What is 1/2 minus 7/8? (Answer: -3/8)

Exact Answer

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Problem: What is 1/2 minus 7/8?
Formula / Expression: 1/2 − 7/8
Final Answer: -3/8
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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 7/8 by 1 so both fractions share the common base 8.
Working: 1 × 4/2 × 4 = 4/8 and 7 × 1/8 × 1 = 7/8

Step 3: Subtract the Numerators
Now subtract the numerators (4 − 7 = -3) and keep the common denominator 8 unchanged.
Working: 4 − 7/8 = -3/8

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 3 and 8 is 1, confirming that -3/8 cannot be reduced further—it is already in its simplest irreducible form.
Working: -3/8

Step 5: Decimal & Percentage Representation
Dividing the numerator -3 by denominator 8 yields an exact terminating decimal of -0.375 (or -37.5%).
Working: -3 ÷ 8 = -0.375 (-37.5%)

Key Values:
- Simplified Fraction: -3/8
- Mixed Number Form: -3/8
- Decimal Value: -0.375
- Percentage: -37.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-minus-7-8/
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1/2 − 7/8 = -3/8

Simplified Fraction

-3/8

Mixed Number

Proper (-3/8)

Decimal Value

-0.375

Percentage

-37.5%

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Step-by-Step Solution: 1/2 − 7/8

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 7/8 by 1 so both fractions share the common base 8.

1 × 4/2 × 4 = 4/8 and 7 × 1/8 × 1 = 7/8

Step 3

Subtract the Numerators

Now subtract the numerators (4 − 7 = -3) and keep the common denominator 8 unchanged.

4 − 7/8 = -3/8

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 3 and 8 is 1, confirming that -3/8 cannot be reduced further—it is already in its simplest irreducible form.

-3/8

Step 5

Decimal & Percentage Representation

Dividing the numerator -3 by denominator 8 yields an exact terminating decimal of -0.375 (or -37.5%).

-3 ÷ 8 = -0.375 (-37.5%)

Visual Representation

The diagram below illustrates 1/2 minus 7/8 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-3/8`
Mixed Number Form	`-3/8`
Decimal Form	`-0.375`
Percentage	`-37.5%`

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Frequently Asked Questions

What is 1/2 minus 7/8 as a fraction?

1/2 − 7/8 in simplest fraction form is -3/8.

What is 1/2 minus 7/8 as a decimal?

1/2 − 7/8 converted to a decimal is -0.375.

What is 1/2 minus 7/8 as a percentage?

1/2 − 7/8 expressed as a percentage is -37.5%.

Does 1/2 minus 7/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (-0.375) because the denominator in simplest terms contains only prime factors 2 and/or 5.