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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 4 is an exact multiple of 2 (2 × 2 = 4). The Least Common Denominator (LCD) is simply 4, meaning we only need to scale one fraction.
Working: LCD(2, 4) = 4

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

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

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

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 4 yields an exact terminating decimal of -0.25 (or -25%).
Working: -1 ÷ 4 = -0.25 (-25%)

Key Values:
- Simplified Fraction: -1/4
- Mixed Number Form: -1/4
- Decimal Value: -0.25
- Percentage: -25%

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Solved with FractionsCalc:
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1/2 − 3/4 = -1/4

Simplified Fraction

-1/4

Mixed Number

Proper (-1/4)

Decimal Value

-0.25

Percentage

-25%

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Step-by-Step Solution: 1/2 − 3/4

Step 1

Find the Least Common Denominator (LCD)

Notice that 4 is an exact multiple of 2 (2 × 2 = 4). The Least Common Denominator (LCD) is simply 4, meaning we only need to scale one fraction.

LCD(2, 4) = 4

Step 2

Convert to Equivalent Fractions with Common Denominator 4

Multiply the numerator and denominator of 1/2 by 2, and multiply the numerator and denominator of 3/4 by 1 so both fractions share the common base 4.

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

Step 3

Subtract the Numerators

Now subtract the numerators (2 − 3 = -1) and keep the common denominator 4 unchanged.

2 − 3/4 = -1/4

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 4 is 1, confirming that -1/4 cannot be reduced further—it is already in its simplest irreducible form.

-1/4

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 4 yields an exact terminating decimal of -0.25 (or -25%).

-1 ÷ 4 = -0.25 (-25%)

Visual Representation

The diagram below illustrates 1/2 minus 3/4 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/4`
Mixed Number Form	`-1/4`
Decimal Form	`-0.25`
Percentage	`-25%`

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Frequently Asked Questions

What is 1/2 minus 3/4 as a fraction?

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

What is 1/2 minus 3/4 as a decimal?

1/2 − 3/4 converted to a decimal is -0.25.

What is 1/2 minus 3/4 as a percentage?

1/2 − 3/4 expressed as a percentage is -25%.

Does 1/2 minus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (-0.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.