What is 4/9 plus 9/13? (Answer: 133/117)

Exact Answer

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Problem: What is 4/9 plus 9/13?
Formula / Expression: 4/9 + 9/13
Final Answer: 1 16/117 (133/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
Working: LCD(9, 13) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 4/9 by 13, and multiply the numerator and denominator of 9/13 by 9 so both fractions share the common base 117.
Working: 4 × 13/9 × 13 = 52/117 and 9 × 9/13 × 9 = 81/117

Step 3: Add the Numerators
Now add the numerators (52 + 81 = 133) and keep the common denominator 117 unchanged.
Working: 52 + 81/117 = 133/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 133 and 117 is 1, confirming that 133/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 133/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (133) is greater than the denominator (117), divide 133 by 117: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/117.
Working: 133/117 = 1 16/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 133 by denominator 117 produces a repeating decimal (approximately 1.136752, or 113.6752%).
Working: 133 ÷ 117 = 1.136752 (113.6752%)

Key Values:
- Simplified Fraction: 133/117
- Mixed Number Form: 1 16/117
- Decimal Value: 1.136752
- Percentage: 113.6752%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-9-13/
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4/9 + 9/13 = 133/117

Simplified Fraction

133/117

Mixed Number

1 16/117

Decimal Value

1.136752

Percentage

113.6752%

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Step-by-Step Solution: 4/9 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 4/9 by 13, and multiply the numerator and denominator of 9/13 by 9 so both fractions share the common base 117.

4 × 13/9 × 13 = 52/117 and 9 × 9/13 × 9 = 81/117

Step 3

Add the Numerators

Now add the numerators (52 + 81 = 133) and keep the common denominator 117 unchanged.

52 + 81/117 = 133/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 133 and 117 is 1, confirming that 133/117 cannot be reduced further—it is already in its simplest irreducible form.

133/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (133) is greater than the denominator (117), divide 133 by 117: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/117.

133/117 = 116/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 133 by denominator 117 produces a repeating decimal (approximately 1.136752, or 113.6752%).

133 ÷ 117 = 1.136752 (113.6752%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`133/117`
Mixed Number Form	`1 16/117`
Decimal Form	`1.136752`
Percentage	`113.6752%`

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Frequently Asked Questions

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

4/9 + 9/13 in simplest fraction form is 133/117 (or 1 16/117 as a mixed number).

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

4/9 + 9/13 converted to a decimal is 1.136752.

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

4/9 + 9/13 expressed as a percentage is 113.6752%.

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

Because the numerator is greater than the denominator, the improper fraction 133/117 can be written as the mixed number 1 16/117.

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

It results in a repeating decimal (approximately 1.136752...) because the denominator contains prime factors other than 2 and 5.