What is 4/23 plus 11/13? (Answer: 305/299)

Exact Answer

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Problem: What is 4/23 plus 11/13?
Formula / Expression: 4/23 + 11/13
Final Answer: 1 6/299 (305/299)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.
Working: LCD(23, 13) = 299

Step 2: Convert to Equivalent Fractions with Common Denominator 299
Multiply the numerator and denominator of 4/23 by 13, and multiply the numerator and denominator of 11/13 by 23 so both fractions share the common base 299.
Working: 4 × 13/23 × 13 = 52/299 and 11 × 23/13 × 23 = 253/299

Step 3: Add the Numerators
Now add the numerators (52 + 253 = 305) and keep the common denominator 299 unchanged.
Working: 52 + 253/299 = 305/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 305 and 299 is 1, confirming that 305/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 305/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (305) is greater than the denominator (299), divide 305 by 299: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/299.
Working: 305/299 = 1 6/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 305 by denominator 299 produces a repeating decimal (approximately 1.020067, or 102.0067%).
Working: 305 ÷ 299 = 1.020067 (102.0067%)

Key Values:
- Simplified Fraction: 305/299
- Mixed Number Form: 1 6/299
- Decimal Value: 1.020067
- Percentage: 102.0067%

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Solved with FractionsCalc:
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4/23 + 11/13 = 305/299

Simplified Fraction

305/299

Mixed Number

1 6/299

Decimal Value

1.020067

Percentage

102.0067%

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Step-by-Step Solution: 4/23 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.

LCD(23, 13) = 299

Step 2

Convert to Equivalent Fractions with Common Denominator 299

Multiply the numerator and denominator of 4/23 by 13, and multiply the numerator and denominator of 11/13 by 23 so both fractions share the common base 299.

4 × 13/23 × 13 = 52/299 and 11 × 23/13 × 23 = 253/299

Step 3

Add the Numerators

Now add the numerators (52 + 253 = 305) and keep the common denominator 299 unchanged.

52 + 253/299 = 305/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 305 and 299 is 1, confirming that 305/299 cannot be reduced further—it is already in its simplest irreducible form.

305/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (305) is greater than the denominator (299), divide 305 by 299: it goes in 1 whole time(s) with a remainder of 6, giving the mixed number 1 6/299.

305/299 = 16/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 305 by denominator 299 produces a repeating decimal (approximately 1.020067, or 102.0067%).

305 ÷ 299 = 1.020067 (102.0067%)

Visual Representation

The diagram below illustrates 4/23 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`305/299`
Mixed Number Form	`1 6/299`
Decimal Form	`1.020067`
Percentage	`102.0067%`

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Frequently Asked Questions

What is 4/23 plus 11/13 as a fraction?

4/23 + 11/13 in simplest fraction form is 305/299 (or 1 6/299 as a mixed number).

What is 4/23 plus 11/13 as a decimal?

4/23 + 11/13 converted to a decimal is 1.020067.

What is 4/23 plus 11/13 as a percentage?

4/23 + 11/13 expressed as a percentage is 102.0067%.

How do you write 4/23 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 305/299 can be written as the mixed number 1 6/299.

Does 4/23 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.020067...) because the denominator contains prime factors other than 2 and 5.