What is 1/13 plus 4/9? (Answer: 61/117)

Exact Answer

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Problem: What is 1/13 plus 4/9?
Formula / Expression: 1/13 + 4/9
Final Answer: 61/117
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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 1/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.
Working: 1 × 9/13 × 9 = 9/117 and 4 × 13/9 × 13 = 52/117

Step 3: Add the Numerators
Now add the numerators (9 + 52 = 61) and keep the common denominator 117 unchanged.
Working: 9 + 52/117 = 61/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 117 is 1, confirming that 61/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 117 produces a repeating decimal (approximately 0.521368, or 52.1368%).
Working: 61 ÷ 117 = 0.521368 (52.1368%)

Key Values:
- Simplified Fraction: 61/117
- Mixed Number Form: 61/117
- Decimal Value: 0.521368
- Percentage: 52.1368%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-13-plus-4-9/
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1/13 + 4/9 = 61/117

Simplified Fraction

61/117

Mixed Number

Proper (61/117)

Decimal Value

0.521368

Percentage

52.1368%

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Step-by-Step Solution: 1/13 + 4/9

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 1/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.

1 × 9/13 × 9 = 9/117 and 4 × 13/9 × 13 = 52/117

Step 3

Add the Numerators

Now add the numerators (9 + 52 = 61) and keep the common denominator 117 unchanged.

9 + 52/117 = 61/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 117 is 1, confirming that 61/117 cannot be reduced further—it is already in its simplest irreducible form.

61/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 117 produces a repeating decimal (approximately 0.521368, or 52.1368%).

61 ÷ 117 = 0.521368 (52.1368%)

Visual Representation

The diagram below illustrates 1/13 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/117`
Mixed Number Form	`61/117`
Decimal Form	`0.521368`
Percentage	`52.1368%`

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Frequently Asked Questions

What is 1/13 plus 4/9 as a fraction?

1/13 + 4/9 in simplest fraction form is 61/117.

What is 1/13 plus 4/9 as a decimal?

1/13 + 4/9 converted to a decimal is 0.521368.

What is 1/13 plus 4/9 as a percentage?

1/13 + 4/9 expressed as a percentage is 52.1368%.

Does 1/13 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.521368...) because the denominator contains prime factors other than 2 and 5.