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

Exact Answer

==================================================
Problem: What is 1/2 minus 1/3?
Formula / Expression: 1/2 − 1/3
Final Answer: 1/6
==================================================

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 1/3 by 2 so both fractions share the common base 6.
Working: 1 × 3/2 × 3 = 3/6 and 1 × 2/3 × 2 = 2/6

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

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

1/2 − 1/3 = 1/6

Simplified Fraction

1/6

Mixed Number

Proper (1/6)

Decimal Value

0.166667

Percentage

16.6667%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/2 − 1/3

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 1/3 by 2 so both fractions share the common base 6.

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

Step 3

Subtract the Numerators

Now subtract the numerators (3 − 2 = 1) and keep the common denominator 6 unchanged.

3 − 2/6 = 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 1/3 visually:

−

Summary & Alternative Representations

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

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

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

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

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

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

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

Does 1/2 minus 1/3 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.