What is 2/52 minus 2/21? (Answer: -31/546)

Exact Answer

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Problem: What is 2/52 minus 2/21?
Formula / Expression: 2/52 − 2/21
Final Answer: -31/546
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.
Working: LCD(52, 21) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 2/52 by 21, and multiply the numerator and denominator of 2/21 by 52 so both fractions share the common base 1092.
Working: 2 × 21/52 × 21 = 42/1092 and 2 × 52/21 × 52 = 104/1092

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 104 = -62) and keep the common denominator 1092 unchanged.
Working: 42 − 104/1092 = -62/1092

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 1092, which is 2. Divide both the numerator and denominator by 2.
Working: -62 ÷ 2/1092 ÷ 2 = -31/546

Step 5: Decimal & Percentage Representation
Dividing the numerator -31 by denominator 546 produces a repeating decimal (approximately -0.056777, or -5.6777%).
Working: -31 ÷ 546 = -0.056777 (-5.6777%)

Key Values:
- Simplified Fraction: -31/546
- Mixed Number Form: -31/546
- Decimal Value: -0.056777
- Percentage: -5.6777%

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Solved with FractionsCalc:
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2/52 − 2/21 = -31/546

Simplified Fraction

-31/546

Mixed Number

Proper (-31/546)

Decimal Value

-0.056777

Percentage

-5.6777%

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Step-by-Step Solution: 2/52 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.

LCD(52, 21) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 2/52 by 21, and multiply the numerator and denominator of 2/21 by 52 so both fractions share the common base 1092.

2 × 21/52 × 21 = 42/1092 and 2 × 52/21 × 52 = 104/1092

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 104 = -62) and keep the common denominator 1092 unchanged.

42 − 104/1092 = -62/1092

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 1092, which is 2. Divide both the numerator and denominator by 2.

-62 ÷ 2/1092 ÷ 2 = -31/546

Step 5

Decimal & Percentage Representation

Dividing the numerator -31 by denominator 546 produces a repeating decimal (approximately -0.056777, or -5.6777%).

-31 ÷ 546 = -0.056777 (-5.6777%)

Visual Representation

The diagram below illustrates 2/52 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-31/546`
Mixed Number Form	`-31/546`
Decimal Form	`-0.056777`
Percentage	`-5.6777%`

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Frequently Asked Questions

What is 2/52 minus 2/21 as a fraction?

2/52 − 2/21 in simplest fraction form is -31/546.

What is 2/52 minus 2/21 as a decimal?

2/52 − 2/21 converted to a decimal is -0.056777.

What is 2/52 minus 2/21 as a percentage?

2/52 − 2/21 expressed as a percentage is -5.6777%.

Does 2/52 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.056777...) because the denominator contains prime factors other than 2 and 5.