What is 2/11 plus 9/23? (Answer: 145/253)

Exact Answer

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Problem: What is 2/11 plus 9/23?
Formula / Expression: 2/11 + 9/23
Final Answer: 145/253
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 23 = 253.
Working: LCD(11, 23) = 253

Step 2: Convert to Equivalent Fractions with Common Denominator 253
Multiply the numerator and denominator of 2/11 by 23, and multiply the numerator and denominator of 9/23 by 11 so both fractions share the common base 253.
Working: 2 × 23/11 × 23 = 46/253 and 9 × 11/23 × 11 = 99/253

Step 3: Add the Numerators
Now add the numerators (46 + 99 = 145) and keep the common denominator 253 unchanged.
Working: 46 + 99/253 = 145/253

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 145 and 253 is 1, confirming that 145/253 cannot be reduced further—it is already in its simplest irreducible form.
Working: 145/253

Step 5: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 253 produces a repeating decimal (approximately 0.573123, or 57.3123%).
Working: 145 ÷ 253 = 0.573123 (57.3123%)

Key Values:
- Simplified Fraction: 145/253
- Mixed Number Form: 145/253
- Decimal Value: 0.573123
- Percentage: 57.3123%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-11-plus-9-23/
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2/11 + 9/23 = 145/253

Simplified Fraction

145/253

Mixed Number

Proper (145/253)

Decimal Value

0.573123

Percentage

57.3123%

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Step-by-Step Solution: 2/11 + 9/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 23 = 253.

LCD(11, 23) = 253

Step 2

Convert to Equivalent Fractions with Common Denominator 253

Multiply the numerator and denominator of 2/11 by 23, and multiply the numerator and denominator of 9/23 by 11 so both fractions share the common base 253.

2 × 23/11 × 23 = 46/253 and 9 × 11/23 × 11 = 99/253

Step 3

Add the Numerators

Now add the numerators (46 + 99 = 145) and keep the common denominator 253 unchanged.

46 + 99/253 = 145/253

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 145 and 253 is 1, confirming that 145/253 cannot be reduced further—it is already in its simplest irreducible form.

145/253

Step 5

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 253 produces a repeating decimal (approximately 0.573123, or 57.3123%).

145 ÷ 253 = 0.573123 (57.3123%)

Visual Representation

The diagram below illustrates 2/11 plus 9/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/253`
Mixed Number Form	`145/253`
Decimal Form	`0.573123`
Percentage	`57.3123%`

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Frequently Asked Questions

What is 2/11 plus 9/23 as a fraction?

2/11 + 9/23 in simplest fraction form is 145/253.

What is 2/11 plus 9/23 as a decimal?

2/11 + 9/23 converted to a decimal is 0.573123.

What is 2/11 plus 9/23 as a percentage?

2/11 + 9/23 expressed as a percentage is 57.3123%.

Does 2/11 plus 9/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.573123...) because the denominator contains prime factors other than 2 and 5.