What is 4/9 plus 7/13? (Answer: 115/117)

Exact Answer

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Problem: What is 4/9 plus 7/13?
Formula / Expression: 4/9 + 7/13
Final Answer: 115/117
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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 7/13 by 9 so both fractions share the common base 117.
Working: 4 × 13/9 × 13 = 52/117 and 7 × 9/13 × 9 = 63/117

Step 3: Add the Numerators
Now add the numerators (52 + 63 = 115) and keep the common denominator 117 unchanged.
Working: 52 + 63/117 = 115/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 115 and 117 is 1, confirming that 115/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 115/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 115 by denominator 117 produces a repeating decimal (approximately 0.982906, or 98.2906%).
Working: 115 ÷ 117 = 0.982906 (98.2906%)

Key Values:
- Simplified Fraction: 115/117
- Mixed Number Form: 115/117
- Decimal Value: 0.982906
- Percentage: 98.2906%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-7-13/
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4/9 + 7/13 = 115/117

Simplified Fraction

115/117

Mixed Number

Proper (115/117)

Decimal Value

0.982906

Percentage

98.2906%

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Step-by-Step Solution: 4/9 + 7/13

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 7/13 by 9 so both fractions share the common base 117.

4 × 13/9 × 13 = 52/117 and 7 × 9/13 × 9 = 63/117

Step 3

Add the Numerators

Now add the numerators (52 + 63 = 115) and keep the common denominator 117 unchanged.

52 + 63/117 = 115/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 115 and 117 is 1, confirming that 115/117 cannot be reduced further—it is already in its simplest irreducible form.

115/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 115 by denominator 117 produces a repeating decimal (approximately 0.982906, or 98.2906%).

115 ÷ 117 = 0.982906 (98.2906%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`115/117`
Mixed Number Form	`115/117`
Decimal Form	`0.982906`
Percentage	`98.2906%`

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Frequently Asked Questions

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

4/9 + 7/13 in simplest fraction form is 115/117.

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

4/9 + 7/13 converted to a decimal is 0.982906.

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

4/9 + 7/13 expressed as a percentage is 98.2906%.

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

It results in a repeating decimal (approximately 0.982906...) because the denominator contains prime factors other than 2 and 5.