What is 1/11 plus 8/21? (Answer: 109/231)

Exact Answer

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Problem: What is 1/11 plus 8/21?
Formula / Expression: 1/11 + 8/21
Final Answer: 109/231
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 21 = 231.
Working: LCD(11, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 1/11 by 21, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.
Working: 1 × 21/11 × 21 = 21/231 and 8 × 11/21 × 11 = 88/231

Step 3: Add the Numerators
Now add the numerators (21 + 88 = 109) and keep the common denominator 231 unchanged.
Working: 21 + 88/231 = 109/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 231 is 1, confirming that 109/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 231 produces a repeating decimal (approximately 0.471861, or 47.1861%).
Working: 109 ÷ 231 = 0.471861 (47.1861%)

Key Values:
- Simplified Fraction: 109/231
- Mixed Number Form: 109/231
- Decimal Value: 0.471861
- Percentage: 47.1861%

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Solved with FractionsCalc:
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1/11 + 8/21 = 109/231

Simplified Fraction

109/231

Mixed Number

Proper (109/231)

Decimal Value

0.471861

Percentage

47.1861%

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Step-by-Step Solution: 1/11 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 21 = 231.

LCD(11, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 1/11 by 21, and multiply the numerator and denominator of 8/21 by 11 so both fractions share the common base 231.

1 × 21/11 × 21 = 21/231 and 8 × 11/21 × 11 = 88/231

Step 3

Add the Numerators

Now add the numerators (21 + 88 = 109) and keep the common denominator 231 unchanged.

21 + 88/231 = 109/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 231 is 1, confirming that 109/231 cannot be reduced further—it is already in its simplest irreducible form.

109/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 231 produces a repeating decimal (approximately 0.471861, or 47.1861%).

109 ÷ 231 = 0.471861 (47.1861%)

Visual Representation

The diagram below illustrates 1/11 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/231`
Mixed Number Form	`109/231`
Decimal Form	`0.471861`
Percentage	`47.1861%`

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Frequently Asked Questions

What is 1/11 plus 8/21 as a fraction?

1/11 + 8/21 in simplest fraction form is 109/231.

What is 1/11 plus 8/21 as a decimal?

1/11 + 8/21 converted to a decimal is 0.471861.

What is 1/11 plus 8/21 as a percentage?

1/11 + 8/21 expressed as a percentage is 47.1861%.

Does 1/11 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.471861...) because the denominator contains prime factors other than 2 and 5.