What is 5/6 + 3/4?
Calculate 5/6 + 3/4 with a complete step-by-step solution. Learn how to add fractions and understand the process.
Answer:
5/6 + 3/4 = \frac{19}{12}
Step-by-Step Solution
Step 1
Identify the Fractions
We need to add two fractions: 5/6 and 3/4
To add fractions, they must have the same denominator (bottom number).
\frac{5}{6} + \frac{3}{4} = ?
Step 2
Find the Least Common Denominator (LCD)
The denominators are different (6 and 4), so we need to find a common denominator.
The LCD is the smallest number that both 6 and 4 divide into evenly.
Since GCD(6, 4) = 2, we calculate LCD = (6 × 4) ÷ 2 = 12
\text{LCD}(6, 4) = 12
Step 3
Convert First Fraction
Multiply 5/6 to get denominator of 12:
Multiply both top and bottom by 2
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
Step 4
Convert Second Fraction
Multiply 3/4 to get denominator of 12:
Multiply both top and bottom by 3
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
Step 5
Add the Fractions
Now both fractions have the same denominator (12).
Add the numerators: 10 + 9 = 19
\frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12}
Step 6
Convert to Mixed Number
Since 19 > 12, we can write this as a mixed number.
19 ÷ 12 = 1 remainder 7
\frac{19}{12} = 1\frac{7}{12}