What is 2/13 plus 4/9? (Answer: 70/117)

Exact Answer

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Problem: What is 2/13 plus 4/9?
Formula / Expression: 2/13 + 4/9
Final Answer: 70/117
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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 2/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.
Working: 2 × 9/13 × 9 = 18/117 and 4 × 13/9 × 13 = 52/117

Step 3: Add the Numerators
Now add the numerators (18 + 52 = 70) and keep the common denominator 117 unchanged.
Working: 18 + 52/117 = 70/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 70 and 117 is 1, confirming that 70/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 70/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 70 by denominator 117 produces a repeating decimal (approximately 0.598291, or 59.8291%).
Working: 70 ÷ 117 = 0.598291 (59.8291%)

Key Values:
- Simplified Fraction: 70/117
- Mixed Number Form: 70/117
- Decimal Value: 0.598291
- Percentage: 59.8291%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-4-9/
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2/13 + 4/9 = 70/117

Simplified Fraction

70/117

Mixed Number

Proper (70/117)

Decimal Value

0.598291

Percentage

59.8291%

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Step-by-Step Solution: 2/13 + 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 2/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.

2 × 9/13 × 9 = 18/117 and 4 × 13/9 × 13 = 52/117

Step 3

Add the Numerators

Now add the numerators (18 + 52 = 70) and keep the common denominator 117 unchanged.

18 + 52/117 = 70/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 70 and 117 is 1, confirming that 70/117 cannot be reduced further—it is already in its simplest irreducible form.

70/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 70 by denominator 117 produces a repeating decimal (approximately 0.598291, or 59.8291%).

70 ÷ 117 = 0.598291 (59.8291%)

Visual Representation

The diagram below illustrates 2/13 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`70/117`
Mixed Number Form	`70/117`
Decimal Form	`0.598291`
Percentage	`59.8291%`

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Frequently Asked Questions

What is 2/13 plus 4/9 as a fraction?

2/13 + 4/9 in simplest fraction form is 70/117.

What is 2/13 plus 4/9 as a decimal?

2/13 + 4/9 converted to a decimal is 0.598291.

What is 2/13 plus 4/9 as a percentage?

2/13 + 4/9 expressed as a percentage is 59.8291%.

Does 2/13 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.598291...) because the denominator contains prime factors other than 2 and 5.