What is 10/23 plus 6/13? (Answer: 268/299)

Exact Answer

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Problem: What is 10/23 plus 6/13?
Formula / Expression: 10/23 + 6/13
Final Answer: 268/299
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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 10/23 by 13, and multiply the numerator and denominator of 6/13 by 23 so both fractions share the common base 299.
Working: 10 × 13/23 × 13 = 130/299 and 6 × 23/13 × 23 = 138/299

Step 3: Add the Numerators
Now add the numerators (130 + 138 = 268) and keep the common denominator 299 unchanged.
Working: 130 + 138/299 = 268/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 268 and 299 is 1, confirming that 268/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 268/299

Step 5: Decimal & Percentage Representation
Dividing the numerator 268 by denominator 299 produces a repeating decimal (approximately 0.896321, or 89.6321%).
Working: 268 ÷ 299 = 0.896321 (89.6321%)

Key Values:
- Simplified Fraction: 268/299
- Mixed Number Form: 268/299
- Decimal Value: 0.896321
- Percentage: 89.6321%

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10/23 + 6/13 = 268/299

Simplified Fraction

268/299

Mixed Number

Proper (268/299)

Decimal Value

0.896321

Percentage

89.6321%

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Step-by-Step Solution: 10/23 + 6/13

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 10/23 by 13, and multiply the numerator and denominator of 6/13 by 23 so both fractions share the common base 299.

10 × 13/23 × 13 = 130/299 and 6 × 23/13 × 23 = 138/299

Step 3

Add the Numerators

Now add the numerators (130 + 138 = 268) and keep the common denominator 299 unchanged.

130 + 138/299 = 268/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 268 and 299 is 1, confirming that 268/299 cannot be reduced further—it is already in its simplest irreducible form.

268/299

Step 5

Decimal & Percentage Representation

Dividing the numerator 268 by denominator 299 produces a repeating decimal (approximately 0.896321, or 89.6321%).

268 ÷ 299 = 0.896321 (89.6321%)

Visual Representation

The diagram below illustrates 10/23 plus 6/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`268/299`
Mixed Number Form	`268/299`
Decimal Form	`0.896321`
Percentage	`89.6321%`

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Frequently Asked Questions

What is 10/23 plus 6/13 as a fraction?

10/23 + 6/13 in simplest fraction form is 268/299.

What is 10/23 plus 6/13 as a decimal?

10/23 + 6/13 converted to a decimal is 0.896321.

What is 10/23 plus 6/13 as a percentage?

10/23 + 6/13 expressed as a percentage is 89.6321%.

Does 10/23 plus 6/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.896321...) because the denominator contains prime factors other than 2 and 5.