Solve: Adding Unit Fractions 1/18 + 1/6 Step-by-Step

Question

118+16= \frac{1}{18}+\frac{1}{6}=

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore multiply by 3, to get the common denominator 18
00:19 Calculate the multiplications
00:24 Add under the common denominator
00:30 Calculate the numerator
00:37 Reduce the fraction as much as possible
00:40 Remember to divide both numerator and denominator
00:43 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to add the fractions 118\frac{1}{18} and 16\frac{1}{6}:

Step 1: Find the least common denominator
The denominators are 18 and 6. The least common multiple of 18 and 6 is 18.

Step 2: Convert each fraction to have the least common denominator
The fraction 118\frac{1}{18} already has the denominator 18, so it remains 118\frac{1}{18}.
To convert 16\frac{1}{6} to a fraction with denominator 18, multiply both the numerator and denominator by 3: 1×36×3=318\frac{1 \times 3}{6 \times 3} = \frac{3}{18}.

Step 3: Add the converted fractions
Now that both fractions have the same denominator, add them:
118+318=1+318=418\frac{1}{18} + \frac{3}{18} = \frac{1 + 3}{18} = \frac{4}{18}.

Step 4: Simplify the resulting fraction
418\frac{4}{18} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
4÷218÷2=29\frac{4 \div 2}{18 \div 2} = \frac{2}{9}.

Therefore, the sum of 118\frac{1}{18} and 16\frac{1}{6} is 29\frac{2}{9}.

Answer

29 \frac{2}{9}