What is 8/15 plus 10/13? (Answer: 254/195)

Exact Answer

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Problem: What is 8/15 plus 10/13?
Formula / Expression: 8/15 + 10/13
Final Answer: 1 59/195 (254/195)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 13 = 195.
Working: LCD(15, 13) = 195

Step 2: Convert to Equivalent Fractions with Common Denominator 195
Multiply the numerator and denominator of 8/15 by 13, and multiply the numerator and denominator of 10/13 by 15 so both fractions share the common base 195.
Working: 8 × 13/15 × 13 = 104/195 and 10 × 15/13 × 15 = 150/195

Step 3: Add the Numerators
Now add the numerators (104 + 150 = 254) and keep the common denominator 195 unchanged.
Working: 104 + 150/195 = 254/195

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 254 and 195 is 1, confirming that 254/195 cannot be reduced further—it is already in its simplest irreducible form.
Working: 254/195

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (254) is greater than the denominator (195), divide 254 by 195: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/195.
Working: 254/195 = 1 59/195

Step 6: Decimal & Percentage Representation
Dividing the numerator 254 by denominator 195 produces a repeating decimal (approximately 1.302564, or 130.2564%).
Working: 254 ÷ 195 = 1.302564 (130.2564%)

Key Values:
- Simplified Fraction: 254/195
- Mixed Number Form: 1 59/195
- Decimal Value: 1.302564
- Percentage: 130.2564%

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Solved with FractionsCalc:
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8/15 + 10/13 = 254/195

Simplified Fraction

254/195

Mixed Number

1 59/195

Decimal Value

1.302564

Percentage

130.2564%

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Step-by-Step Solution: 8/15 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 13 = 195.

LCD(15, 13) = 195

Step 2

Convert to Equivalent Fractions with Common Denominator 195

Multiply the numerator and denominator of 8/15 by 13, and multiply the numerator and denominator of 10/13 by 15 so both fractions share the common base 195.

8 × 13/15 × 13 = 104/195 and 10 × 15/13 × 15 = 150/195

Step 3

Add the Numerators

Now add the numerators (104 + 150 = 254) and keep the common denominator 195 unchanged.

104 + 150/195 = 254/195

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 254 and 195 is 1, confirming that 254/195 cannot be reduced further—it is already in its simplest irreducible form.

254/195

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (254) is greater than the denominator (195), divide 254 by 195: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/195.

254/195 = 159/195

Step 6

Decimal & Percentage Representation

Dividing the numerator 254 by denominator 195 produces a repeating decimal (approximately 1.302564, or 130.2564%).

254 ÷ 195 = 1.302564 (130.2564%)

Visual Representation

The diagram below illustrates 8/15 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`254/195`
Mixed Number Form	`1 59/195`
Decimal Form	`1.302564`
Percentage	`130.2564%`

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Frequently Asked Questions

What is 8/15 plus 10/13 as a fraction?

8/15 + 10/13 in simplest fraction form is 254/195 (or 1 59/195 as a mixed number).

What is 8/15 plus 10/13 as a decimal?

8/15 + 10/13 converted to a decimal is 1.302564.

What is 8/15 plus 10/13 as a percentage?

8/15 + 10/13 expressed as a percentage is 130.2564%.

How do you write 8/15 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 254/195 can be written as the mixed number 1 59/195.

Does 8/15 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.302564...) because the denominator contains prime factors other than 2 and 5.