What is 2/8 minus 8/21? (Answer: -11/84)

Exact Answer

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Problem: What is 2/8 minus 8/21?
Formula / Expression: 2/8 − 8/21
Final Answer: -11/84
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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 8/21 by 8 so both fractions share the common base 168.
Working: 2 × 21/8 × 21 = 42/168 and 8 × 8/21 × 8 = 64/168

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 64 = -22) and keep the common denominator 168 unchanged.
Working: 42 − 64/168 = -22/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: -22 ÷ 2/168 ÷ 2 = -11/84

Step 5: Decimal & Percentage Representation
Dividing the numerator -11 by denominator 84 produces a repeating decimal (approximately -0.130952, or -13.0952%).
Working: -11 ÷ 84 = -0.130952 (-13.0952%)

Key Values:
- Simplified Fraction: -11/84
- Mixed Number Form: -11/84
- Decimal Value: -0.130952
- Percentage: -13.0952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-minus-8-21/
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2/8 − 8/21 = -11/84

Simplified Fraction

-11/84

Mixed Number

Proper (-11/84)

Decimal Value

-0.130952

Percentage

-13.0952%

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Step-by-Step Solution: 2/8 − 8/21

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 8/21 by 8 so both fractions share the common base 168.

2 × 21/8 × 21 = 42/168 and 8 × 8/21 × 8 = 64/168

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 64 = -22) and keep the common denominator 168 unchanged.

42 − 64/168 = -22/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 168, which is 2. Divide both the numerator and denominator by 2.

-22 ÷ 2/168 ÷ 2 = -11/84

Step 5

Decimal & Percentage Representation

Dividing the numerator -11 by denominator 84 produces a repeating decimal (approximately -0.130952, or -13.0952%).

-11 ÷ 84 = -0.130952 (-13.0952%)

Visual Representation

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

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Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-11/84`
Mixed Number Form	`-11/84`
Decimal Form	`-0.130952`
Percentage	`-13.0952%`

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Frequently Asked Questions

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

2/8 − 8/21 in simplest fraction form is -11/84.

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

2/8 − 8/21 converted to a decimal is -0.130952.

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

2/8 − 8/21 expressed as a percentage is -13.0952%.

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

It results in a repeating decimal (approximately -0.130952...) because the denominator contains prime factors other than 2 and 5.