What is 2/3 minus 3/4? (Answer: -1/12)

Exact Answer

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Problem: What is 2/3 minus 3/4?
Formula / Expression: 2/3 − 3/4
Final Answer: -1/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 4 = 12.
Working: LCD(3, 4) = 12

Step 2: Convert to Equivalent Fractions with Common Denominator 12
Multiply the numerator and denominator of 2/3 by 4, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.
Working: 2 × 4/3 × 4 = 8/12 and 3 × 3/4 × 3 = 9/12

Step 3: Subtract the Numerators
Now subtract the numerators (8 − 9 = -1) and keep the common denominator 12 unchanged.
Working: 8 − 9/12 = -1/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 1 and 12 is 1, confirming that -1/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: -1/12

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 12 produces a repeating decimal (approximately -0.083333, or -8.3333%).
Working: -1 ÷ 12 = -0.083333 (-8.3333%)

Key Values:
- Simplified Fraction: -1/12
- Mixed Number Form: -1/12
- Decimal Value: -0.083333
- Percentage: -8.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-minus-3-4/
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2/3 − 3/4 = -1/12

Simplified Fraction

-1/12

Mixed Number

Proper (-1/12)

Decimal Value

-0.083333

Percentage

-8.3333%

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Step-by-Step Solution: 2/3 − 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 4 = 12.

LCD(3, 4) = 12

Step 2

Convert to Equivalent Fractions with Common Denominator 12

Multiply the numerator and denominator of 2/3 by 4, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.

2 × 4/3 × 4 = 8/12 and 3 × 3/4 × 3 = 9/12

Step 3

Subtract the Numerators

Now subtract the numerators (8 − 9 = -1) and keep the common denominator 12 unchanged.

8 − 9/12 = -1/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 12 is 1, confirming that -1/12 cannot be reduced further—it is already in its simplest irreducible form.

-1/12

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 12 produces a repeating decimal (approximately -0.083333, or -8.3333%).

-1 ÷ 12 = -0.083333 (-8.3333%)

Visual Representation

The diagram below illustrates 2/3 minus 3/4 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/12`
Mixed Number Form	`-1/12`
Decimal Form	`-0.083333`
Percentage	`-8.3333%`

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Frequently Asked Questions

What is 2/3 minus 3/4 as a fraction?

2/3 − 3/4 in simplest fraction form is -1/12.

What is 2/3 minus 3/4 as a decimal?

2/3 − 3/4 converted to a decimal is -0.083333.

What is 2/3 minus 3/4 as a percentage?

2/3 − 3/4 expressed as a percentage is -8.3333%.

Does 2/3 minus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.083333...) because the denominator contains prime factors other than 2 and 5.