What is 2/29 plus 2/23? (Answer: 104/667)

Exact Answer

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Problem: What is 2/29 plus 2/23?
Formula / Expression: 2/29 + 2/23
Final Answer: 104/667
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 23 = 667.
Working: LCD(29, 23) = 667

Step 2: Convert to Equivalent Fractions with Common Denominator 667
Multiply the numerator and denominator of 2/29 by 23, and multiply the numerator and denominator of 2/23 by 29 so both fractions share the common base 667.
Working: 2 × 23/29 × 23 = 46/667 and 2 × 29/23 × 29 = 58/667

Step 3: Add the Numerators
Now add the numerators (46 + 58 = 104) and keep the common denominator 667 unchanged.
Working: 46 + 58/667 = 104/667

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 104 and 667 is 1, confirming that 104/667 cannot be reduced further—it is already in its simplest irreducible form.
Working: 104/667

Step 5: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 667 produces a repeating decimal (approximately 0.155922, or 15.5922%).
Working: 104 ÷ 667 = 0.155922 (15.5922%)

Key Values:
- Simplified Fraction: 104/667
- Mixed Number Form: 104/667
- Decimal Value: 0.155922
- Percentage: 15.5922%

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Solved with FractionsCalc:
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2/29 + 2/23 = 104/667

Simplified Fraction

104/667

Mixed Number

Proper (104/667)

Decimal Value

0.155922

Percentage

15.5922%

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Step-by-Step Solution: 2/29 + 2/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 23 = 667.

LCD(29, 23) = 667

Step 2

Convert to Equivalent Fractions with Common Denominator 667

Multiply the numerator and denominator of 2/29 by 23, and multiply the numerator and denominator of 2/23 by 29 so both fractions share the common base 667.

2 × 23/29 × 23 = 46/667 and 2 × 29/23 × 29 = 58/667

Step 3

Add the Numerators

Now add the numerators (46 + 58 = 104) and keep the common denominator 667 unchanged.

46 + 58/667 = 104/667

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 104 and 667 is 1, confirming that 104/667 cannot be reduced further—it is already in its simplest irreducible form.

104/667

Step 5

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 667 produces a repeating decimal (approximately 0.155922, or 15.5922%).

104 ÷ 667 = 0.155922 (15.5922%)

Visual Representation

The diagram below illustrates 2/29 plus 2/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/667`
Mixed Number Form	`104/667`
Decimal Form	`0.155922`
Percentage	`15.5922%`

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Frequently Asked Questions

What is 2/29 plus 2/23 as a fraction?

2/29 + 2/23 in simplest fraction form is 104/667.

What is 2/29 plus 2/23 as a decimal?

2/29 + 2/23 converted to a decimal is 0.155922.

What is 2/29 plus 2/23 as a percentage?

2/29 + 2/23 expressed as a percentage is 15.5922%.

Does 2/29 plus 2/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.155922...) because the denominator contains prime factors other than 2 and 5.