What is 2/13 plus 3/9? (Answer: 19/39)

Exact Answer

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Problem: What is 2/13 plus 3/9?
Formula / Expression: 2/13 + 3/9
Final Answer: 19/39
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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 2/13 by 9, and multiply the numerator and denominator of 3/9 by 13 so both fractions share the common base 117.
Working: 2 × 9/13 × 9 = 18/117 and 3 × 13/9 × 13 = 39/117

Step 3: Add the Numerators
Now add the numerators (18 + 39 = 57) and keep the common denominator 117 unchanged.
Working: 18 + 39/117 = 57/117

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 117, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/117 ÷ 3 = 19/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 39 produces a repeating decimal (approximately 0.487179, or 48.7179%).
Working: 19 ÷ 39 = 0.487179 (48.7179%)

Key Values:
- Simplified Fraction: 19/39
- Mixed Number Form: 19/39
- Decimal Value: 0.487179
- Percentage: 48.7179%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-3-9/
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2/13 + 3/9 = 19/39

Simplified Fraction

19/39

Mixed Number

Proper (19/39)

Decimal Value

0.487179

Percentage

48.7179%

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Step-by-Step Solution: 2/13 + 3/9

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 2/13 by 9, and multiply the numerator and denominator of 3/9 by 13 so both fractions share the common base 117.

2 × 9/13 × 9 = 18/117 and 3 × 13/9 × 13 = 39/117

Step 3

Add the Numerators

Now add the numerators (18 + 39 = 57) and keep the common denominator 117 unchanged.

18 + 39/117 = 57/117

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 117, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/117 ÷ 3 = 19/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 39 produces a repeating decimal (approximately 0.487179, or 48.7179%).

19 ÷ 39 = 0.487179 (48.7179%)

Visual Representation

The diagram below illustrates 2/13 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/39`
Mixed Number Form	`19/39`
Decimal Form	`0.487179`
Percentage	`48.7179%`

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Frequently Asked Questions

What is 2/13 plus 3/9 as a fraction?

2/13 + 3/9 in simplest fraction form is 19/39.

What is 2/13 plus 3/9 as a decimal?

2/13 + 3/9 converted to a decimal is 0.487179.

What is 2/13 plus 3/9 as a percentage?

2/13 + 3/9 expressed as a percentage is 48.7179%.

Does 2/13 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.487179...) because the denominator contains prime factors other than 2 and 5.