Solve: Adding Fractions 3/4 + 1/6 Step by Step

Question

34+16= \frac{3}{4}+\frac{1}{6}=

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the least common denominator
00:06 We'll multiply each fraction by 3 and 2 respectively, to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:22 Let's calculate the products
00:27 Add under the common denominator
00:33 Calculate the numerator
00:36 And this is the solution to the question

Step-by-Step Solution

To solve the problem of adding the fractions 34\frac{3}{4} and 16\frac{1}{6}, we need to find a common denominator.

  • Step 1: Find the LCM of the denominators:
    The denominators are 4 and 6. The LCM of 4 and 6 is 12.
  • Step 2: Convert each fraction to have the common denominator:
    - Convert 34\frac{3}{4} to an equivalent fraction with a denominator of 12. To do this, multiply both the numerator and the denominator by 3:
    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}.
    - Convert 16\frac{1}{6} to an equivalent fraction with a denominator of 12. Multiply both the numerator and the denominator by 2:
    16=1×26×2=212\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}.
  • Step 3: Add the fractions:
    Now that both fractions have the same denominator, add the numerators:
    912+212=1112\frac{9}{12} + \frac{2}{12} = \frac{11}{12}.
  • Step 4: Simplify if necessary:
    The fraction 1112\frac{11}{12} is already in its simplest form.

Therefore, the solution to the problem 34+16\frac{3}{4} + \frac{1}{6} is 1112\frac{11}{12}.

Answer

1112 \frac{11}{12}