What is 2/31 minus 2/21? (Answer: -20/651)

Exact Answer

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Problem: What is 2/31 minus 2/21?
Formula / Expression: 2/31 − 2/21
Final Answer: -20/651
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.
Working: LCD(31, 21) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 2/31 by 21, and multiply the numerator and denominator of 2/21 by 31 so both fractions share the common base 651.
Working: 2 × 21/31 × 21 = 42/651 and 2 × 31/21 × 31 = 62/651

Step 3: Subtract the Numerators
Now subtract the numerators (42 − 62 = -20) and keep the common denominator 651 unchanged.
Working: 42 − 62/651 = -20/651

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 20 and 651 is 1, confirming that -20/651 cannot be reduced further—it is already in its simplest irreducible form.
Working: -20/651

Step 5: Decimal & Percentage Representation
Dividing the numerator -20 by denominator 651 produces a repeating decimal (approximately -0.030722, or -3.0722%).
Working: -20 ÷ 651 = -0.030722 (-3.0722%)

Key Values:
- Simplified Fraction: -20/651
- Mixed Number Form: -20/651
- Decimal Value: -0.030722
- Percentage: -3.0722%

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Solved with FractionsCalc:
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2/31 − 2/21 = -20/651

Simplified Fraction

-20/651

Mixed Number

Proper (-20/651)

Decimal Value

-0.030722

Percentage

-3.0722%

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Step-by-Step Solution: 2/31 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 31 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 31 × 21 = 651.

LCD(31, 21) = 651

Step 2

Convert to Equivalent Fractions with Common Denominator 651

Multiply the numerator and denominator of 2/31 by 21, and multiply the numerator and denominator of 2/21 by 31 so both fractions share the common base 651.

2 × 21/31 × 21 = 42/651 and 2 × 31/21 × 31 = 62/651

Step 3

Subtract the Numerators

Now subtract the numerators (42 − 62 = -20) and keep the common denominator 651 unchanged.

42 − 62/651 = -20/651

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 20 and 651 is 1, confirming that -20/651 cannot be reduced further—it is already in its simplest irreducible form.

-20/651

Step 5

Decimal & Percentage Representation

Dividing the numerator -20 by denominator 651 produces a repeating decimal (approximately -0.030722, or -3.0722%).

-20 ÷ 651 = -0.030722 (-3.0722%)

Visual Representation

The diagram below illustrates 2/31 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-20/651`
Mixed Number Form	`-20/651`
Decimal Form	`-0.030722`
Percentage	`-3.0722%`

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Frequently Asked Questions

What is 2/31 minus 2/21 as a fraction?

2/31 − 2/21 in simplest fraction form is -20/651.

What is 2/31 minus 2/21 as a decimal?

2/31 − 2/21 converted to a decimal is -0.030722.

What is 2/31 minus 2/21 as a percentage?

2/31 − 2/21 expressed as a percentage is -3.0722%.

Does 2/31 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.030722...) because the denominator contains prime factors other than 2 and 5.