What is 2/3 + 4/5?
Calculate 2/3 + 4/5 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
2/3 + 4/5 = \frac{22}{15}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 2/3 and 4/5
To add fractions, they must have the same denominator (bottom number).
\frac{2}{3} + \frac{4}{5} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (3 and 5), so we need to find a common denominator.
The LCD is the smallest number that both 3 and 5 divide into evenly.
LCD = 3 × 5 = 15
\text{LCD}(3, 5) = 15
Step 3
Convert First Fraction
Multiply 2/3 to get denominator of 15:
Multiply both top and bottom by 5
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
Step 4
Convert Second Fraction
Multiply 4/5 to get denominator of 15:
Multiply both top and bottom by 3
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
Step 5
Add the Fractions
Now both fractions have the same denominator (15).
Add the numerators: 10 + 12 = 22
\frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15}
Step 6
Convert to Mixed Number
Since 22 > 15, we can write this as a mixed number.
22 ÷ 15 = 1 remainder 7
\frac{22}{15} = 1\frac{7}{15}