What is 13/21 plus 9/13? (Answer: 358/273)

Exact Answer

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Problem: What is 13/21 plus 9/13?
Formula / Expression: 13/21 + 9/13
Final Answer: 1 85/273 (358/273)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.
Working: LCD(21, 13) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 13/21 by 13, and multiply the numerator and denominator of 9/13 by 21 so both fractions share the common base 273.
Working: 13 × 13/21 × 13 = 169/273 and 9 × 21/13 × 21 = 189/273

Step 3: Add the Numerators
Now add the numerators (169 + 189 = 358) and keep the common denominator 273 unchanged.
Working: 169 + 189/273 = 358/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 358 and 273 is 1, confirming that 358/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 358/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (358) is greater than the denominator (273), divide 358 by 273: it goes in 1 whole time(s) with a remainder of 85, giving the mixed number 1 85/273.
Working: 358/273 = 1 85/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 358 by denominator 273 produces a repeating decimal (approximately 1.311355, or 131.1355%).
Working: 358 ÷ 273 = 1.311355 (131.1355%)

Key Values:
- Simplified Fraction: 358/273
- Mixed Number Form: 1 85/273
- Decimal Value: 1.311355
- Percentage: 131.1355%

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Solved with FractionsCalc:
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13/21 + 9/13 = 358/273

Simplified Fraction

358/273

Mixed Number

1 85/273

Decimal Value

1.311355

Percentage

131.1355%

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Step-by-Step Solution: 13/21 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 13 = 273.

LCD(21, 13) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 13/21 by 13, and multiply the numerator and denominator of 9/13 by 21 so both fractions share the common base 273.

13 × 13/21 × 13 = 169/273 and 9 × 21/13 × 21 = 189/273

Step 3

Add the Numerators

Now add the numerators (169 + 189 = 358) and keep the common denominator 273 unchanged.

169 + 189/273 = 358/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 358 and 273 is 1, confirming that 358/273 cannot be reduced further—it is already in its simplest irreducible form.

358/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (358) is greater than the denominator (273), divide 358 by 273: it goes in 1 whole time(s) with a remainder of 85, giving the mixed number 1 85/273.

358/273 = 185/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 358 by denominator 273 produces a repeating decimal (approximately 1.311355, or 131.1355%).

358 ÷ 273 = 1.311355 (131.1355%)

Visual Representation

The diagram below illustrates 13/21 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`358/273`
Mixed Number Form	`1 85/273`
Decimal Form	`1.311355`
Percentage	`131.1355%`

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Frequently Asked Questions

What is 13/21 plus 9/13 as a fraction?

13/21 + 9/13 in simplest fraction form is 358/273 (or 1 85/273 as a mixed number).

What is 13/21 plus 9/13 as a decimal?

13/21 + 9/13 converted to a decimal is 1.311355.

What is 13/21 plus 9/13 as a percentage?

13/21 + 9/13 expressed as a percentage is 131.1355%.

How do you write 13/21 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 358/273 can be written as the mixed number 1 85/273.

Does 13/21 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.311355...) because the denominator contains prime factors other than 2 and 5.