What is 2/9 plus 10/13? (Answer: 116/117)

Exact Answer

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Problem: What is 2/9 plus 10/13?
Formula / Expression: 2/9 + 10/13
Final Answer: 116/117
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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 2/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.
Working: 2 × 13/9 × 13 = 26/117 and 10 × 9/13 × 9 = 90/117

Step 3: Add the Numerators
Now add the numerators (26 + 90 = 116) and keep the common denominator 117 unchanged.
Working: 26 + 90/117 = 116/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 116 and 117 is 1, confirming that 116/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 116/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 117 produces a repeating decimal (approximately 0.991453, or 99.1453%).
Working: 116 ÷ 117 = 0.991453 (99.1453%)

Key Values:
- Simplified Fraction: 116/117
- Mixed Number Form: 116/117
- Decimal Value: 0.991453
- Percentage: 99.1453%

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Solved with FractionsCalc:
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2/9 + 10/13 = 116/117

Simplified Fraction

116/117

Mixed Number

Proper (116/117)

Decimal Value

0.991453

Percentage

99.1453%

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Step-by-Step Solution: 2/9 + 10/13

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 2/9 by 13, and multiply the numerator and denominator of 10/13 by 9 so both fractions share the common base 117.

2 × 13/9 × 13 = 26/117 and 10 × 9/13 × 9 = 90/117

Step 3

Add the Numerators

Now add the numerators (26 + 90 = 116) and keep the common denominator 117 unchanged.

26 + 90/117 = 116/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 116 and 117 is 1, confirming that 116/117 cannot be reduced further—it is already in its simplest irreducible form.

116/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 117 produces a repeating decimal (approximately 0.991453, or 99.1453%).

116 ÷ 117 = 0.991453 (99.1453%)

Visual Representation

The diagram below illustrates 2/9 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/117`
Mixed Number Form	`116/117`
Decimal Form	`0.991453`
Percentage	`99.1453%`

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Frequently Asked Questions

What is 2/9 plus 10/13 as a fraction?

2/9 + 10/13 in simplest fraction form is 116/117.

What is 2/9 plus 10/13 as a decimal?

2/9 + 10/13 converted to a decimal is 0.991453.

What is 2/9 plus 10/13 as a percentage?

2/9 + 10/13 expressed as a percentage is 99.1453%.

Does 2/9 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.991453...) because the denominator contains prime factors other than 2 and 5.