What is 1/2 minus 5/8? (Answer: -1/8)

Exact Answer

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Problem: What is 1/2 minus 5/8?
Formula / Expression: 1/2 − 5/8
Final Answer: -1/8
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 8 is an exact multiple of 2 (2 × 4 = 8). The Least Common Denominator (LCD) is simply 8, meaning we only need to scale one fraction.
Working: LCD(2, 8) = 8

Step 2: Convert to Equivalent Fractions with Common Denominator 8
Multiply the numerator and denominator of 1/2 by 4, and multiply the numerator and denominator of 5/8 by 1 so both fractions share the common base 8.
Working: 1 × 4/2 × 4 = 4/8 and 5 × 1/8 × 1 = 5/8

Step 3: Subtract the Numerators
Now subtract the numerators (4 − 5 = -1) and keep the common denominator 8 unchanged.
Working: 4 − 5/8 = -1/8

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 1 and 8 is 1, confirming that -1/8 cannot be reduced further—it is already in its simplest irreducible form.
Working: -1/8

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 8 yields an exact terminating decimal of -0.125 (or -12.5%).
Working: -1 ÷ 8 = -0.125 (-12.5%)

Key Values:
- Simplified Fraction: -1/8
- Mixed Number Form: -1/8
- Decimal Value: -0.125
- Percentage: -12.5%

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1/2 − 5/8 = -1/8

Simplified Fraction

-1/8

Mixed Number

Proper (-1/8)

Decimal Value

-0.125

Percentage

-12.5%

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Step-by-Step Solution: 1/2 − 5/8

Step 1

Find the Least Common Denominator (LCD)

Notice that 8 is an exact multiple of 2 (2 × 4 = 8). The Least Common Denominator (LCD) is simply 8, meaning we only need to scale one fraction.

LCD(2, 8) = 8

Step 2

Convert to Equivalent Fractions with Common Denominator 8

Multiply the numerator and denominator of 1/2 by 4, and multiply the numerator and denominator of 5/8 by 1 so both fractions share the common base 8.

1 × 4/2 × 4 = 4/8 and 5 × 1/8 × 1 = 5/8

Step 3

Subtract the Numerators

Now subtract the numerators (4 − 5 = -1) and keep the common denominator 8 unchanged.

4 − 5/8 = -1/8

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 1 and 8 is 1, confirming that -1/8 cannot be reduced further—it is already in its simplest irreducible form.

-1/8

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 8 yields an exact terminating decimal of -0.125 (or -12.5%).

-1 ÷ 8 = -0.125 (-12.5%)

Visual Representation

The diagram below illustrates 1/2 minus 5/8 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/8`
Mixed Number Form	`-1/8`
Decimal Form	`-0.125`
Percentage	`-12.5%`

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Frequently Asked Questions

What is 1/2 minus 5/8 as a fraction?

1/2 − 5/8 in simplest fraction form is -1/8.

What is 1/2 minus 5/8 as a decimal?

1/2 − 5/8 converted to a decimal is -0.125.

What is 1/2 minus 5/8 as a percentage?

1/2 − 5/8 expressed as a percentage is -12.5%.

Does 1/2 minus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (-0.125) because the denominator in simplest terms contains only prime factors 2 and/or 5.