What is 3/13 plus 4/9? (Answer: 79/117)

Exact Answer

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Problem: What is 3/13 plus 4/9?
Formula / Expression: 3/13 + 4/9
Final Answer: 79/117
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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 3/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.
Working: 3 × 9/13 × 9 = 27/117 and 4 × 13/9 × 13 = 52/117

Step 3: Add the Numerators
Now add the numerators (27 + 52 = 79) and keep the common denominator 117 unchanged.
Working: 27 + 52/117 = 79/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 117 is 1, confirming that 79/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 117 produces a repeating decimal (approximately 0.675214, or 67.5214%).
Working: 79 ÷ 117 = 0.675214 (67.5214%)

Key Values:
- Simplified Fraction: 79/117
- Mixed Number Form: 79/117
- Decimal Value: 0.675214
- Percentage: 67.5214%

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Solved with FractionsCalc:
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3/13 + 4/9 = 79/117

Simplified Fraction

79/117

Mixed Number

Proper (79/117)

Decimal Value

0.675214

Percentage

67.5214%

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Step-by-Step Solution: 3/13 + 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 3/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.

3 × 9/13 × 9 = 27/117 and 4 × 13/9 × 13 = 52/117

Step 3

Add the Numerators

Now add the numerators (27 + 52 = 79) and keep the common denominator 117 unchanged.

27 + 52/117 = 79/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 117 is 1, confirming that 79/117 cannot be reduced further—it is already in its simplest irreducible form.

79/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 117 produces a repeating decimal (approximately 0.675214, or 67.5214%).

79 ÷ 117 = 0.675214 (67.5214%)

Visual Representation

The diagram below illustrates 3/13 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/117`
Mixed Number Form	`79/117`
Decimal Form	`0.675214`
Percentage	`67.5214%`

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Frequently Asked Questions

What is 3/13 plus 4/9 as a fraction?

3/13 + 4/9 in simplest fraction form is 79/117.

What is 3/13 plus 4/9 as a decimal?

3/13 + 4/9 converted to a decimal is 0.675214.

What is 3/13 plus 4/9 as a percentage?

3/13 + 4/9 expressed as a percentage is 67.5214%.

Does 3/13 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.675214...) because the denominator contains prime factors other than 2 and 5.