What is 2/9 plus 13/23? (Answer: 163/207)

Exact Answer

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Problem: What is 2/9 plus 13/23?
Formula / Expression: 2/9 + 13/23
Final Answer: 163/207
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 207
Multiply the numerator and denominator of 2/9 by 23, and multiply the numerator and denominator of 13/23 by 9 so both fractions share the common base 207.
Working: 2 × 23/9 × 23 = 46/207 and 13 × 9/23 × 9 = 117/207

Step 3: Add the Numerators
Now add the numerators (46 + 117 = 163) and keep the common denominator 207 unchanged.
Working: 46 + 117/207 = 163/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 207 is 1, confirming that 163/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 207 produces a repeating decimal (approximately 0.78744, or 78.744%).
Working: 163 ÷ 207 = 0.78744 (78.744%)

Key Values:
- Simplified Fraction: 163/207
- Mixed Number Form: 163/207
- Decimal Value: 0.78744
- Percentage: 78.744%

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Solved with FractionsCalc:
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2/9 + 13/23 = 163/207

Simplified Fraction

163/207

Mixed Number

Proper (163/207)

Decimal Value

0.78744

Percentage

78.744%

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Step-by-Step Solution: 2/9 + 13/23

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 23) = 207

Step 2

Convert to Equivalent Fractions with Common Denominator 207

Multiply the numerator and denominator of 2/9 by 23, and multiply the numerator and denominator of 13/23 by 9 so both fractions share the common base 207.

2 × 23/9 × 23 = 46/207 and 13 × 9/23 × 9 = 117/207

Step 3

Add the Numerators

Now add the numerators (46 + 117 = 163) and keep the common denominator 207 unchanged.

46 + 117/207 = 163/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 207 is 1, confirming that 163/207 cannot be reduced further—it is already in its simplest irreducible form.

163/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 207 produces a repeating decimal (approximately 0.78744, or 78.744%).

163 ÷ 207 = 0.78744 (78.744%)

Visual Representation

The diagram below illustrates 2/9 plus 13/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/207`
Mixed Number Form	`163/207`
Decimal Form	`0.78744`
Percentage	`78.744%`

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Frequently Asked Questions

What is 2/9 plus 13/23 as a fraction?

2/9 + 13/23 in simplest fraction form is 163/207.

What is 2/9 plus 13/23 as a decimal?

2/9 + 13/23 converted to a decimal is 0.78744.

What is 2/9 plus 13/23 as a percentage?

2/9 + 13/23 expressed as a percentage is 78.744%.

Does 2/9 plus 13/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.78744...) because the denominator contains prime factors other than 2 and 5.