What is 5/6 + 1/2?

Calculate 5/6 + 1/2 with a complete step-by-step solution. Learn how to add fractions and understand the process.

Answer: 5/6 + 1/2 = \frac{4}{3}

Step-by-Step Solution

Step 1 Identify the Fractions

We need to add two fractions: 5/6 and 1/2

To add fractions, they must have the same denominator (bottom number).

\frac{5}{6} + \frac{1}{2} = ?

Step 2 Find the Least Common Denominator (LCD)

The denominators are different (6 and 2), so we need to find a common denominator.

The LCD is the smallest number that both 6 and 2 divide into evenly.

Since GCD(6, 2) = 2, we calculate LCD = (6 × 2) ÷ 2 = 6

\text{LCD}(6, 2) = 6

Step 3 Convert First Fraction

Multiply 5/6 to get denominator of 6:

Multiply both top and bottom by 1

\frac{5}{6} = \frac{5 \times 1}{6 \times 1} = \frac{5}{6}

Step 4 Convert Second Fraction

Multiply 1/2 to get denominator of 6:

Multiply both top and bottom by 3

\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

Step 5 Add the Fractions

Now both fractions have the same denominator (6).

Add the numerators: 5 + 3 = 8

\frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6}

Step 6 Simplify the Result

We can simplify by dividing both by their GCF (2).

Numerator: 8 ÷ 2 = 4

Denominator: 6 ÷ 2 = 3

\frac{8}{6} = \frac{4}{3}

Step 7 Convert to Mixed Number

Since 4 > 3, we can write this as a mixed number.

4 ÷ 3 = 1 remainder 1

\frac{4}{3} = 1\frac{1}{3}