What is 2/23 plus 5/9? (Answer: 133/207)

Exact Answer

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Problem: What is 2/23 plus 5/9?
Formula / Expression: 2/23 + 5/9
Final Answer: 133/207
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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 5/9 by 23 so both fractions share the common base 207.
Working: 2 × 9/23 × 9 = 18/207 and 5 × 23/9 × 23 = 115/207

Step 3: Add the Numerators
Now add the numerators (18 + 115 = 133) and keep the common denominator 207 unchanged.
Working: 18 + 115/207 = 133/207

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 207 is 1, confirming that 133/207 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 207 produces a repeating decimal (approximately 0.642512, or 64.2512%).
Working: 133 ÷ 207 = 0.642512 (64.2512%)

Key Values:
- Simplified Fraction: 133/207
- Mixed Number Form: 133/207
- Decimal Value: 0.642512
- Percentage: 64.2512%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-5-9/
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2/23 + 5/9 = 133/207

Simplified Fraction

133/207

Mixed Number

Proper (133/207)

Decimal Value

0.642512

Percentage

64.2512%

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Step-by-Step Solution: 2/23 + 5/9

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 5/9 by 23 so both fractions share the common base 207.

2 × 9/23 × 9 = 18/207 and 5 × 23/9 × 23 = 115/207

Step 3

Add the Numerators

Now add the numerators (18 + 115 = 133) and keep the common denominator 207 unchanged.

18 + 115/207 = 133/207

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 207 is 1, confirming that 133/207 cannot be reduced further—it is already in its simplest irreducible form.

133/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 207 produces a repeating decimal (approximately 0.642512, or 64.2512%).

133 ÷ 207 = 0.642512 (64.2512%)

Visual Representation

The diagram below illustrates 2/23 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/207`
Mixed Number Form	`133/207`
Decimal Form	`0.642512`
Percentage	`64.2512%`

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Frequently Asked Questions

What is 2/23 plus 5/9 as a fraction?

2/23 + 5/9 in simplest fraction form is 133/207.

What is 2/23 plus 5/9 as a decimal?

2/23 + 5/9 converted to a decimal is 0.642512.

What is 2/23 plus 5/9 as a percentage?

2/23 + 5/9 expressed as a percentage is 64.2512%.

Does 2/23 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.642512...) because the denominator contains prime factors other than 2 and 5.