What is 3/5 + 4/7?
Calculate 3/5 + 4/7 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
3/5 + 4/7 = \frac{41}{35}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 3/5 and 4/7
To add fractions, they must have the same denominator (bottom number).
\frac{3}{5} + \frac{4}{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 3/5 to get denominator of 35:
Multiply both top and bottom by 7
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
Step 4
Convert Second Fraction
Multiply 4/7 to get denominator of 35:
Multiply both top and bottom by 5
\frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
Step 5
Add the Fractions
Now both fractions have the same denominator (35).
Add the numerators: 21 + 20 = 41
\frac{21}{35} + \frac{20}{35} = \frac{21 + 20}{35} = \frac{41}{35}
Step 6
Convert to Mixed Number
Since 41 > 35, we can write this as a mixed number.
41 ÷ 35 = 1 remainder 6
\frac{41}{35} = 1\frac{6}{35}