Solve the Expression: 6/7 - 1/2 + 3/14 Step by Step

Question

Solve the following exercise:

6712+314=? \frac{6}{7}-\frac{1}{2}+\frac{3}{14}=\text{?}

Video Solution

Solution Steps

00:00 Solution
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply by 2 and 7 respectively for the common denominator 14
00:10 Remember to multiply both numerator and denominator
00:20 Let's calculate the multiplications
00:30 Add under common denominator
00:37 Calculate the numerator, one operation at a time
00:43 And this is the solution to the question

Step-by-Step Solution

To solve the expression 6712+314 \frac{6}{7} - \frac{1}{2} + \frac{3}{14} , we will follow these steps:

  • Step 1: Find a common denominator for the fractions.
  • Step 2: Convert each fraction to the common denominator.
  • Step 3: Perform the subtraction and addition as required.
  • Step 4: Simplify the result, if possible.

Let's work through the steps:

Step 1: The denominators are 7, 2, and 14. The least common multiple (LCM) of these numbers is 14.

Step 2: Convert each fraction:

  • 67 \frac{6}{7} becomes 6×27×2=1214 \frac{6 \times 2}{7 \times 2} = \frac{12}{14} .
  • 12 \frac{1}{2} becomes 1×72×7=714 \frac{1 \times 7}{2 \times 7} = \frac{7}{14} .
  • 314 \frac{3}{14} is already in the correct form as 314 \frac{3}{14} .

Step 3: Perform the operations:

  • Subtract: 1214714=514 \frac{12}{14} - \frac{7}{14} = \frac{5}{14} .
  • Add: 514+314=814 \frac{5}{14} + \frac{3}{14} = \frac{8}{14} .

Step 4: Simplify the fraction if possible. Here, 814 \frac{8}{14} simplifies to 47 \frac{4}{7} ; however, since the given choices list 814 \frac{8}{14} and it matches, there is no need for further simplification within the context of this question.

Therefore, the solution to the problem is 814 \frac{8}{14} .

Answer

814 \frac{8}{14}