What is 3/7 plus 9/13? (Answer: 102/91)

Exact Answer

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Problem: What is 3/7 plus 9/13?
Formula / Expression: 3/7 + 9/13
Final Answer: 1 11/91 (102/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.
Working: LCD(7, 13) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 3/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.
Working: 3 × 13/7 × 13 = 39/91 and 9 × 7/13 × 7 = 63/91

Step 3: Add the Numerators
Now add the numerators (39 + 63 = 102) and keep the common denominator 91 unchanged.
Working: 39 + 63/91 = 102/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 102 and 91 is 1, confirming that 102/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 102/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (102) is greater than the denominator (91), divide 102 by 91: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/91.
Working: 102/91 = 1 11/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 102 by denominator 91 produces a repeating decimal (approximately 1.120879, or 112.0879%).
Working: 102 ÷ 91 = 1.120879 (112.0879%)

Key Values:
- Simplified Fraction: 102/91
- Mixed Number Form: 1 11/91
- Decimal Value: 1.120879
- Percentage: 112.0879%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-9-13/
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3/7 + 9/13 = 102/91

Simplified Fraction

102/91

Mixed Number

1 11/91

Decimal Value

1.120879

Percentage

112.0879%

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Step-by-Step Solution: 3/7 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.

LCD(7, 13) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 3/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.

3 × 13/7 × 13 = 39/91 and 9 × 7/13 × 7 = 63/91

Step 3

Add the Numerators

Now add the numerators (39 + 63 = 102) and keep the common denominator 91 unchanged.

39 + 63/91 = 102/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 102 and 91 is 1, confirming that 102/91 cannot be reduced further—it is already in its simplest irreducible form.

102/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (102) is greater than the denominator (91), divide 102 by 91: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/91.

102/91 = 111/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 102 by denominator 91 produces a repeating decimal (approximately 1.120879, or 112.0879%).

102 ÷ 91 = 1.120879 (112.0879%)

Visual Representation

The diagram below illustrates 3/7 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`102/91`
Mixed Number Form	`1 11/91`
Decimal Form	`1.120879`
Percentage	`112.0879%`

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Frequently Asked Questions

What is 3/7 plus 9/13 as a fraction?

3/7 + 9/13 in simplest fraction form is 102/91 (or 1 11/91 as a mixed number).

What is 3/7 plus 9/13 as a decimal?

3/7 + 9/13 converted to a decimal is 1.120879.

What is 3/7 plus 9/13 as a percentage?

3/7 + 9/13 expressed as a percentage is 112.0879%.

How do you write 3/7 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 102/91 can be written as the mixed number 1 11/91.

Does 3/7 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.120879...) because the denominator contains prime factors other than 2 and 5.