What is 3/5 + 2/3?
Calculate 3/5 + 2/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
3/5 + 2/3 = \frac{19}{15}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 3/5 and 2/3
To add fractions, they must have the same denominator (bottom number).
\frac{3}{5} + \frac{2}{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 3/5 to get denominator of 15:
Multiply both top and bottom by 3
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
Step 4
Convert Second 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 5
Add the Fractions
Now both fractions have the same denominator (15).
Add the numerators: 9 + 10 = 19
\frac{9}{15} + \frac{10}{15} = \frac{9 + 10}{15} = \frac{19}{15}
Step 6
Convert to Mixed Number
Since 19 > 15, we can write this as a mixed number.
19 ÷ 15 = 1 remainder 4
\frac{19}{15} = 1\frac{4}{15}