What is 2/29 plus 2/11? (Answer: 80/319)

Exact Answer

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Problem: What is 2/29 plus 2/11?
Formula / Expression: 2/29 + 2/11
Final Answer: 80/319
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 11 = 319.
Working: LCD(29, 11) = 319

Step 2: Convert to Equivalent Fractions with Common Denominator 319
Multiply the numerator and denominator of 2/29 by 11, and multiply the numerator and denominator of 2/11 by 29 so both fractions share the common base 319.
Working: 2 × 11/29 × 11 = 22/319 and 2 × 29/11 × 29 = 58/319

Step 3: Add the Numerators
Now add the numerators (22 + 58 = 80) and keep the common denominator 319 unchanged.
Working: 22 + 58/319 = 80/319

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 80 and 319 is 1, confirming that 80/319 cannot be reduced further—it is already in its simplest irreducible form.
Working: 80/319

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 319 produces a repeating decimal (approximately 0.250784, or 25.0784%).
Working: 80 ÷ 319 = 0.250784 (25.0784%)

Key Values:
- Simplified Fraction: 80/319
- Mixed Number Form: 80/319
- Decimal Value: 0.250784
- Percentage: 25.0784%

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Solved with FractionsCalc:
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2/29 + 2/11 = 80/319

Simplified Fraction

80/319

Mixed Number

Proper (80/319)

Decimal Value

0.250784

Percentage

25.0784%

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Step-by-Step Solution: 2/29 + 2/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 11 = 319.

LCD(29, 11) = 319

Step 2

Convert to Equivalent Fractions with Common Denominator 319

Multiply the numerator and denominator of 2/29 by 11, and multiply the numerator and denominator of 2/11 by 29 so both fractions share the common base 319.

2 × 11/29 × 11 = 22/319 and 2 × 29/11 × 29 = 58/319

Step 3

Add the Numerators

Now add the numerators (22 + 58 = 80) and keep the common denominator 319 unchanged.

22 + 58/319 = 80/319

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 80 and 319 is 1, confirming that 80/319 cannot be reduced further—it is already in its simplest irreducible form.

80/319

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 319 produces a repeating decimal (approximately 0.250784, or 25.0784%).

80 ÷ 319 = 0.250784 (25.0784%)

Visual Representation

The diagram below illustrates 2/29 plus 2/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/319`
Mixed Number Form	`80/319`
Decimal Form	`0.250784`
Percentage	`25.0784%`

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Frequently Asked Questions

What is 2/29 plus 2/11 as a fraction?

2/29 + 2/11 in simplest fraction form is 80/319.

What is 2/29 plus 2/11 as a decimal?

2/29 + 2/11 converted to a decimal is 0.250784.

What is 2/29 plus 2/11 as a percentage?

2/29 + 2/11 expressed as a percentage is 25.0784%.

Does 2/29 plus 2/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.250784...) because the denominator contains prime factors other than 2 and 5.