Solve: 1/2 - 1/6 - 3/12 Fraction Subtraction Problem

Question

Solve the following exercise:

1216312=? \frac{1}{2}-\frac{1}{6}-\frac{3}{12}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply by 6, by 2 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:22 Let's calculate the multiplications
00:28 Subtract under the common denominator
00:32 Let's calculate the numerator
00:43 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to subtract three fractions: 1216312\frac{1}{2} - \frac{1}{6} - \frac{3}{12}.

First, let's find the least common denominator (LCD) for the fractions. The denominators are 2, 6, and 12. The smallest number that all these denominators divide evenly into is 12, so the LCD is 12.

Next, convert each fraction to have 12 as the denominator:

  • 12=1×62×6=612\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
  • 16=1×26×2=212\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
  • 312\frac{3}{12} is already with denominator 12

Now, perform the subtraction using these equivalent fractions:

612212312\frac{6}{12} - \frac{2}{12} - \frac{3}{12}

Subtract the fractions in sequence while keeping the common denominator:

612212=412\frac{6}{12} - \frac{2}{12} = \frac{4}{12}

Then, 412312=112\frac{4}{12} - \frac{3}{12} = \frac{1}{12}

The fraction 112\frac{1}{12} is already in its simplest form.

Therefore, the solution to the problem is 112\frac{1}{12}.

Answer

112 \frac{1}{12}