What is 9/14 plus 9/13? (Answer: 243/182)

Exact Answer

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Problem: What is 9/14 plus 9/13?
Formula / Expression: 9/14 + 9/13
Final Answer: 1 61/182 (243/182)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.
Working: LCD(14, 13) = 182

Step 2: Convert to Equivalent Fractions with Common Denominator 182
Multiply the numerator and denominator of 9/14 by 13, and multiply the numerator and denominator of 9/13 by 14 so both fractions share the common base 182.
Working: 9 × 13/14 × 13 = 117/182 and 9 × 14/13 × 14 = 126/182

Step 3: Add the Numerators
Now add the numerators (117 + 126 = 243) and keep the common denominator 182 unchanged.
Working: 117 + 126/182 = 243/182

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 243 and 182 is 1, confirming that 243/182 cannot be reduced further—it is already in its simplest irreducible form.
Working: 243/182

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (243) is greater than the denominator (182), divide 243 by 182: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/182.
Working: 243/182 = 1 61/182

Step 6: Decimal & Percentage Representation
Dividing the numerator 243 by denominator 182 produces a repeating decimal (approximately 1.335165, or 133.5165%).
Working: 243 ÷ 182 = 1.335165 (133.5165%)

Key Values:
- Simplified Fraction: 243/182
- Mixed Number Form: 1 61/182
- Decimal Value: 1.335165
- Percentage: 133.5165%

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Solved with FractionsCalc:
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9/14 + 9/13 = 243/182

Simplified Fraction

243/182

Mixed Number

1 61/182

Decimal Value

1.335165

Percentage

133.5165%

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Step-by-Step Solution: 9/14 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 13 = 182.

LCD(14, 13) = 182

Step 2

Convert to Equivalent Fractions with Common Denominator 182

Multiply the numerator and denominator of 9/14 by 13, and multiply the numerator and denominator of 9/13 by 14 so both fractions share the common base 182.

9 × 13/14 × 13 = 117/182 and 9 × 14/13 × 14 = 126/182

Step 3

Add the Numerators

Now add the numerators (117 + 126 = 243) and keep the common denominator 182 unchanged.

117 + 126/182 = 243/182

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 243 and 182 is 1, confirming that 243/182 cannot be reduced further—it is already in its simplest irreducible form.

243/182

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (243) is greater than the denominator (182), divide 243 by 182: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/182.

243/182 = 161/182

Step 6

Decimal & Percentage Representation

Dividing the numerator 243 by denominator 182 produces a repeating decimal (approximately 1.335165, or 133.5165%).

243 ÷ 182 = 1.335165 (133.5165%)

Visual Representation

The diagram below illustrates 9/14 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`243/182`
Mixed Number Form	`1 61/182`
Decimal Form	`1.335165`
Percentage	`133.5165%`

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Frequently Asked Questions

What is 9/14 plus 9/13 as a fraction?

9/14 + 9/13 in simplest fraction form is 243/182 (or 1 61/182 as a mixed number).

What is 9/14 plus 9/13 as a decimal?

9/14 + 9/13 converted to a decimal is 1.335165.

What is 9/14 plus 9/13 as a percentage?

9/14 + 9/13 expressed as a percentage is 133.5165%.

How do you write 9/14 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 243/182 can be written as the mixed number 1 61/182.

Does 9/14 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.335165...) because the denominator contains prime factors other than 2 and 5.