What is 2/9 plus 8/23? (Answer: 118/207)

Exact Answer

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Problem: What is 2/9 plus 8/23?
Formula / Expression: 2/9 + 8/23
Final Answer: 118/207
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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 8/23 by 9 so both fractions share the common base 207.
Working: 2 × 23/9 × 23 = 46/207 and 8 × 9/23 × 9 = 72/207

Step 3: Add the Numerators
Now add the numerators (46 + 72 = 118) and keep the common denominator 207 unchanged.
Working: 46 + 72/207 = 118/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 118 and 207 is 1, confirming that 118/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 118/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 118 by denominator 207 produces a repeating decimal (approximately 0.570048, or 57.0048%).
Working: 118 ÷ 207 = 0.570048 (57.0048%)

Key Values:
- Simplified Fraction: 118/207
- Mixed Number Form: 118/207
- Decimal Value: 0.570048
- Percentage: 57.0048%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-8-23/
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2/9 + 8/23 = 118/207

Simplified Fraction

118/207

Mixed Number

Proper (118/207)

Decimal Value

0.570048

Percentage

57.0048%

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Step-by-Step Solution: 2/9 + 8/23

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 8/23 by 9 so both fractions share the common base 207.

2 × 23/9 × 23 = 46/207 and 8 × 9/23 × 9 = 72/207

Step 3

Add the Numerators

Now add the numerators (46 + 72 = 118) and keep the common denominator 207 unchanged.

46 + 72/207 = 118/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 118 and 207 is 1, confirming that 118/207 cannot be reduced further—it is already in its simplest irreducible form.

118/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 118 by denominator 207 produces a repeating decimal (approximately 0.570048, or 57.0048%).

118 ÷ 207 = 0.570048 (57.0048%)

Visual Representation

The diagram below illustrates 2/9 plus 8/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`118/207`
Mixed Number Form	`118/207`
Decimal Form	`0.570048`
Percentage	`57.0048%`

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Frequently Asked Questions

What is 2/9 plus 8/23 as a fraction?

2/9 + 8/23 in simplest fraction form is 118/207.

What is 2/9 plus 8/23 as a decimal?

2/9 + 8/23 converted to a decimal is 0.570048.

What is 2/9 plus 8/23 as a percentage?

2/9 + 8/23 expressed as a percentage is 57.0048%.

Does 2/9 plus 8/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.570048...) because the denominator contains prime factors other than 2 and 5.