What is 4/13 plus 5/9? (Answer: 101/117)

Exact Answer

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Problem: What is 4/13 plus 5/9?
Formula / Expression: 4/13 + 5/9
Final Answer: 101/117
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 4/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.
Working: 4 × 9/13 × 9 = 36/117 and 5 × 13/9 × 13 = 65/117

Step 3: Add the Numerators
Now add the numerators (36 + 65 = 101) and keep the common denominator 117 unchanged.
Working: 36 + 65/117 = 101/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 117 is 1, confirming that 101/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 117 produces a repeating decimal (approximately 0.863248, or 86.3248%).
Working: 101 ÷ 117 = 0.863248 (86.3248%)

Key Values:
- Simplified Fraction: 101/117
- Mixed Number Form: 101/117
- Decimal Value: 0.863248
- Percentage: 86.3248%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-13-plus-5-9/
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4/13 + 5/9 = 101/117

Simplified Fraction

101/117

Mixed Number

Proper (101/117)

Decimal Value

0.863248

Percentage

86.3248%

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Step-by-Step Solution: 4/13 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 4/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.

4 × 9/13 × 9 = 36/117 and 5 × 13/9 × 13 = 65/117

Step 3

Add the Numerators

Now add the numerators (36 + 65 = 101) and keep the common denominator 117 unchanged.

36 + 65/117 = 101/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 117 is 1, confirming that 101/117 cannot be reduced further—it is already in its simplest irreducible form.

101/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 117 produces a repeating decimal (approximately 0.863248, or 86.3248%).

101 ÷ 117 = 0.863248 (86.3248%)

Visual Representation

The diagram below illustrates 4/13 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/117`
Mixed Number Form	`101/117`
Decimal Form	`0.863248`
Percentage	`86.3248%`

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Frequently Asked Questions

What is 4/13 plus 5/9 as a fraction?

4/13 + 5/9 in simplest fraction form is 101/117.

What is 4/13 plus 5/9 as a decimal?

4/13 + 5/9 converted to a decimal is 0.863248.

What is 4/13 plus 5/9 as a percentage?

4/13 + 5/9 expressed as a percentage is 86.3248%.

Does 4/13 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.863248...) because the denominator contains prime factors other than 2 and 5.