Solve the Fraction Equation: 1/2 - 1/8 - 1/4 Step-by-Step

Question

Solve the following exercise:

121814=? \frac{1}{2}-\frac{1}{8}-\frac{1}{4}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the smallest common denominator
00:06 Therefore multiply 4, 2 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:21 Let's calculate the multiplications
00:31 Subtract under the common denominator
00:36 Let's calculate the numerator
00:39 Reduce the fraction as much as possible
00:42 Remember to divide both numerator and denominator
00:45 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Find the least common denominator of the fractions involved.
  • Step 2: Rewrite each fraction using this common denominator.
  • Step 3: Subtract the fractions sequentially.

Now, let's work through each step:

First, we determine the least common denominator (LCD) of the fractions 12 \frac{1}{2} , 18 \frac{1}{8} , and 14 \frac{1}{4} . The denominators are 2, 8, and 4. The least common multiple of these numbers is 8. Thus, the LCD is 8.

Next, we rewrite each fraction with the common denominator of 8:

  • 12=48\frac{1}{2} = \frac{4}{8}
  • 18=18\frac{1}{8} = \frac{1}{8}
  • 14=28\frac{1}{4} = \frac{2}{8}

Now, we perform the subtraction:

121814=481828\frac{1}{2} - \frac{1}{8} - \frac{1}{4} = \frac{4}{8} - \frac{1}{8} - \frac{2}{8}

First, subtract 18\frac{1}{8} from 48\frac{4}{8}:

4818=38 \frac{4}{8} - \frac{1}{8} = \frac{3}{8}

Then, subtract 28\frac{2}{8} from 38\frac{3}{8}:

3828=18 \frac{3}{8} - \frac{2}{8} = \frac{1}{8}

Therefore, the solution to the problem is 18\frac{1}{8}.

Answer

18 \frac{1}{8}