What is 1/6 plus 1/2? (Answer: 2/3)

Exact Answer

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Problem: What is 1/6 plus 1/2?
Formula / Expression: 1/6 + 1/2
Final Answer: 2/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 6 is an exact multiple of 2 (2 × 3 = 6). The Least Common Denominator (LCD) is simply 6, meaning we only need to scale one fraction.
Working: LCD(6, 2) = 6

Step 2: Convert to Equivalent Fractions with Common Denominator 6
Multiply the numerator and denominator of 1/6 by 1, and multiply the numerator and denominator of 1/2 by 3 so both fractions share the common base 6.
Working: 1 × 1/6 × 1 = 1/6 and 1 × 3/2 × 3 = 3/6

Step 3: Add the Numerators
Now add the numerators (1 + 3 = 4) and keep the common denominator 6 unchanged.
Working: 1 + 3/6 = 4/6

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 4 and 6, which is 2. Divide both the numerator and denominator by 2.
Working: 4 ÷ 2/6 ÷ 2 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-6-plus-1-2/
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1/6 + 1/2 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 1/6 + 1/2

Step 1

Find the Least Common Denominator (LCD)

Notice that 6 is an exact multiple of 2 (2 × 3 = 6). The Least Common Denominator (LCD) is simply 6, meaning we only need to scale one fraction.

LCD(6, 2) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

Multiply the numerator and denominator of 1/6 by 1, and multiply the numerator and denominator of 1/2 by 3 so both fractions share the common base 6.

1 × 1/6 × 1 = 1/6 and 1 × 3/2 × 3 = 3/6

Step 3

Add the Numerators

Now add the numerators (1 + 3 = 4) and keep the common denominator 6 unchanged.

1 + 3/6 = 4/6

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 4 and 6, which is 2. Divide both the numerator and denominator by 2.

4 ÷ 2/6 ÷ 2 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 1/6 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 1/6 plus 1/2 as a fraction?

1/6 + 1/2 in simplest fraction form is 2/3.

What is 1/6 plus 1/2 as a decimal?

1/6 + 1/2 converted to a decimal is 0.666667.

What is 1/6 plus 1/2 as a percentage?

1/6 + 1/2 expressed as a percentage is 66.6667%.

Does 1/6 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.