What is 11/23 plus 2/3? (Answer: 79/69)

Exact Answer

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Problem: What is 11/23 plus 2/3?
Formula / Expression: 11/23 + 2/3
Final Answer: 1 10/69 (79/69)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.
Working: LCD(23, 3) = 69

Step 2: Convert to Equivalent Fractions with Common Denominator 69
Multiply the numerator and denominator of 11/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.
Working: 11 × 3/23 × 3 = 33/69 and 2 × 23/3 × 23 = 46/69

Step 3: Add the Numerators
Now add the numerators (33 + 46 = 79) and keep the common denominator 69 unchanged.
Working: 33 + 46/69 = 79/69

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 69 is 1, confirming that 79/69 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/69

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (69), divide 79 by 69: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/69.
Working: 79/69 = 1 10/69

Step 6: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 69 produces a repeating decimal (approximately 1.144928, or 114.4928%).
Working: 79 ÷ 69 = 1.144928 (114.4928%)

Key Values:
- Simplified Fraction: 79/69
- Mixed Number Form: 1 10/69
- Decimal Value: 1.144928
- Percentage: 114.4928%

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Solved with FractionsCalc:
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11/23 + 2/3 = 79/69

Simplified Fraction

79/69

Mixed Number

1 10/69

Decimal Value

1.144928

Percentage

114.4928%

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Step-by-Step Solution: 11/23 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.

LCD(23, 3) = 69

Step 2

Convert to Equivalent Fractions with Common Denominator 69

Multiply the numerator and denominator of 11/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.

11 × 3/23 × 3 = 33/69 and 2 × 23/3 × 23 = 46/69

Step 3

Add the Numerators

Now add the numerators (33 + 46 = 79) and keep the common denominator 69 unchanged.

33 + 46/69 = 79/69

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 69 is 1, confirming that 79/69 cannot be reduced further—it is already in its simplest irreducible form.

79/69

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (79) is greater than the denominator (69), divide 79 by 69: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/69.

79/69 = 110/69

Step 6

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 69 produces a repeating decimal (approximately 1.144928, or 114.4928%).

79 ÷ 69 = 1.144928 (114.4928%)

Visual Representation

The diagram below illustrates 11/23 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/69`
Mixed Number Form	`1 10/69`
Decimal Form	`1.144928`
Percentage	`114.4928%`

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Frequently Asked Questions

What is 11/23 plus 2/3 as a fraction?

11/23 + 2/3 in simplest fraction form is 79/69 (or 1 10/69 as a mixed number).

What is 11/23 plus 2/3 as a decimal?

11/23 + 2/3 converted to a decimal is 1.144928.

What is 11/23 plus 2/3 as a percentage?

11/23 + 2/3 expressed as a percentage is 114.4928%.

How do you write 11/23 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 79/69 can be written as the mixed number 1 10/69.

Does 11/23 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.144928...) because the denominator contains prime factors other than 2 and 5.