What is 2/39 plus 15/21? (Answer: 209/273)

Exact Answer

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Problem: What is 2/39 plus 15/21?
Formula / Expression: 2/39 + 15/21
Final Answer: 209/273
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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 15/21 by 13 so both fractions share the common base 273.
Working: 2 × 7/39 × 7 = 14/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (14 + 195 = 209) and keep the common denominator 273 unchanged.
Working: 14 + 195/273 = 209/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 273 is 1, confirming that 209/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 273 produces a repeating decimal (approximately 0.765568, or 76.5568%).
Working: 209 ÷ 273 = 0.765568 (76.5568%)

Key Values:
- Simplified Fraction: 209/273
- Mixed Number Form: 209/273
- Decimal Value: 0.765568
- Percentage: 76.5568%

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Solved with FractionsCalc:
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2/39 + 15/21 = 209/273

Simplified Fraction

209/273

Mixed Number

Proper (209/273)

Decimal Value

0.765568

Percentage

76.5568%

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Step-by-Step Solution: 2/39 + 15/21

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 15/21 by 13 so both fractions share the common base 273.

2 × 7/39 × 7 = 14/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (14 + 195 = 209) and keep the common denominator 273 unchanged.

14 + 195/273 = 209/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 273 is 1, confirming that 209/273 cannot be reduced further—it is already in its simplest irreducible form.

209/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 273 produces a repeating decimal (approximately 0.765568, or 76.5568%).

209 ÷ 273 = 0.765568 (76.5568%)

Visual Representation

The diagram below illustrates 2/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/273`
Mixed Number Form	`209/273`
Decimal Form	`0.765568`
Percentage	`76.5568%`

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Frequently Asked Questions

What is 2/39 plus 15/21 as a fraction?

2/39 + 15/21 in simplest fraction form is 209/273.

What is 2/39 plus 15/21 as a decimal?

2/39 + 15/21 converted to a decimal is 0.765568.

What is 2/39 plus 15/21 as a percentage?

2/39 + 15/21 expressed as a percentage is 76.5568%.

Does 2/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.765568...) because the denominator contains prime factors other than 2 and 5.