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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(7, 21) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 2/7 by 3, and multiply the numerator and denominator of 8/21 by 1 so both fractions share the common base 21.
Working: 2 × 3/7 × 3 = 6/21 and 8 × 1/21 × 1 = 8/21

Step 3: Subtract the Numerators
Now subtract the numerators (6 − 8 = -2) and keep the common denominator 21 unchanged.
Working: 6 − 8/21 = -2/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 2 and 21 is 1, confirming that -2/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: -2/21

Step 5: Decimal & Percentage Representation
Dividing the numerator -2 by denominator 21 produces a repeating decimal (approximately -0.095238, or -9.5238%).
Working: -2 ÷ 21 = -0.095238 (-9.5238%)

Key Values:
- Simplified Fraction: -2/21
- Mixed Number Form: -2/21
- Decimal Value: -0.095238
- Percentage: -9.5238%

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

Simplified Fraction

-2/21

Mixed Number

Proper (-2/21)

Decimal Value

-0.095238

Percentage

-9.5238%

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Step-by-Step Solution: 2/7 − 8/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(7, 21) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 2/7 by 3, and multiply the numerator and denominator of 8/21 by 1 so both fractions share the common base 21.

2 × 3/7 × 3 = 6/21 and 8 × 1/21 × 1 = 8/21

Step 3

Subtract the Numerators

Now subtract the numerators (6 − 8 = -2) and keep the common denominator 21 unchanged.

6 − 8/21 = -2/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 2 and 21 is 1, confirming that -2/21 cannot be reduced further—it is already in its simplest irreducible form.

-2/21

Step 5

Decimal & Percentage Representation

Dividing the numerator -2 by denominator 21 produces a repeating decimal (approximately -0.095238, or -9.5238%).

-2 ÷ 21 = -0.095238 (-9.5238%)

Visual Representation

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

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-2/21`
Mixed Number Form	`-2/21`
Decimal Form	`-0.095238`
Percentage	`-9.5238%`

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Frequently Asked Questions

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

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

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

2/7 − 8/21 converted to a decimal is -0.095238.

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

2/7 − 8/21 expressed as a percentage is -9.5238%.

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

It results in a repeating decimal (approximately -0.095238...) because the denominator contains prime factors other than 2 and 5.