What is 3/9 plus 7/13? (Answer: 34/39)

Exact Answer

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Problem: What is 3/9 plus 7/13?
Formula / Expression: 3/9 + 7/13
Final Answer: 34/39
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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 3/9 by 13, and multiply the numerator and denominator of 7/13 by 9 so both fractions share the common base 117.
Working: 3 × 13/9 × 13 = 39/117 and 7 × 9/13 × 9 = 63/117

Step 3: Add the Numerators
Now add the numerators (39 + 63 = 102) and keep the common denominator 117 unchanged.
Working: 39 + 63/117 = 102/117

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 117, which is 3. Divide both the numerator and denominator by 3.
Working: 102 ÷ 3/117 ÷ 3 = 34/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).
Working: 34 ÷ 39 = 0.871795 (87.1795%)

Key Values:
- Simplified Fraction: 34/39
- Mixed Number Form: 34/39
- Decimal Value: 0.871795
- Percentage: 87.1795%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-7-13/
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3/9 + 7/13 = 34/39

Simplified Fraction

34/39

Mixed Number

Proper (34/39)

Decimal Value

0.871795

Percentage

87.1795%

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Step-by-Step Solution: 3/9 + 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 3/9 by 13, and multiply the numerator and denominator of 7/13 by 9 so both fractions share the common base 117.

3 × 13/9 × 13 = 39/117 and 7 × 9/13 × 9 = 63/117

Step 3

Add the Numerators

Now add the numerators (39 + 63 = 102) and keep the common denominator 117 unchanged.

39 + 63/117 = 102/117

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 117, which is 3. Divide both the numerator and denominator by 3.

102 ÷ 3/117 ÷ 3 = 34/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 39 produces a repeating decimal (approximately 0.871795, or 87.1795%).

34 ÷ 39 = 0.871795 (87.1795%)

Visual Representation

The diagram below illustrates 3/9 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/39`
Mixed Number Form	`34/39`
Decimal Form	`0.871795`
Percentage	`87.1795%`

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Frequently Asked Questions

What is 3/9 plus 7/13 as a fraction?

3/9 + 7/13 in simplest fraction form is 34/39.

What is 3/9 plus 7/13 as a decimal?

3/9 + 7/13 converted to a decimal is 0.871795.

What is 3/9 plus 7/13 as a percentage?

3/9 + 7/13 expressed as a percentage is 87.1795%.

Does 3/9 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.871795...) because the denominator contains prime factors other than 2 and 5.