What is 3/8 plus 9/13? (Answer: 111/104)

Exact Answer

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Problem: What is 3/8 plus 9/13?
Formula / Expression: 3/8 + 9/13
Final Answer: 1 7/104 (111/104)
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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 9/13 by 8 so both fractions share the common base 104.
Working: 3 × 13/8 × 13 = 39/104 and 9 × 8/13 × 8 = 72/104

Step 3: Add the Numerators
Now add the numerators (39 + 72 = 111) and keep the common denominator 104 unchanged.
Working: 39 + 72/104 = 111/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 111 and 104 is 1, confirming that 111/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 111/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (111) is greater than the denominator (104), divide 111 by 104: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/104.
Working: 111/104 = 1 7/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 111 by denominator 104 produces a repeating decimal (approximately 1.067308, or 106.7308%).
Working: 111 ÷ 104 = 1.067308 (106.7308%)

Key Values:
- Simplified Fraction: 111/104
- Mixed Number Form: 1 7/104
- Decimal Value: 1.067308
- Percentage: 106.7308%

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Solved with FractionsCalc:
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3/8 + 9/13 = 111/104

Simplified Fraction

111/104

Mixed Number

1 7/104

Decimal Value

1.067308

Percentage

106.7308%

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Step-by-Step Solution: 3/8 + 9/13

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 9/13 by 8 so both fractions share the common base 104.

3 × 13/8 × 13 = 39/104 and 9 × 8/13 × 8 = 72/104

Step 3

Add the Numerators

Now add the numerators (39 + 72 = 111) and keep the common denominator 104 unchanged.

39 + 72/104 = 111/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 111 and 104 is 1, confirming that 111/104 cannot be reduced further—it is already in its simplest irreducible form.

111/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (111) is greater than the denominator (104), divide 111 by 104: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/104.

111/104 = 17/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 111 by denominator 104 produces a repeating decimal (approximately 1.067308, or 106.7308%).

111 ÷ 104 = 1.067308 (106.7308%)

Visual Representation

The diagram below illustrates 3/8 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`111/104`
Mixed Number Form	`1 7/104`
Decimal Form	`1.067308`
Percentage	`106.7308%`

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Frequently Asked Questions

What is 3/8 plus 9/13 as a fraction?

3/8 + 9/13 in simplest fraction form is 111/104 (or 1 7/104 as a mixed number).

What is 3/8 plus 9/13 as a decimal?

3/8 + 9/13 converted to a decimal is 1.067308.

What is 3/8 plus 9/13 as a percentage?

3/8 + 9/13 expressed as a percentage is 106.7308%.

How do you write 3/8 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 111/104 can be written as the mixed number 1 7/104.

Does 3/8 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.067308...) because the denominator contains prime factors other than 2 and 5.