What is 5/8 + 2/3?
Calculate 5/8 + 2/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
5/8 + 2/3 = \frac{31}{24}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 5/8 and 2/3
To add fractions, they must have the same denominator (bottom number).
\frac{5}{8} + \frac{2}{3} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (8 and 3), so we need to find a common denominator.
The LCD is the smallest number that both 8 and 3 divide into evenly.
LCD = 8 × 3 = 24
\text{LCD}(8, 3) = 24
Step 3
Convert First Fraction
Multiply 5/8 to get denominator of 24:
Multiply both top and bottom by 3
\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}
Step 4
Convert Second Fraction
Multiply 2/3 to get denominator of 24:
Multiply both top and bottom by 8
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
Step 5
Add the Fractions
Now both fractions have the same denominator (24).
Add the numerators: 15 + 16 = 31
\frac{15}{24} + \frac{16}{24} = \frac{15 + 16}{24} = \frac{31}{24}
Step 6
Convert to Mixed Number
Since 31 > 24, we can write this as a mixed number.
31 ÷ 24 = 1 remainder 7
\frac{31}{24} = 1\frac{7}{24}