What is 4/7 plus 9/13? (Answer: 115/91)

Exact Answer

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Problem: What is 4/7 plus 9/13?
Formula / Expression: 4/7 + 9/13
Final Answer: 1 24/91 (115/91)
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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 4/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.
Working: 4 × 13/7 × 13 = 52/91 and 9 × 7/13 × 7 = 63/91

Step 3: Add the Numerators
Now add the numerators (52 + 63 = 115) and keep the common denominator 91 unchanged.
Working: 52 + 63/91 = 115/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 91 is 1, confirming that 115/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 115/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (115) is greater than the denominator (91), divide 115 by 91: it goes in 1 whole time(s) with a remainder of 24, giving the mixed number 1 24/91.
Working: 115/91 = 1 24/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 115 by denominator 91 produces a repeating decimal (approximately 1.263736, or 126.3736%).
Working: 115 ÷ 91 = 1.263736 (126.3736%)

Key Values:
- Simplified Fraction: 115/91
- Mixed Number Form: 1 24/91
- Decimal Value: 1.263736
- Percentage: 126.3736%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-7-plus-9-13/
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4/7 + 9/13 = 115/91

Simplified Fraction

115/91

Mixed Number

1 24/91

Decimal Value

1.263736

Percentage

126.3736%

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Step-by-Step Solution: 4/7 + 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 4/7 by 13, and multiply the numerator and denominator of 9/13 by 7 so both fractions share the common base 91.

4 × 13/7 × 13 = 52/91 and 9 × 7/13 × 7 = 63/91

Step 3

Add the Numerators

Now add the numerators (52 + 63 = 115) and keep the common denominator 91 unchanged.

52 + 63/91 = 115/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 115 and 91 is 1, confirming that 115/91 cannot be reduced further—it is already in its simplest irreducible form.

115/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (115) is greater than the denominator (91), divide 115 by 91: it goes in 1 whole time(s) with a remainder of 24, giving the mixed number 1 24/91.

115/91 = 124/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 115 by denominator 91 produces a repeating decimal (approximately 1.263736, or 126.3736%).

115 ÷ 91 = 1.263736 (126.3736%)

Visual Representation

The diagram below illustrates 4/7 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`115/91`
Mixed Number Form	`1 24/91`
Decimal Form	`1.263736`
Percentage	`126.3736%`

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Frequently Asked Questions

What is 4/7 plus 9/13 as a fraction?

4/7 + 9/13 in simplest fraction form is 115/91 (or 1 24/91 as a mixed number).

What is 4/7 plus 9/13 as a decimal?

4/7 + 9/13 converted to a decimal is 1.263736.

What is 4/7 plus 9/13 as a percentage?

4/7 + 9/13 expressed as a percentage is 126.3736%.

How do you write 4/7 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 115/91 can be written as the mixed number 1 24/91.

Does 4/7 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.263736...) because the denominator contains prime factors other than 2 and 5.