What is 2/27 minus 2/21? (Answer: -4/189)

Exact Answer

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Problem: What is 2/27 minus 2/21?
Formula / Expression: 2/27 − 2/21
Final Answer: -4/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 2/27 by 7, and multiply the numerator and denominator of 2/21 by 9 so both fractions share the common base 189.
Working: 2 × 7/27 × 7 = 14/189 and 2 × 9/21 × 9 = 18/189

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 18 = -4) and keep the common denominator 189 unchanged.
Working: 14 − 18/189 = -4/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 4 and 189 is 1, confirming that -4/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: -4/189

Step 5: Decimal & Percentage Representation
Dividing the numerator -4 by denominator 189 produces a repeating decimal (approximately -0.021164, or -2.1164%).
Working: -4 ÷ 189 = -0.021164 (-2.1164%)

Key Values:
- Simplified Fraction: -4/189
- Mixed Number Form: -4/189
- Decimal Value: -0.021164
- Percentage: -2.1164%

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Solved with FractionsCalc:
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2/27 − 2/21 = -4/189

Simplified Fraction

-4/189

Mixed Number

Proper (-4/189)

Decimal Value

-0.021164

Percentage

-2.1164%

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Step-by-Step Solution: 2/27 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 2/27 by 7, and multiply the numerator and denominator of 2/21 by 9 so both fractions share the common base 189.

2 × 7/27 × 7 = 14/189 and 2 × 9/21 × 9 = 18/189

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 18 = -4) and keep the common denominator 189 unchanged.

14 − 18/189 = -4/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 4 and 189 is 1, confirming that -4/189 cannot be reduced further—it is already in its simplest irreducible form.

-4/189

Step 5

Decimal & Percentage Representation

Dividing the numerator -4 by denominator 189 produces a repeating decimal (approximately -0.021164, or -2.1164%).

-4 ÷ 189 = -0.021164 (-2.1164%)

Visual Representation

The diagram below illustrates 2/27 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-4/189`
Mixed Number Form	`-4/189`
Decimal Form	`-0.021164`
Percentage	`-2.1164%`

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Frequently Asked Questions

What is 2/27 minus 2/21 as a fraction?

2/27 − 2/21 in simplest fraction form is -4/189.

What is 2/27 minus 2/21 as a decimal?

2/27 − 2/21 converted to a decimal is -0.021164.

What is 2/27 minus 2/21 as a percentage?

2/27 − 2/21 expressed as a percentage is -2.1164%.

Does 2/27 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.021164...) because the denominator contains prime factors other than 2 and 5.