What is 2/5 minus 11/21? (Answer: -13/105)

Exact Answer

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Problem: What is 2/5 minus 11/21?
Formula / Expression: 2/5 − 11/21
Final Answer: -13/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.
Working: LCD(5, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 2 × 21/5 × 21 = 42/105 and 11 × 5/21 × 5 = 55/105

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 55 = -13) and keep the common denominator 105 unchanged.
Working: 42 − 55/105 = -13/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 105 is 1, confirming that -13/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: -13/105

Step 5: Decimal & Percentage Representation
Dividing the numerator -13 by denominator 105 produces a repeating decimal (approximately -0.12381, or -12.381%).
Working: -13 ÷ 105 = -0.12381 (-12.381%)

Key Values:
- Simplified Fraction: -13/105
- Mixed Number Form: -13/105
- Decimal Value: -0.12381
- Percentage: -12.381%

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Solved with FractionsCalc:
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2/5 − 11/21 = -13/105

Simplified Fraction

-13/105

Mixed Number

Proper (-13/105)

Decimal Value

-0.12381

Percentage

-12.381%

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Step-by-Step Solution: 2/5 − 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.

LCD(5, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/5 by 21, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

2 × 21/5 × 21 = 42/105 and 11 × 5/21 × 5 = 55/105

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 55 = -13) and keep the common denominator 105 unchanged.

42 − 55/105 = -13/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 105 is 1, confirming that -13/105 cannot be reduced further—it is already in its simplest irreducible form.

-13/105

Step 5

Decimal & Percentage Representation

Dividing the numerator -13 by denominator 105 produces a repeating decimal (approximately -0.12381, or -12.381%).

-13 ÷ 105 = -0.12381 (-12.381%)

Visual Representation

The diagram below illustrates 2/5 minus 11/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-13/105`
Mixed Number Form	`-13/105`
Decimal Form	`-0.12381`
Percentage	`-12.381%`

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Frequently Asked Questions

What is 2/5 minus 11/21 as a fraction?

2/5 − 11/21 in simplest fraction form is -13/105.

What is 2/5 minus 11/21 as a decimal?

2/5 − 11/21 converted to a decimal is -0.12381.

What is 2/5 minus 11/21 as a percentage?

2/5 − 11/21 expressed as a percentage is -12.381%.

Does 2/5 minus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.12381...) because the denominator contains prime factors other than 2 and 5.