What is 11/23 plus 11/21? (Answer: 484/483)

Exact Answer

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Problem: What is 11/23 plus 11/21?
Formula / Expression: 11/23 + 11/21
Final Answer: 1 1/483 (484/483)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.
Working: LCD(23, 21) = 483

Step 2: Convert to Equivalent Fractions with Common Denominator 483
Multiply the numerator and denominator of 11/23 by 21, and multiply the numerator and denominator of 11/21 by 23 so both fractions share the common base 483.
Working: 11 × 21/23 × 21 = 231/483 and 11 × 23/21 × 23 = 253/483

Step 3: Add the Numerators
Now add the numerators (231 + 253 = 484) and keep the common denominator 483 unchanged.
Working: 231 + 253/483 = 484/483

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 484 and 483 is 1, confirming that 484/483 cannot be reduced further—it is already in its simplest irreducible form.
Working: 484/483

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (484) is greater than the denominator (483), divide 484 by 483: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/483.
Working: 484/483 = 1 1/483

Step 6: Decimal & Percentage Representation
Dividing the numerator 484 by denominator 483 produces a repeating decimal (approximately 1.00207, or 100.207%).
Working: 484 ÷ 483 = 1.00207 (100.207%)

Key Values:
- Simplified Fraction: 484/483
- Mixed Number Form: 1 1/483
- Decimal Value: 1.00207
- Percentage: 100.207%

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Solved with FractionsCalc:
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11/23 + 11/21 = 484/483

Simplified Fraction

484/483

Mixed Number

1 1/483

Decimal Value

1.00207

Percentage

100.207%

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Step-by-Step Solution: 11/23 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.

LCD(23, 21) = 483

Step 2

Convert to Equivalent Fractions with Common Denominator 483

Multiply the numerator and denominator of 11/23 by 21, and multiply the numerator and denominator of 11/21 by 23 so both fractions share the common base 483.

11 × 21/23 × 21 = 231/483 and 11 × 23/21 × 23 = 253/483

Step 3

Add the Numerators

Now add the numerators (231 + 253 = 484) and keep the common denominator 483 unchanged.

231 + 253/483 = 484/483

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 484 and 483 is 1, confirming that 484/483 cannot be reduced further—it is already in its simplest irreducible form.

484/483

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (484) is greater than the denominator (483), divide 484 by 483: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/483.

484/483 = 11/483

Step 6

Decimal & Percentage Representation

Dividing the numerator 484 by denominator 483 produces a repeating decimal (approximately 1.00207, or 100.207%).

484 ÷ 483 = 1.00207 (100.207%)

Visual Representation

The diagram below illustrates 11/23 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`484/483`
Mixed Number Form	`1 1/483`
Decimal Form	`1.00207`
Percentage	`100.207%`

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Frequently Asked Questions

What is 11/23 plus 11/21 as a fraction?

11/23 + 11/21 in simplest fraction form is 484/483 (or 1 1/483 as a mixed number).

What is 11/23 plus 11/21 as a decimal?

11/23 + 11/21 converted to a decimal is 1.00207.

What is 11/23 plus 11/21 as a percentage?

11/23 + 11/21 expressed as a percentage is 100.207%.

How do you write 11/23 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 484/483 can be written as the mixed number 1 1/483.

Does 11/23 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.00207...) because the denominator contains prime factors other than 2 and 5.