What is 1/7 minus 1/2? (Answer: -5/14)

Exact Answer

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Problem: What is 1/7 minus 1/2?
Formula / Expression: 1/7 − 1/2
Final Answer: -5/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 2 = 14.
Working: LCD(7, 2) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 1/7 by 2, and multiply the numerator and denominator of 1/2 by 7 so both fractions share the common base 14.
Working: 1 × 2/7 × 2 = 2/14 and 1 × 7/2 × 7 = 7/14

Step 3: Subtract the Numerators
Now subtract the numerators (2 − 7 = -5) and keep the common denominator 14 unchanged.
Working: 2 − 7/14 = -5/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 5 and 14 is 1, confirming that -5/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: -5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator -5 by denominator 14 produces a repeating decimal (approximately -0.357143, or -35.7143%).
Working: -5 ÷ 14 = -0.357143 (-35.7143%)

Key Values:
- Simplified Fraction: -5/14
- Mixed Number Form: -5/14
- Decimal Value: -0.357143
- Percentage: -35.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-minus-1-2/
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1/7 − 1/2 = -5/14

Simplified Fraction

-5/14

Mixed Number

Proper (-5/14)

Decimal Value

-0.357143

Percentage

-35.7143%

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Step-by-Step Solution: 1/7 − 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 2 = 14.

LCD(7, 2) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 1/7 by 2, and multiply the numerator and denominator of 1/2 by 7 so both fractions share the common base 14.

1 × 2/7 × 2 = 2/14 and 1 × 7/2 × 7 = 7/14

Step 3

Subtract the Numerators

Now subtract the numerators (2 − 7 = -5) and keep the common denominator 14 unchanged.

2 − 7/14 = -5/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 5 and 14 is 1, confirming that -5/14 cannot be reduced further—it is already in its simplest irreducible form.

-5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator -5 by denominator 14 produces a repeating decimal (approximately -0.357143, or -35.7143%).

-5 ÷ 14 = -0.357143 (-35.7143%)

Visual Representation

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

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-5/14`
Mixed Number Form	`-5/14`
Decimal Form	`-0.357143`
Percentage	`-35.7143%`

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Frequently Asked Questions

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

1/7 − 1/2 in simplest fraction form is -5/14.

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

1/7 − 1/2 converted to a decimal is -0.357143.

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

1/7 − 1/2 expressed as a percentage is -35.7143%.

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

It results in a repeating decimal (approximately -0.357143...) because the denominator contains prime factors other than 2 and 5.