What is 1/6 + 1/3?

Calculate 1/6 + 1/3 with a complete step-by-step solution. Learn how to add fractions and understand the process.

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

Step-by-Step Solution

Step 1 Identify the Fractions

We need to add two fractions: 1/6 and 1/3

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

\frac{1}{6} + \frac{1}{3} = ?

Step 2 Find the Least Common Denominator (LCD)

The denominators are different (6 and 3), so we need to find a common denominator.

The LCD is the smallest number that both 6 and 3 divide into evenly.

Since GCD(6, 3) = 3, we calculate LCD = (6 × 3) ÷ 3 = 6

\text{LCD}(6, 3) = 6

Step 3 Convert First Fraction

Multiply 1/6 to get denominator of 6:

Multiply both top and bottom by 1

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

Step 4 Convert Second Fraction

Multiply 1/3 to get denominator of 6:

Multiply both top and bottom by 2

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

Step 5 Add the Fractions

Now both fractions have the same denominator (6).

Add the numerators: 1 + 2 = 3

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

Step 6 Simplify the Result

We can simplify by dividing both by their GCF (3).

Numerator: 3 ÷ 3 = 1

Denominator: 6 ÷ 3 = 2

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