What is 10/22 plus 11/21? (Answer: 226/231)

Exact Answer

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Problem: What is 10/22 plus 11/21?
Formula / Expression: 10/22 + 11/21
Final Answer: 226/231
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 462
Multiply the numerator and denominator of 10/22 by 21, and multiply the numerator and denominator of 11/21 by 22 so both fractions share the common base 462.
Working: 10 × 21/22 × 21 = 210/462 and 11 × 22/21 × 22 = 242/462

Step 3: Add the Numerators
Now add the numerators (210 + 242 = 452) and keep the common denominator 462 unchanged.
Working: 210 + 242/462 = 452/462

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 452 and 462, which is 2. Divide both the numerator and denominator by 2.
Working: 452 ÷ 2/462 ÷ 2 = 226/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 226 by denominator 231 produces a repeating decimal (approximately 0.978355, or 97.8355%).
Working: 226 ÷ 231 = 0.978355 (97.8355%)

Key Values:
- Simplified Fraction: 226/231
- Mixed Number Form: 226/231
- Decimal Value: 0.978355
- Percentage: 97.8355%

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Solved with FractionsCalc:
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10/22 + 11/21 = 226/231

Simplified Fraction

226/231

Mixed Number

Proper (226/231)

Decimal Value

0.978355

Percentage

97.8355%

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Step-by-Step Solution: 10/22 + 11/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 21) = 462

Step 2

Convert to Equivalent Fractions with Common Denominator 462

Multiply the numerator and denominator of 10/22 by 21, and multiply the numerator and denominator of 11/21 by 22 so both fractions share the common base 462.

10 × 21/22 × 21 = 210/462 and 11 × 22/21 × 22 = 242/462

Step 3

Add the Numerators

Now add the numerators (210 + 242 = 452) and keep the common denominator 462 unchanged.

210 + 242/462 = 452/462

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 452 and 462, which is 2. Divide both the numerator and denominator by 2.

452 ÷ 2/462 ÷ 2 = 226/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 226 by denominator 231 produces a repeating decimal (approximately 0.978355, or 97.8355%).

226 ÷ 231 = 0.978355 (97.8355%)

Visual Representation

The diagram below illustrates 10/22 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`226/231`
Mixed Number Form	`226/231`
Decimal Form	`0.978355`
Percentage	`97.8355%`

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Frequently Asked Questions

What is 10/22 plus 11/21 as a fraction?

10/22 + 11/21 in simplest fraction form is 226/231.

What is 10/22 plus 11/21 as a decimal?

10/22 + 11/21 converted to a decimal is 0.978355.

What is 10/22 plus 11/21 as a percentage?

10/22 + 11/21 expressed as a percentage is 97.8355%.

Does 10/22 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.978355...) because the denominator contains prime factors other than 2 and 5.