What is 1/2 + 2/3?
Calculate 1/2 + 2/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
1/2 + 2/3 = \frac{7}{6}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 1/2 and 2/3
To add fractions, they must have the same denominator (bottom number).
\frac{1}{2} + \frac{2}{3} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (2 and 3), so we need to find a common denominator.
The LCD is the smallest number that both 2 and 3 divide into evenly.
LCD = 2 × 3 = 6
\text{LCD}(2, 3) = 6
Step 3
Convert First Fraction
Multiply 1/2 to get denominator of 6:
Multiply both top and bottom by 3
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
Step 4
Convert Second 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 5
Add the Fractions
Now both fractions have the same denominator (6).
Add the numerators: 3 + 4 = 7
\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}
Step 6
Convert to Mixed Number
Since 7 > 6, we can write this as a mixed number.
7 ÷ 6 = 1 remainder 1
\frac{7}{6} = 1\frac{1}{6}