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