What is 11/21 plus 9/13? (Answer: 332/273)

Exact Answer

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Problem: What is 11/21 plus 9/13?
Formula / Expression: 11/21 + 9/13
Final Answer: 1 59/273 (332/273)
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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 11/21 by 13, and multiply the numerator and denominator of 9/13 by 21 so both fractions share the common base 273.
Working: 11 × 13/21 × 13 = 143/273 and 9 × 21/13 × 21 = 189/273

Step 3: Add the Numerators
Now add the numerators (143 + 189 = 332) and keep the common denominator 273 unchanged.
Working: 143 + 189/273 = 332/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 332 and 273 is 1, confirming that 332/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 332/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (332) is greater than the denominator (273), divide 332 by 273: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/273.
Working: 332/273 = 1 59/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 332 by denominator 273 produces a repeating decimal (approximately 1.216117, or 121.6117%).
Working: 332 ÷ 273 = 1.216117 (121.6117%)

Key Values:
- Simplified Fraction: 332/273
- Mixed Number Form: 1 59/273
- Decimal Value: 1.216117
- Percentage: 121.6117%

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Solved with FractionsCalc:
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11/21 + 9/13 = 332/273

Simplified Fraction

332/273

Mixed Number

1 59/273

Decimal Value

1.216117

Percentage

121.6117%

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Step-by-Step Solution: 11/21 + 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 11/21 by 13, and multiply the numerator and denominator of 9/13 by 21 so both fractions share the common base 273.

11 × 13/21 × 13 = 143/273 and 9 × 21/13 × 21 = 189/273

Step 3

Add the Numerators

Now add the numerators (143 + 189 = 332) and keep the common denominator 273 unchanged.

143 + 189/273 = 332/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 332 and 273 is 1, confirming that 332/273 cannot be reduced further—it is already in its simplest irreducible form.

332/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (332) is greater than the denominator (273), divide 332 by 273: it goes in 1 whole time(s) with a remainder of 59, giving the mixed number 1 59/273.

332/273 = 159/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 332 by denominator 273 produces a repeating decimal (approximately 1.216117, or 121.6117%).

332 ÷ 273 = 1.216117 (121.6117%)

Visual Representation

The diagram below illustrates 11/21 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`332/273`
Mixed Number Form	`1 59/273`
Decimal Form	`1.216117`
Percentage	`121.6117%`

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Frequently Asked Questions

What is 11/21 plus 9/13 as a fraction?

11/21 + 9/13 in simplest fraction form is 332/273 (or 1 59/273 as a mixed number).

What is 11/21 plus 9/13 as a decimal?

11/21 + 9/13 converted to a decimal is 1.216117.

What is 11/21 plus 9/13 as a percentage?

11/21 + 9/13 expressed as a percentage is 121.6117%.

How do you write 11/21 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 332/273 can be written as the mixed number 1 59/273.

Does 11/21 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.216117...) because the denominator contains prime factors other than 2 and 5.