What is 2/3 + 1/6?
Calculate 2/3 + 1/6 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
2/3 + 1/6 = \frac{5}{6}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 2/3 and 1/6
To add fractions, they must have the same denominator (bottom number).
\frac{2}{3} + \frac{1}{6} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (3 and 6), so we need to find a common denominator.
The LCD is the smallest number that both 3 and 6 divide into evenly.
Since GCD(3, 6) = 3, we calculate LCD = (3 × 6) ÷ 3 = 6
\text{LCD}(3, 6) = 6
Step 3
Convert First Fraction
Multiply 2/3 to get denominator of 6:
Multiply both top and bottom by 2
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
Step 4
Convert Second Fraction
Multiply 1/6 to get denominator of 6:
Multiply both top and bottom by 1
\frac{1}{6} = \frac{1 \times 1}{6 \times 1} = \frac{1}{6}
Step 5
Add the Fractions
Now both fractions have the same denominator (6).
Add the numerators: 4 + 1 = 5
\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}