What is 3/4 + 3/8?
Calculate 3/4 + 3/8 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
3/4 + 3/8 = \frac{9}{8}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 3/4 and 3/8
To add fractions, they must have the same denominator (bottom number).
\frac{3}{4} + \frac{3}{8} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (4 and 8), so we need to find a common denominator.
The LCD is the smallest number that both 4 and 8 divide into evenly.
Since GCD(4, 8) = 4, we calculate LCD = (4 × 8) ÷ 4 = 8
\text{LCD}(4, 8) = 8
Step 3
Convert First Fraction
Multiply 3/4 to get denominator of 8:
Multiply both top and bottom by 2
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
Step 4
Convert Second Fraction
Multiply 3/8 to get denominator of 8:
Multiply both top and bottom by 1
\frac{3}{8} = \frac{3 \times 1}{8 \times 1} = \frac{3}{8}
Step 5
Add the Fractions
Now both fractions have the same denominator (8).
Add the numerators: 6 + 3 = 9
\frac{6}{8} + \frac{3}{8} = \frac{6 + 3}{8} = \frac{9}{8}
Step 6
Convert to Mixed Number
Since 9 > 8, we can write this as a mixed number.
9 ÷ 8 = 1 remainder 1
\frac{9}{8} = 1\frac{1}{8}