What is 1/9 plus 3/13? (Answer: 40/117)

Exact Answer

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Problem: What is 1/9 plus 3/13?
Formula / Expression: 1/9 + 3/13
Final Answer: 40/117
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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 1/9 by 13, and multiply the numerator and denominator of 3/13 by 9 so both fractions share the common base 117.
Working: 1 × 13/9 × 13 = 13/117 and 3 × 9/13 × 9 = 27/117

Step 3: Add the Numerators
Now add the numerators (13 + 27 = 40) and keep the common denominator 117 unchanged.
Working: 13 + 27/117 = 40/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 40 and 117 is 1, confirming that 40/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 40/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 117 produces a repeating decimal (approximately 0.34188, or 34.188%).
Working: 40 ÷ 117 = 0.34188 (34.188%)

Key Values:
- Simplified Fraction: 40/117
- Mixed Number Form: 40/117
- Decimal Value: 0.34188
- Percentage: 34.188%

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Solved with FractionsCalc:
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1/9 + 3/13 = 40/117

Simplified Fraction

40/117

Mixed Number

Proper (40/117)

Decimal Value

0.34188

Percentage

34.188%

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Step-by-Step Solution: 1/9 + 3/13

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 1/9 by 13, and multiply the numerator and denominator of 3/13 by 9 so both fractions share the common base 117.

1 × 13/9 × 13 = 13/117 and 3 × 9/13 × 9 = 27/117

Step 3

Add the Numerators

Now add the numerators (13 + 27 = 40) and keep the common denominator 117 unchanged.

13 + 27/117 = 40/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 40 and 117 is 1, confirming that 40/117 cannot be reduced further—it is already in its simplest irreducible form.

40/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 117 produces a repeating decimal (approximately 0.34188, or 34.188%).

40 ÷ 117 = 0.34188 (34.188%)

Visual Representation

The diagram below illustrates 1/9 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/117`
Mixed Number Form	`40/117`
Decimal Form	`0.34188`
Percentage	`34.188%`

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Frequently Asked Questions

What is 1/9 plus 3/13 as a fraction?

1/9 + 3/13 in simplest fraction form is 40/117.

What is 1/9 plus 3/13 as a decimal?

1/9 + 3/13 converted to a decimal is 0.34188.

What is 1/9 plus 3/13 as a percentage?

1/9 + 3/13 expressed as a percentage is 34.188%.

Does 1/9 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.34188...) because the denominator contains prime factors other than 2 and 5.