What is 2/39 minus 2/21? (Answer: -4/91)

Exact Answer

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Problem: What is 2/39 minus 2/21?
Formula / Expression: 2/39 − 2/21
Final Answer: -4/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 2/39 by 7, and multiply the numerator and denominator of 2/21 by 13 so both fractions share the common base 273.
Working: 2 × 7/39 × 7 = 14/273 and 2 × 13/21 × 13 = 26/273

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 26 = -12) and keep the common denominator 273 unchanged.
Working: 14 − 26/273 = -12/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: -12 ÷ 3/273 ÷ 3 = -4/91

Step 5: Decimal & Percentage Representation
Dividing the numerator -4 by denominator 91 produces a repeating decimal (approximately -0.043956, or -4.3956%).
Working: -4 ÷ 91 = -0.043956 (-4.3956%)

Key Values:
- Simplified Fraction: -4/91
- Mixed Number Form: -4/91
- Decimal Value: -0.043956
- Percentage: -4.3956%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-39-minus-2-21/
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2/39 − 2/21 = -4/91

Simplified Fraction

-4/91

Mixed Number

Proper (-4/91)

Decimal Value

-0.043956

Percentage

-4.3956%

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Step-by-Step Solution: 2/39 − 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 2/39 by 7, and multiply the numerator and denominator of 2/21 by 13 so both fractions share the common base 273.

2 × 7/39 × 7 = 14/273 and 2 × 13/21 × 13 = 26/273

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 26 = -12) and keep the common denominator 273 unchanged.

14 − 26/273 = -12/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 273, which is 3. Divide both the numerator and denominator by 3.

-12 ÷ 3/273 ÷ 3 = -4/91

Step 5

Decimal & Percentage Representation

Dividing the numerator -4 by denominator 91 produces a repeating decimal (approximately -0.043956, or -4.3956%).

-4 ÷ 91 = -0.043956 (-4.3956%)

Visual Representation

The diagram below illustrates 2/39 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-4/91`
Mixed Number Form	`-4/91`
Decimal Form	`-0.043956`
Percentage	`-4.3956%`

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Frequently Asked Questions

What is 2/39 minus 2/21 as a fraction?

2/39 − 2/21 in simplest fraction form is -4/91.

What is 2/39 minus 2/21 as a decimal?

2/39 − 2/21 converted to a decimal is -0.043956.

What is 2/39 minus 2/21 as a percentage?

2/39 − 2/21 expressed as a percentage is -4.3956%.

Does 2/39 minus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.043956...) because the denominator contains prime factors other than 2 and 5.