

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More Subtracting Fractions with Unlike Denominators Examples

Example 1 easy

Subtract [formula].

Example 2 medium

A runner completed [formula] of a race, then stopped. If the race is [formula] km long, what fractio

Example 3 easy

Compute [formula].

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