What is 1/3 minus 3/4? (Answer: -5/12)

Exact Answer

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Problem: What is 1/3 minus 3/4?
Formula / Expression: 1/3 − 3/4
Final Answer: -5/12
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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 1/3 by 4, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.
Working: 1 × 4/3 × 4 = 4/12 and 3 × 3/4 × 3 = 9/12

Step 3: Subtract the Numerators
Now subtract the numerators (4 − 9 = -5) and keep the common denominator 12 unchanged.
Working: 4 − 9/12 = -5/12

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 12 is 1, confirming that -5/12 cannot be reduced further—it is already in its simplest irreducible form.
Working: -5/12

Step 5: Decimal & Percentage Representation
Dividing the numerator -5 by denominator 12 produces a repeating decimal (approximately -0.416667, or -41.6667%).
Working: -5 ÷ 12 = -0.416667 (-41.6667%)

Key Values:
- Simplified Fraction: -5/12
- Mixed Number Form: -5/12
- Decimal Value: -0.416667
- Percentage: -41.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-minus-3-4/
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1/3 − 3/4 = -5/12

Simplified Fraction

-5/12

Mixed Number

Proper (-5/12)

Decimal Value

-0.416667

Percentage

-41.6667%

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Step-by-Step Solution: 1/3 − 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 1/3 by 4, and multiply the numerator and denominator of 3/4 by 3 so both fractions share the common base 12.

1 × 4/3 × 4 = 4/12 and 3 × 3/4 × 3 = 9/12

Step 3

Subtract the Numerators

Now subtract the numerators (4 − 9 = -5) and keep the common denominator 12 unchanged.

4 − 9/12 = -5/12

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 12 is 1, confirming that -5/12 cannot be reduced further—it is already in its simplest irreducible form.

-5/12

Step 5

Decimal & Percentage Representation

Dividing the numerator -5 by denominator 12 produces a repeating decimal (approximately -0.416667, or -41.6667%).

-5 ÷ 12 = -0.416667 (-41.6667%)

Visual Representation

The diagram below illustrates 1/3 minus 3/4 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-5/12`
Mixed Number Form	`-5/12`
Decimal Form	`-0.416667`
Percentage	`-41.6667%`

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Frequently Asked Questions

What is 1/3 minus 3/4 as a fraction?

1/3 − 3/4 in simplest fraction form is -5/12.

What is 1/3 minus 3/4 as a decimal?

1/3 − 3/4 converted to a decimal is -0.416667.

What is 1/3 minus 3/4 as a percentage?

1/3 − 3/4 expressed as a percentage is -41.6667%.

Does 1/3 minus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.416667...) because the denominator contains prime factors other than 2 and 5.