What is 2/5 + 3/4?
Calculate 2/5 + 3/4 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
2/5 + 3/4 = \frac{23}{20}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 2/5 and 3/4
To add fractions, they must have the same denominator (bottom number).
\frac{2}{5} + \frac{3}{4} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (5 and 4), so we need to find a common denominator.
The LCD is the smallest number that both 5 and 4 divide into evenly.
LCD = 5 × 4 = 20
\text{LCD}(5, 4) = 20
Step 3
Convert First Fraction
Multiply 2/5 to get denominator of 20:
Multiply both top and bottom by 4
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
Step 4
Convert Second Fraction
Multiply 3/4 to get denominator of 20:
Multiply both top and bottom by 5
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
Step 5
Add the Fractions
Now both fractions have the same denominator (20).
Add the numerators: 8 + 15 = 23
\frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}
Step 6
Convert to Mixed Number
Since 23 > 20, we can write this as a mixed number.
23 ÷ 20 = 1 remainder 3
\frac{23}{20} = 1\frac{3}{20}