What is 2/23 plus 6/9? (Answer: 52/69)

Exact Answer

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Problem: What is 2/23 plus 6/9?
Formula / Expression: 2/23 + 6/9
Final Answer: 52/69
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.
Working: LCD(23, 9) = 207

Step 2: Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 2/23 by 9, and multiply the numerator and denominator of 6/9 by 23 so both fractions share the common base 207.
Working: 2 × 9/23 × 9 = 18/207 and 6 × 23/9 × 23 = 138/207

Step 3: Add the Numerators
Now add the numerators (18 + 138 = 156) and keep the common denominator 207 unchanged.
Working: 18 + 138/207 = 156/207

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 156 and 207, which is 3. Divide both the numerator and denominator by 3.
Working: 156 ÷ 3/207 ÷ 3 = 52/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 69 produces a repeating decimal (approximately 0.753623, or 75.3623%).
Working: 52 ÷ 69 = 0.753623 (75.3623%)

Key Values:
- Simplified Fraction: 52/69
- Mixed Number Form: 52/69
- Decimal Value: 0.753623
- Percentage: 75.3623%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-6-9/
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2/23 + 6/9 = 52/69

Simplified Fraction

52/69

Mixed Number

Proper (52/69)

Decimal Value

0.753623

Percentage

75.3623%

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Step-by-Step Solution: 2/23 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 9 = 207.

LCD(23, 9) = 207

Step 2

Convert to Equivalent Fractions with Common Denominator 207

Multiply the numerator and denominator of 2/23 by 9, and multiply the numerator and denominator of 6/9 by 23 so both fractions share the common base 207.

2 × 9/23 × 9 = 18/207 and 6 × 23/9 × 23 = 138/207

Step 3

Add the Numerators

Now add the numerators (18 + 138 = 156) and keep the common denominator 207 unchanged.

18 + 138/207 = 156/207

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 156 and 207, which is 3. Divide both the numerator and denominator by 3.

156 ÷ 3/207 ÷ 3 = 52/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 69 produces a repeating decimal (approximately 0.753623, or 75.3623%).

52 ÷ 69 = 0.753623 (75.3623%)

Visual Representation

The diagram below illustrates 2/23 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/69`
Mixed Number Form	`52/69`
Decimal Form	`0.753623`
Percentage	`75.3623%`

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Frequently Asked Questions

What is 2/23 plus 6/9 as a fraction?

2/23 + 6/9 in simplest fraction form is 52/69.

What is 2/23 plus 6/9 as a decimal?

2/23 + 6/9 converted to a decimal is 0.753623.

What is 2/23 plus 6/9 as a percentage?

2/23 + 6/9 expressed as a percentage is 75.3623%.

Does 2/23 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.753623...) because the denominator contains prime factors other than 2 and 5.