What is 3/13 plus 3/9? (Answer: 22/39)

Exact Answer

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Problem: What is 3/13 plus 3/9?
Formula / Expression: 3/13 + 3/9
Final Answer: 22/39
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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 3/13 by 9, and multiply the numerator and denominator of 3/9 by 13 so both fractions share the common base 117.
Working: 3 × 9/13 × 9 = 27/117 and 3 × 13/9 × 13 = 39/117

Step 3: Add the Numerators
Now add the numerators (27 + 39 = 66) and keep the common denominator 117 unchanged.
Working: 27 + 39/117 = 66/117

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 117, which is 3. Divide both the numerator and denominator by 3.
Working: 66 ÷ 3/117 ÷ 3 = 22/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 39 produces a repeating decimal (approximately 0.564103, or 56.4103%).
Working: 22 ÷ 39 = 0.564103 (56.4103%)

Key Values:
- Simplified Fraction: 22/39
- Mixed Number Form: 22/39
- Decimal Value: 0.564103
- Percentage: 56.4103%

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Solved with FractionsCalc:
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3/13 + 3/9 = 22/39

Simplified Fraction

22/39

Mixed Number

Proper (22/39)

Decimal Value

0.564103

Percentage

56.4103%

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Step-by-Step Solution: 3/13 + 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 3/13 by 9, and multiply the numerator and denominator of 3/9 by 13 so both fractions share the common base 117.

3 × 9/13 × 9 = 27/117 and 3 × 13/9 × 13 = 39/117

Step 3

Add the Numerators

Now add the numerators (27 + 39 = 66) and keep the common denominator 117 unchanged.

27 + 39/117 = 66/117

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 117, which is 3. Divide both the numerator and denominator by 3.

66 ÷ 3/117 ÷ 3 = 22/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 39 produces a repeating decimal (approximately 0.564103, or 56.4103%).

22 ÷ 39 = 0.564103 (56.4103%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/39`
Mixed Number Form	`22/39`
Decimal Form	`0.564103`
Percentage	`56.4103%`

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Frequently Asked Questions

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

3/13 + 3/9 in simplest fraction form is 22/39.

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

3/13 + 3/9 converted to a decimal is 0.564103.

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

3/13 + 3/9 expressed as a percentage is 56.4103%.

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

It results in a repeating decimal (approximately 0.564103...) because the denominator contains prime factors other than 2 and 5.