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

Exact Answer

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

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

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

Step 3: Subtract the Numerators
Now subtract the numerators (4 − 3 = 1) and keep the common denominator 6 unchanged.
Working: 4 − 3/6 = 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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2/3 − 1/2 = 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: 2/3 − 1/2

Step 1

Find the Least Common Denominator (LCD)

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

LCD(3, 2) = 6

Step 2

Convert to Equivalent Fractions with Common Denominator 6

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

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

Step 3

Subtract the Numerators

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

4 − 3/6 = 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 2/3 minus 1/2 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 2/3 minus 1/2 as a fraction?

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

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

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

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

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

Does 2/3 minus 1/2 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.