What is 2/23 plus 2/6? (Answer: 29/69)

Exact Answer

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Problem: What is 2/23 plus 2/6?
Formula / Expression: 2/23 + 2/6
Final Answer: 29/69
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 6 = 138.
Working: LCD(23, 6) = 138

Step 2: Convert to Equivalent Fractions with Common Denominator 138
Multiply the numerator and denominator of 2/23 by 6, and multiply the numerator and denominator of 2/6 by 23 so both fractions share the common base 138.
Working: 2 × 6/23 × 6 = 12/138 and 2 × 23/6 × 23 = 46/138

Step 3: Add the Numerators
Now add the numerators (12 + 46 = 58) and keep the common denominator 138 unchanged.
Working: 12 + 46/138 = 58/138

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 138, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/138 ÷ 2 = 29/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 69 produces a repeating decimal (approximately 0.42029, or 42.029%).
Working: 29 ÷ 69 = 0.42029 (42.029%)

Key Values:
- Simplified Fraction: 29/69
- Mixed Number Form: 29/69
- Decimal Value: 0.42029
- Percentage: 42.029%

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Solved with FractionsCalc:
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2/23 + 2/6 = 29/69

Simplified Fraction

29/69

Mixed Number

Proper (29/69)

Decimal Value

0.42029

Percentage

42.029%

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Step-by-Step Solution: 2/23 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 6 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 6 = 138.

LCD(23, 6) = 138

Step 2

Convert to Equivalent Fractions with Common Denominator 138

Multiply the numerator and denominator of 2/23 by 6, and multiply the numerator and denominator of 2/6 by 23 so both fractions share the common base 138.

2 × 6/23 × 6 = 12/138 and 2 × 23/6 × 23 = 46/138

Step 3

Add the Numerators

Now add the numerators (12 + 46 = 58) and keep the common denominator 138 unchanged.

12 + 46/138 = 58/138

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 138, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/138 ÷ 2 = 29/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 69 produces a repeating decimal (approximately 0.42029, or 42.029%).

29 ÷ 69 = 0.42029 (42.029%)

Visual Representation

The diagram below illustrates 2/23 plus 2/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/69`
Mixed Number Form	`29/69`
Decimal Form	`0.42029`
Percentage	`42.029%`

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Frequently Asked Questions

What is 2/23 plus 2/6 as a fraction?

2/23 + 2/6 in simplest fraction form is 29/69.

What is 2/23 plus 2/6 as a decimal?

2/23 + 2/6 converted to a decimal is 0.42029.

What is 2/23 plus 2/6 as a percentage?

2/23 + 2/6 expressed as a percentage is 42.029%.

Does 2/23 plus 2/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.42029...) because the denominator contains prime factors other than 2 and 5.