What is 2/8 minus 9/21? (Answer: -5/28)

Exact Answer

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Problem: What is 2/8 minus 9/21?
Formula / Expression: 2/8 − 9/21
Final Answer: -5/28
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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 9/21 by 8 so both fractions share the common base 168.
Working: 2 × 21/8 × 21 = 42/168 and 9 × 8/21 × 8 = 72/168

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 72 = -30) and keep the common denominator 168 unchanged.
Working: 42 − 72/168 = -30/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 168, which is 6. Divide both the numerator and denominator by 6.
Working: -30 ÷ 6/168 ÷ 6 = -5/28

Step 5: Decimal & Percentage Representation
Dividing the numerator -5 by denominator 28 produces a repeating decimal (approximately -0.178571, or -17.8571%).
Working: -5 ÷ 28 = -0.178571 (-17.8571%)

Key Values:
- Simplified Fraction: -5/28
- Mixed Number Form: -5/28
- Decimal Value: -0.178571
- Percentage: -17.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-minus-9-21/
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2/8 − 9/21 = -5/28

Simplified Fraction

-5/28

Mixed Number

Proper (-5/28)

Decimal Value

-0.178571

Percentage

-17.8571%

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Step-by-Step Solution: 2/8 − 9/21

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 9/21 by 8 so both fractions share the common base 168.

2 × 21/8 × 21 = 42/168 and 9 × 8/21 × 8 = 72/168

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 72 = -30) and keep the common denominator 168 unchanged.

42 − 72/168 = -30/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 168, which is 6. Divide both the numerator and denominator by 6.

-30 ÷ 6/168 ÷ 6 = -5/28

Step 5

Decimal & Percentage Representation

Dividing the numerator -5 by denominator 28 produces a repeating decimal (approximately -0.178571, or -17.8571%).

-5 ÷ 28 = -0.178571 (-17.8571%)

Visual Representation

The diagram below illustrates 2/8 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-5/28`
Mixed Number Form	`-5/28`
Decimal Form	`-0.178571`
Percentage	`-17.8571%`

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Frequently Asked Questions

What is 2/8 minus 9/21 as a fraction?

2/8 − 9/21 in simplest fraction form is -5/28.

What is 2/8 minus 9/21 as a decimal?

2/8 − 9/21 converted to a decimal is -0.178571.

What is 2/8 minus 9/21 as a percentage?

2/8 − 9/21 expressed as a percentage is -17.8571%.

Does 2/8 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.178571...) because the denominator contains prime factors other than 2 and 5.