What is 4/5 + 1/2?
Calculate 4/5 + 1/2 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
4/5 + 1/2 = \frac{13}{10}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 4/5 and 1/2
To add fractions, they must have the same denominator (bottom number).
\frac{4}{5} + \frac{1}{2} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (5 and 2), so we need to find a common denominator.
The LCD is the smallest number that both 5 and 2 divide into evenly.
LCD = 5 × 2 = 10
\text{LCD}(5, 2) = 10
Step 3
Convert First Fraction
Multiply 4/5 to get denominator of 10:
Multiply both top and bottom by 2
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
Step 4
Convert Second Fraction
Multiply 1/2 to get denominator of 10:
Multiply both top and bottom by 5
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
Step 5
Add the Fractions
Now both fractions have the same denominator (10).
Add the numerators: 8 + 5 = 13
\frac{8}{10} + \frac{5}{10} = \frac{8 + 5}{10} = \frac{13}{10}
Step 6
Convert to Mixed Number
Since 13 > 10, we can write this as a mixed number.
13 ÷ 10 = 1 remainder 3
\frac{13}{10} = 1\frac{3}{10}