What is 11/21 plus 12/22? (Answer: 247/231)

Exact Answer

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Problem: What is 11/21 plus 12/22?
Formula / Expression: 11/21 + 12/22
Final Answer: 1 16/231 (247/231)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 22 = 462.
Working: LCD(21, 22) = 462

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 11/21 by 22, and multiply the numerator and denominator of 12/22 by 21 so both fractions share the common base 462.
Working: 11 × 22/21 × 22 = 242/462 and 12 × 21/22 × 21 = 252/462

Step 3: Add the Numerators
Now add the numerators (242 + 252 = 494) and keep the common denominator 462 unchanged.
Working: 242 + 252/462 = 494/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 494 and 462, which is 2. Divide both the numerator and denominator by 2.
Working: 494 ÷ 2/462 ÷ 2 = 247/231

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (247) is greater than the denominator (231), divide 247 by 231: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/231.
Working: 247/231 = 1 16/231

Step 6: Decimal & Percentage Representation
Dividing the numerator 247 by denominator 231 produces a repeating decimal (approximately 1.069264, or 106.9264%).
Working: 247 ÷ 231 = 1.069264 (106.9264%)

Key Values:
- Simplified Fraction: 247/231
- Mixed Number Form: 1 16/231
- Decimal Value: 1.069264
- Percentage: 106.9264%

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11/21 + 12/22 = 247/231

Simplified Fraction

247/231

Mixed Number

1 16/231

Decimal Value

1.069264

Percentage

106.9264%

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Step-by-Step Solution: 11/21 + 12/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 22 = 462.

LCD(21, 22) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 11/21 by 22, and multiply the numerator and denominator of 12/22 by 21 so both fractions share the common base 462.

11 × 22/21 × 22 = 242/462 and 12 × 21/22 × 21 = 252/462

Step 3

Add the Numerators

Now add the numerators (242 + 252 = 494) and keep the common denominator 462 unchanged.

242 + 252/462 = 494/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 494 and 462, which is 2. Divide both the numerator and denominator by 2.

494 ÷ 2/462 ÷ 2 = 247/231

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (247) is greater than the denominator (231), divide 247 by 231: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/231.

247/231 = 116/231

Step 6

Decimal & Percentage Representation

Dividing the numerator 247 by denominator 231 produces a repeating decimal (approximately 1.069264, or 106.9264%).

247 ÷ 231 = 1.069264 (106.9264%)

Visual Representation

The diagram below illustrates 11/21 plus 12/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`247/231`
Mixed Number Form	`1 16/231`
Decimal Form	`1.069264`
Percentage	`106.9264%`

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Frequently Asked Questions

What is 11/21 plus 12/22 as a fraction?

11/21 + 12/22 in simplest fraction form is 247/231 (or 1 16/231 as a mixed number).

What is 11/21 plus 12/22 as a decimal?

11/21 + 12/22 converted to a decimal is 1.069264.

What is 11/21 plus 12/22 as a percentage?

11/21 + 12/22 expressed as a percentage is 106.9264%.

How do you write 11/21 plus 12/22 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 247/231 can be written as the mixed number 1 16/231.

Does 11/21 plus 12/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.069264...) because the denominator contains prime factors other than 2 and 5.