What is 3/23 plus 3/13? (Answer: 108/299)

Exact Answer

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Problem: What is 3/23 plus 3/13?
Formula / Expression: 3/23 + 3/13
Final Answer: 108/299
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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 3/23 by 13, and multiply the numerator and denominator of 3/13 by 23 so both fractions share the common base 299.
Working: 3 × 13/23 × 13 = 39/299 and 3 × 23/13 × 23 = 69/299

Step 3: Add the Numerators
Now add the numerators (39 + 69 = 108) and keep the common denominator 299 unchanged.
Working: 39 + 69/299 = 108/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 108 and 299 is 1, confirming that 108/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 108/299

Step 5: Decimal & Percentage Representation
Dividing the numerator 108 by denominator 299 produces a repeating decimal (approximately 0.361204, or 36.1204%).
Working: 108 ÷ 299 = 0.361204 (36.1204%)

Key Values:
- Simplified Fraction: 108/299
- Mixed Number Form: 108/299
- Decimal Value: 0.361204
- Percentage: 36.1204%

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3/23 + 3/13 = 108/299

Simplified Fraction

108/299

Mixed Number

Proper (108/299)

Decimal Value

0.361204

Percentage

36.1204%

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Step-by-Step Solution: 3/23 + 3/13

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 3/23 by 13, and multiply the numerator and denominator of 3/13 by 23 so both fractions share the common base 299.

3 × 13/23 × 13 = 39/299 and 3 × 23/13 × 23 = 69/299

Step 3

Add the Numerators

Now add the numerators (39 + 69 = 108) and keep the common denominator 299 unchanged.

39 + 69/299 = 108/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 108 and 299 is 1, confirming that 108/299 cannot be reduced further—it is already in its simplest irreducible form.

108/299

Step 5

Decimal & Percentage Representation

Dividing the numerator 108 by denominator 299 produces a repeating decimal (approximately 0.361204, or 36.1204%).

108 ÷ 299 = 0.361204 (36.1204%)

Visual Representation

The diagram below illustrates 3/23 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`108/299`
Mixed Number Form	`108/299`
Decimal Form	`0.361204`
Percentage	`36.1204%`

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Frequently Asked Questions

What is 3/23 plus 3/13 as a fraction?

3/23 + 3/13 in simplest fraction form is 108/299.

What is 3/23 plus 3/13 as a decimal?

3/23 + 3/13 converted to a decimal is 0.361204.

What is 3/23 plus 3/13 as a percentage?

3/23 + 3/13 expressed as a percentage is 36.1204%.

Does 3/23 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.361204...) because the denominator contains prime factors other than 2 and 5.