What is 2/29 plus 5/9? (Answer: 163/261)

Exact Answer

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Problem: What is 2/29 plus 5/9?
Formula / Expression: 2/29 + 5/9
Final Answer: 163/261
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.
Working: LCD(29, 9) = 261

Step 2: Convert to Equivalent Fractions with Common Denominator 261
Multiply the numerator and denominator of 2/29 by 9, and multiply the numerator and denominator of 5/9 by 29 so both fractions share the common base 261.
Working: 2 × 9/29 × 9 = 18/261 and 5 × 29/9 × 29 = 145/261

Step 3: Add the Numerators
Now add the numerators (18 + 145 = 163) and keep the common denominator 261 unchanged.
Working: 18 + 145/261 = 163/261

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 261 is 1, confirming that 163/261 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/261

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 261 produces a repeating decimal (approximately 0.624521, or 62.4521%).
Working: 163 ÷ 261 = 0.624521 (62.4521%)

Key Values:
- Simplified Fraction: 163/261
- Mixed Number Form: 163/261
- Decimal Value: 0.624521
- Percentage: 62.4521%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-29-plus-5-9/
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2/29 + 5/9 = 163/261

Simplified Fraction

163/261

Mixed Number

Proper (163/261)

Decimal Value

0.624521

Percentage

62.4521%

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Step-by-Step Solution: 2/29 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 9 = 261.

LCD(29, 9) = 261

Step 2

Convert to Equivalent Fractions with Common Denominator 261

Multiply the numerator and denominator of 2/29 by 9, and multiply the numerator and denominator of 5/9 by 29 so both fractions share the common base 261.

2 × 9/29 × 9 = 18/261 and 5 × 29/9 × 29 = 145/261

Step 3

Add the Numerators

Now add the numerators (18 + 145 = 163) and keep the common denominator 261 unchanged.

18 + 145/261 = 163/261

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 261 is 1, confirming that 163/261 cannot be reduced further—it is already in its simplest irreducible form.

163/261

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 261 produces a repeating decimal (approximately 0.624521, or 62.4521%).

163 ÷ 261 = 0.624521 (62.4521%)

Visual Representation

The diagram below illustrates 2/29 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/261`
Mixed Number Form	`163/261`
Decimal Form	`0.624521`
Percentage	`62.4521%`

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Frequently Asked Questions

What is 2/29 plus 5/9 as a fraction?

2/29 + 5/9 in simplest fraction form is 163/261.

What is 2/29 plus 5/9 as a decimal?

2/29 + 5/9 converted to a decimal is 0.624521.

What is 2/29 plus 5/9 as a percentage?

2/29 + 5/9 expressed as a percentage is 62.4521%.

Does 2/29 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.624521...) because the denominator contains prime factors other than 2 and 5.