What is 10/23 plus 8/13? (Answer: 314/299)

Exact Answer

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Problem: What is 10/23 plus 8/13?
Formula / Expression: 10/23 + 8/13
Final Answer: 1 15/299 (314/299)
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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 8/13 by 23 so both fractions share the common base 299.
Working: 10 × 13/23 × 13 = 130/299 and 8 × 23/13 × 23 = 184/299

Step 3: Add the Numerators
Now add the numerators (130 + 184 = 314) and keep the common denominator 299 unchanged.
Working: 130 + 184/299 = 314/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 314 and 299 is 1, confirming that 314/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 314/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (314) is greater than the denominator (299), divide 314 by 299: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/299.
Working: 314/299 = 1 15/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 314 by denominator 299 produces a repeating decimal (approximately 1.050167, or 105.0167%).
Working: 314 ÷ 299 = 1.050167 (105.0167%)

Key Values:
- Simplified Fraction: 314/299
- Mixed Number Form: 1 15/299
- Decimal Value: 1.050167
- Percentage: 105.0167%

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Solved with FractionsCalc:
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10/23 + 8/13 = 314/299

Simplified Fraction

314/299

Mixed Number

1 15/299

Decimal Value

1.050167

Percentage

105.0167%

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Step-by-Step Solution: 10/23 + 8/13

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 8/13 by 23 so both fractions share the common base 299.

10 × 13/23 × 13 = 130/299 and 8 × 23/13 × 23 = 184/299

Step 3

Add the Numerators

Now add the numerators (130 + 184 = 314) and keep the common denominator 299 unchanged.

130 + 184/299 = 314/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 314 and 299 is 1, confirming that 314/299 cannot be reduced further—it is already in its simplest irreducible form.

314/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (314) is greater than the denominator (299), divide 314 by 299: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/299.

314/299 = 115/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 314 by denominator 299 produces a repeating decimal (approximately 1.050167, or 105.0167%).

314 ÷ 299 = 1.050167 (105.0167%)

Visual Representation

The diagram below illustrates 10/23 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`314/299`
Mixed Number Form	`1 15/299`
Decimal Form	`1.050167`
Percentage	`105.0167%`

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Frequently Asked Questions

What is 10/23 plus 8/13 as a fraction?

10/23 + 8/13 in simplest fraction form is 314/299 (or 1 15/299 as a mixed number).

What is 10/23 plus 8/13 as a decimal?

10/23 + 8/13 converted to a decimal is 1.050167.

What is 10/23 plus 8/13 as a percentage?

10/23 + 8/13 expressed as a percentage is 105.0167%.

How do you write 10/23 plus 8/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 314/299 can be written as the mixed number 1 15/299.

Does 10/23 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.050167...) because the denominator contains prime factors other than 2 and 5.