What is 2/5 + 3/7?
Calculate 2/5 + 3/7 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
2/5 + 3/7 = \frac{29}{35}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 2/5 and 3/7
To add fractions, they must have the same denominator (bottom number).
\frac{2}{5} + \frac{3}{7} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (5 and 7), so we need to find a common denominator.
The LCD is the smallest number that both 5 and 7 divide into evenly.
LCD = 5 × 7 = 35
\text{LCD}(5, 7) = 35
Step 3
Convert First Fraction
Multiply 2/5 to get denominator of 35:
Multiply both top and bottom by 7
\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}
Step 4
Convert Second Fraction
Multiply 3/7 to get denominator of 35:
Multiply both top and bottom by 5
\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}
Step 5
Add the Fractions
Now both fractions have the same denominator (35).
Add the numerators: 14 + 15 = 29
\frac{14}{35} + \frac{15}{35} = \frac{14 + 15}{35} = \frac{29}{35}