What is 2/8 minus 10/21? (Answer: -19/84)

Exact Answer

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Problem: What is 2/8 minus 10/21?
Formula / Expression: 2/8 − 10/21
Final Answer: -19/84
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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 10/21 by 8 so both fractions share the common base 168.
Working: 2 × 21/8 × 21 = 42/168 and 10 × 8/21 × 8 = 80/168

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 80 = -38) and keep the common denominator 168 unchanged.
Working: 42 − 80/168 = -38/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: -38 ÷ 2/168 ÷ 2 = -19/84

Step 5: Decimal & Percentage Representation
Dividing the numerator -19 by denominator 84 produces a repeating decimal (approximately -0.22619, or -22.619%).
Working: -19 ÷ 84 = -0.22619 (-22.619%)

Key Values:
- Simplified Fraction: -19/84
- Mixed Number Form: -19/84
- Decimal Value: -0.22619
- Percentage: -22.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-minus-10-21/
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2/8 − 10/21 = -19/84

Simplified Fraction

-19/84

Mixed Number

Proper (-19/84)

Decimal Value

-0.22619

Percentage

-22.619%

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Step-by-Step Solution: 2/8 − 10/21

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 10/21 by 8 so both fractions share the common base 168.

2 × 21/8 × 21 = 42/168 and 10 × 8/21 × 8 = 80/168

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 80 = -38) and keep the common denominator 168 unchanged.

42 − 80/168 = -38/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 168, which is 2. Divide both the numerator and denominator by 2.

-38 ÷ 2/168 ÷ 2 = -19/84

Step 5

Decimal & Percentage Representation

Dividing the numerator -19 by denominator 84 produces a repeating decimal (approximately -0.22619, or -22.619%).

-19 ÷ 84 = -0.22619 (-22.619%)

Visual Representation

The diagram below illustrates 2/8 minus 10/21 visually:

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Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-19/84`
Mixed Number Form	`-19/84`
Decimal Form	`-0.22619`
Percentage	`-22.619%`

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Frequently Asked Questions

What is 2/8 minus 10/21 as a fraction?

2/8 − 10/21 in simplest fraction form is -19/84.

What is 2/8 minus 10/21 as a decimal?

2/8 − 10/21 converted to a decimal is -0.22619.

What is 2/8 minus 10/21 as a percentage?

2/8 − 10/21 expressed as a percentage is -22.619%.

Does 2/8 minus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.22619...) because the denominator contains prime factors other than 2 and 5.