What is 3/11 plus 9/13? (Answer: 138/143)

Exact Answer

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Problem: What is 3/11 plus 9/13?
Formula / Expression: 3/11 + 9/13
Final Answer: 138/143
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 13 = 143.
Working: LCD(11, 13) = 143

Step 2: Convert to Equivalent Fractions with Common Denominator 143
Multiply the numerator and denominator of 3/11 by 13, and multiply the numerator and denominator of 9/13 by 11 so both fractions share the common base 143.
Working: 3 × 13/11 × 13 = 39/143 and 9 × 11/13 × 11 = 99/143

Step 3: Add the Numerators
Now add the numerators (39 + 99 = 138) and keep the common denominator 143 unchanged.
Working: 39 + 99/143 = 138/143

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 138 and 143 is 1, confirming that 138/143 cannot be reduced further—it is already in its simplest irreducible form.
Working: 138/143

Step 5: Decimal & Percentage Representation
Dividing the numerator 138 by denominator 143 produces a repeating decimal (approximately 0.965035, or 96.5035%).
Working: 138 ÷ 143 = 0.965035 (96.5035%)

Key Values:
- Simplified Fraction: 138/143
- Mixed Number Form: 138/143
- Decimal Value: 0.965035
- Percentage: 96.5035%

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3/11 + 9/13 = 138/143

Simplified Fraction

138/143

Mixed Number

Proper (138/143)

Decimal Value

0.965035

Percentage

96.5035%

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Step-by-Step Solution: 3/11 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 13 = 143.

LCD(11, 13) = 143

Step 2

Convert to Equivalent Fractions with Common Denominator 143

Multiply the numerator and denominator of 3/11 by 13, and multiply the numerator and denominator of 9/13 by 11 so both fractions share the common base 143.

3 × 13/11 × 13 = 39/143 and 9 × 11/13 × 11 = 99/143

Step 3

Add the Numerators

Now add the numerators (39 + 99 = 138) and keep the common denominator 143 unchanged.

39 + 99/143 = 138/143

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 138 and 143 is 1, confirming that 138/143 cannot be reduced further—it is already in its simplest irreducible form.

138/143

Step 5

Decimal & Percentage Representation

Dividing the numerator 138 by denominator 143 produces a repeating decimal (approximately 0.965035, or 96.5035%).

138 ÷ 143 = 0.965035 (96.5035%)

Visual Representation

The diagram below illustrates 3/11 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`138/143`
Mixed Number Form	`138/143`
Decimal Form	`0.965035`
Percentage	`96.5035%`

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Frequently Asked Questions

What is 3/11 plus 9/13 as a fraction?

3/11 + 9/13 in simplest fraction form is 138/143.

What is 3/11 plus 9/13 as a decimal?

3/11 + 9/13 converted to a decimal is 0.965035.

What is 3/11 plus 9/13 as a percentage?

3/11 + 9/13 expressed as a percentage is 96.5035%.

Does 3/11 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.965035...) because the denominator contains prime factors other than 2 and 5.