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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 3 = 6.
Working: LCD(2, 3) = 6

Step 2: Convert to Equivalent Fractions with Common Denominator 6
Multiply the numerator and denominator of 1/2 by 3, and multiply the numerator and denominator of 2/3 by 2 so both fractions share the common base 6.
Working: 1 × 3/2 × 3 = 3/6 and 2 × 2/3 × 2 = 4/6

Step 3: Subtract the Numerators
Now subtract the numerators (3 − 4 = -1) and keep the common denominator 6 unchanged.
Working: 3 − 4/6 = -1/6

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 1 and 6 is 1, confirming that -1/6 cannot be reduced further—it is already in its simplest irreducible form.
Working: -1/6

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 6 produces a repeating decimal (approximately -0.166667, or -16.6667%).
Working: -1 ÷ 6 = -0.166667 (-16.6667%)

Key Values:
- Simplified Fraction: -1/6
- Mixed Number Form: -1/6
- Decimal Value: -0.166667
- Percentage: -16.6667%

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

Simplified Fraction

-1/6

Mixed Number

Proper (-1/6)

Decimal Value

-0.166667

Percentage

-16.6667%

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Step-by-Step Solution: 1/2 − 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 3 = 6.

LCD(2, 3) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

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

1 × 3/2 × 3 = 3/6 and 2 × 2/3 × 2 = 4/6

Step 3

Subtract the Numerators

Now subtract the numerators (3 − 4 = -1) and keep the common denominator 6 unchanged.

3 − 4/6 = -1/6

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 6 is 1, confirming that -1/6 cannot be reduced further—it is already in its simplest irreducible form.

-1/6

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 6 produces a repeating decimal (approximately -0.166667, or -16.6667%).

-1 ÷ 6 = -0.166667 (-16.6667%)

Visual Representation

The diagram below illustrates 1/2 minus 2/3 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/6`
Mixed Number Form	`-1/6`
Decimal Form	`-0.166667`
Percentage	`-16.6667%`

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Frequently Asked Questions

What is 1/2 minus 2/3 as a fraction?

1/2 − 2/3 in simplest fraction form is -1/6.

What is 1/2 minus 2/3 as a decimal?

1/2 − 2/3 converted to a decimal is -0.166667.

What is 1/2 minus 2/3 as a percentage?

1/2 − 2/3 expressed as a percentage is -16.6667%.

Does 1/2 minus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.166667...) because the denominator contains prime factors other than 2 and 5.