What is 2/8 minus 7/21? (Answer: -1/12)

Exact Answer

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Problem: What is 2/8 minus 7/21?
Formula / Expression: 2/8 − 7/21
Final Answer: -1/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 2/8 by 21, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.
Working: 2 × 21/8 × 21 = 42/168 and 7 × 8/21 × 8 = 56/168

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 56 = -14) and keep the common denominator 168 unchanged.
Working: 42 − 56/168 = -14/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 168, which is 14. Divide both the numerator and denominator by 14.
Working: -14 ÷ 14/168 ÷ 14 = -1/12

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 12 produces a repeating decimal (approximately -0.083333, or -8.3333%).
Working: -1 ÷ 12 = -0.083333 (-8.3333%)

Key Values:
- Simplified Fraction: -1/12
- Mixed Number Form: -1/12
- Decimal Value: -0.083333
- Percentage: -8.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-minus-7-21/
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2/8 − 7/21 = -1/12

Simplified Fraction

-1/12

Mixed Number

Proper (-1/12)

Decimal Value

-0.083333

Percentage

-8.3333%

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Step-by-Step Solution: 2/8 − 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 2/8 by 21, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.

2 × 21/8 × 21 = 42/168 and 7 × 8/21 × 8 = 56/168

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 56 = -14) and keep the common denominator 168 unchanged.

42 − 56/168 = -14/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 168, which is 14. Divide both the numerator and denominator by 14.

-14 ÷ 14/168 ÷ 14 = -1/12

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 12 produces a repeating decimal (approximately -0.083333, or -8.3333%).

-1 ÷ 12 = -0.083333 (-8.3333%)

Visual Representation

The diagram below illustrates 2/8 minus 7/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/12`
Mixed Number Form	`-1/12`
Decimal Form	`-0.083333`
Percentage	`-8.3333%`

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Frequently Asked Questions

What is 2/8 minus 7/21 as a fraction?

2/8 − 7/21 in simplest fraction form is -1/12.

What is 2/8 minus 7/21 as a decimal?

2/8 − 7/21 converted to a decimal is -0.083333.

What is 2/8 minus 7/21 as a percentage?

2/8 − 7/21 expressed as a percentage is -8.3333%.

Does 2/8 minus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.083333...) because the denominator contains prime factors other than 2 and 5.