What is 4/9 plus 11/13? (Answer: 151/117)

Exact Answer

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Problem: What is 4/9 plus 11/13?
Formula / Expression: 4/9 + 11/13
Final Answer: 1 34/117 (151/117)
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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 11/13 by 9 so both fractions share the common base 117.
Working: 4 × 13/9 × 13 = 52/117 and 11 × 9/13 × 9 = 99/117

Step 3: Add the Numerators
Now add the numerators (52 + 99 = 151) and keep the common denominator 117 unchanged.
Working: 52 + 99/117 = 151/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 151 and 117 is 1, confirming that 151/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 151/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (151) is greater than the denominator (117), divide 151 by 117: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/117.
Working: 151/117 = 1 34/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 117 produces a repeating decimal (approximately 1.290598, or 129.0598%).
Working: 151 ÷ 117 = 1.290598 (129.0598%)

Key Values:
- Simplified Fraction: 151/117
- Mixed Number Form: 1 34/117
- Decimal Value: 1.290598
- Percentage: 129.0598%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-11-13/
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4/9 + 11/13 = 151/117

Simplified Fraction

151/117

Mixed Number

1 34/117

Decimal Value

1.290598

Percentage

129.0598%

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Step-by-Step Solution: 4/9 + 11/13

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 11/13 by 9 so both fractions share the common base 117.

4 × 13/9 × 13 = 52/117 and 11 × 9/13 × 9 = 99/117

Step 3

Add the Numerators

Now add the numerators (52 + 99 = 151) and keep the common denominator 117 unchanged.

52 + 99/117 = 151/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 151 and 117 is 1, confirming that 151/117 cannot be reduced further—it is already in its simplest irreducible form.

151/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (151) is greater than the denominator (117), divide 151 by 117: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/117.

151/117 = 134/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 117 produces a repeating decimal (approximately 1.290598, or 129.0598%).

151 ÷ 117 = 1.290598 (129.0598%)

Visual Representation

The diagram below illustrates 4/9 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/117`
Mixed Number Form	`1 34/117`
Decimal Form	`1.290598`
Percentage	`129.0598%`

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Frequently Asked Questions

What is 4/9 plus 11/13 as a fraction?

4/9 + 11/13 in simplest fraction form is 151/117 (or 1 34/117 as a mixed number).

What is 4/9 plus 11/13 as a decimal?

4/9 + 11/13 converted to a decimal is 1.290598.

What is 4/9 plus 11/13 as a percentage?

4/9 + 11/13 expressed as a percentage is 129.0598%.

How do you write 4/9 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 151/117 can be written as the mixed number 1 34/117.

Does 4/9 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.290598...) because the denominator contains prime factors other than 2 and 5.