What is 2/5 + 1/3?
Calculate 2/5 + 1/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
2/5 + 1/3 = \frac{11}{15}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 2/5 and 1/3
To add fractions, they must have the same denominator (bottom number).
\frac{2}{5} + \frac{1}{3} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (5 and 3), so we need to find a common denominator.
The LCD is the smallest number that both 5 and 3 divide into evenly.
LCD = 5 × 3 = 15
\text{LCD}(5, 3) = 15
Step 3
Convert First Fraction
Multiply 2/5 to get denominator of 15:
Multiply both top and bottom by 3
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
Step 4
Convert Second Fraction
Multiply 1/3 to get denominator of 15:
Multiply both top and bottom by 5
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
Step 5
Add the Fractions
Now both fractions have the same denominator (15).
Add the numerators: 6 + 5 = 11
\frac{6}{15} + \frac{5}{15} = \frac{6 + 5}{15} = \frac{11}{15}