What is 7/8 + 1/2?
Calculate 7/8 + 1/2 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
7/8 + 1/2 = \frac{11}{8}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 7/8 and 1/2
To add fractions, they must have the same denominator (bottom number).
\frac{7}{8} + \frac{1}{2} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (8 and 2), so we need to find a common denominator.
The LCD is the smallest number that both 8 and 2 divide into evenly.
Since GCD(8, 2) = 2, we calculate LCD = (8 × 2) ÷ 2 = 8
\text{LCD}(8, 2) = 8
Step 3
Convert First Fraction
Multiply 7/8 to get denominator of 8:
Multiply both top and bottom by 1
\frac{7}{8} = \frac{7 \times 1}{8 \times 1} = \frac{7}{8}
Step 4
Convert Second Fraction
Multiply 1/2 to get denominator of 8:
Multiply both top and bottom by 4
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
Step 5
Add the Fractions
Now both fractions have the same denominator (8).
Add the numerators: 7 + 4 = 11
\frac{7}{8} + \frac{4}{8} = \frac{7 + 4}{8} = \frac{11}{8}
Step 6
Convert to Mixed Number
Since 11 > 8, we can write this as a mixed number.
11 ÷ 8 = 1 remainder 3
\frac{11}{8} = 1\frac{3}{8}