What is 1/2 minus 5/6? (Answer: -1/3)

Exact Answer

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Problem: What is 1/2 minus 5/6?
Formula / Expression: 1/2 − 5/6
Final Answer: -1/3
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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(2, 6) = 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 5/6 by 1 so both fractions share the common base 6.
Working: 1 × 3/2 × 3 = 3/6 and 5 × 1/6 × 1 = 5/6

Step 3: Subtract the Numerators
Now subtract the numerators (3 − 5 = -2) and keep the common denominator 6 unchanged.
Working: 3 − 5/6 = -2/6

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 6, which is 2. Divide both the numerator and denominator by 2.
Working: -2 ÷ 2/6 ÷ 2 = -1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 3 produces a repeating decimal (approximately -0.333333, or -33.3333%).
Working: -1 ÷ 3 = -0.333333 (-33.3333%)

Key Values:
- Simplified Fraction: -1/3
- Mixed Number Form: -1/3
- Decimal Value: -0.333333
- Percentage: -33.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-minus-5-6/
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1/2 − 5/6 = -1/3

Simplified Fraction

-1/3

Mixed Number

Proper (-1/3)

Decimal Value

-0.333333

Percentage

-33.3333%

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Step-by-Step Solution: 1/2 − 5/6

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(2, 6) = 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 5/6 by 1 so both fractions share the common base 6.

1 × 3/2 × 3 = 3/6 and 5 × 1/6 × 1 = 5/6

Step 3

Subtract the Numerators

Now subtract the numerators (3 − 5 = -2) and keep the common denominator 6 unchanged.

3 − 5/6 = -2/6

Step 4

Simplify the Fraction to Lowest Terms

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

-2 ÷ 2/6 ÷ 2 = -1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 3 produces a repeating decimal (approximately -0.333333, or -33.3333%).

-1 ÷ 3 = -0.333333 (-33.3333%)

Visual Representation

The diagram below illustrates 1/2 minus 5/6 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/3`
Mixed Number Form	`-1/3`
Decimal Form	`-0.333333`
Percentage	`-33.3333%`

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Frequently Asked Questions

What is 1/2 minus 5/6 as a fraction?

1/2 − 5/6 in simplest fraction form is -1/3.

What is 1/2 minus 5/6 as a decimal?

1/2 − 5/6 converted to a decimal is -0.333333.

What is 1/2 minus 5/6 as a percentage?

1/2 − 5/6 expressed as a percentage is -33.3333%.

Does 1/2 minus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.333333...) because the denominator contains prime factors other than 2 and 5.