What is 3/8 plus 10/13? (Answer: 119/104)

Exact Answer

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Problem: What is 3/8 plus 10/13?
Formula / Expression: 3/8 + 10/13
Final Answer: 1 15/104 (119/104)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.
Working: LCD(8, 13) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 3/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.
Working: 3 × 13/8 × 13 = 39/104 and 10 × 8/13 × 8 = 80/104

Step 3: Add the Numerators
Now add the numerators (39 + 80 = 119) and keep the common denominator 104 unchanged.
Working: 39 + 80/104 = 119/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 119 and 104 is 1, confirming that 119/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 119/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (119) is greater than the denominator (104), divide 119 by 104: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/104.
Working: 119/104 = 1 15/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 119 by denominator 104 produces a repeating decimal (approximately 1.144231, or 114.4231%).
Working: 119 ÷ 104 = 1.144231 (114.4231%)

Key Values:
- Simplified Fraction: 119/104
- Mixed Number Form: 1 15/104
- Decimal Value: 1.144231
- Percentage: 114.4231%

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Solved with FractionsCalc:
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3/8 + 10/13 = 119/104

Simplified Fraction

119/104

Mixed Number

1 15/104

Decimal Value

1.144231

Percentage

114.4231%

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Step-by-Step Solution: 3/8 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 3/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.

3 × 13/8 × 13 = 39/104 and 10 × 8/13 × 8 = 80/104

Step 3

Add the Numerators

Now add the numerators (39 + 80 = 119) and keep the common denominator 104 unchanged.

39 + 80/104 = 119/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 119 and 104 is 1, confirming that 119/104 cannot be reduced further—it is already in its simplest irreducible form.

119/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (119) is greater than the denominator (104), divide 119 by 104: it goes in 1 whole time(s) with a remainder of 15, giving the mixed number 1 15/104.

119/104 = 115/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 119 by denominator 104 produces a repeating decimal (approximately 1.144231, or 114.4231%).

119 ÷ 104 = 1.144231 (114.4231%)

Visual Representation

The diagram below illustrates 3/8 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`119/104`
Mixed Number Form	`1 15/104`
Decimal Form	`1.144231`
Percentage	`114.4231%`

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Frequently Asked Questions

What is 3/8 plus 10/13 as a fraction?

3/8 + 10/13 in simplest fraction form is 119/104 (or 1 15/104 as a mixed number).

What is 3/8 plus 10/13 as a decimal?

3/8 + 10/13 converted to a decimal is 1.144231.

What is 3/8 plus 10/13 as a percentage?

3/8 + 10/13 expressed as a percentage is 114.4231%.

How do you write 3/8 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 119/104 can be written as the mixed number 1 15/104.

Does 3/8 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.144231...) because the denominator contains prime factors other than 2 and 5.