What is 3/4 + 2/3?
Calculate 3/4 + 2/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
3/4 + 2/3 = \frac{17}{12}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 3/4 and 2/3
To add fractions, they must have the same denominator (bottom number).
\frac{3}{4} + \frac{2}{3} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (4 and 3), so we need to find a common denominator.
The LCD is the smallest number that both 4 and 3 divide into evenly.
LCD = 4 × 3 = 12
\text{LCD}(4, 3) = 12
Step 3
Convert First Fraction
Multiply 3/4 to get denominator of 12:
Multiply both top and bottom by 3
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
Step 4
Convert Second Fraction
Multiply 2/3 to get denominator of 12:
Multiply both top and bottom by 4
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
Step 5
Add the Fractions
Now both fractions have the same denominator (12).
Add the numerators: 9 + 8 = 17
\frac{9}{12} + \frac{8}{12} = \frac{9 + 8}{12} = \frac{17}{12}
Step 6
Convert to Mixed Number
Since 17 > 12, we can write this as a mixed number.
17 ÷ 12 = 1 remainder 5
\frac{17}{12} = 1\frac{5}{12}