What is 2/4 minus 11/21? (Answer: -1/42)

Exact Answer

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Problem: What is 2/4 minus 11/21?
Formula / Expression: 2/4 − 11/21
Final Answer: -1/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.
Working: LCD(4, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 2 × 21/4 × 21 = 42/84 and 11 × 4/21 × 4 = 44/84

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 44 = -2) and keep the common denominator 84 unchanged.
Working: 42 − 44/84 = -2/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: -2 ÷ 2/84 ÷ 2 = -1/42

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 42 produces a repeating decimal (approximately -0.02381, or -2.381%).
Working: -1 ÷ 42 = -0.02381 (-2.381%)

Key Values:
- Simplified Fraction: -1/42
- Mixed Number Form: -1/42
- Decimal Value: -0.02381
- Percentage: -2.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-4-minus-11-21/
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2/4 − 11/21 = -1/42

Simplified Fraction

-1/42

Mixed Number

Proper (-1/42)

Decimal Value

-0.02381

Percentage

-2.381%

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Step-by-Step Solution: 2/4 − 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.

LCD(4, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

2 × 21/4 × 21 = 42/84 and 11 × 4/21 × 4 = 44/84

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 44 = -2) and keep the common denominator 84 unchanged.

42 − 44/84 = -2/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 2 and 84, which is 2. Divide both the numerator and denominator by 2.

-2 ÷ 2/84 ÷ 2 = -1/42

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 42 produces a repeating decimal (approximately -0.02381, or -2.381%).

-1 ÷ 42 = -0.02381 (-2.381%)

Visual Representation

The diagram below illustrates 2/4 minus 11/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/42`
Mixed Number Form	`-1/42`
Decimal Form	`-0.02381`
Percentage	`-2.381%`

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Frequently Asked Questions

What is 2/4 minus 11/21 as a fraction?

2/4 − 11/21 in simplest fraction form is -1/42.

What is 2/4 minus 11/21 as a decimal?

2/4 − 11/21 converted to a decimal is -0.02381.

What is 2/4 minus 11/21 as a percentage?

2/4 − 11/21 expressed as a percentage is -2.381%.

Does 2/4 minus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.02381...) because the denominator contains prime factors other than 2 and 5.