What is 5/21 plus 3/11? (Answer: 118/231)

Exact Answer

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Problem: What is 5/21 plus 3/11?
Formula / Expression: 5/21 + 3/11
Final Answer: 118/231
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 5/21 by 11, and multiply the numerator and denominator of 3/11 by 21 so both fractions share the common base 231.
Working: 5 × 11/21 × 11 = 55/231 and 3 × 21/11 × 21 = 63/231

Step 3: Add the Numerators
Now add the numerators (55 + 63 = 118) and keep the common denominator 231 unchanged.
Working: 55 + 63/231 = 118/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 118 and 231 is 1, confirming that 118/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 118/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 118 by denominator 231 produces a repeating decimal (approximately 0.510823, or 51.0823%).
Working: 118 ÷ 231 = 0.510823 (51.0823%)

Key Values:
- Simplified Fraction: 118/231
- Mixed Number Form: 118/231
- Decimal Value: 0.510823
- Percentage: 51.0823%

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5/21 + 3/11 = 118/231

Simplified Fraction

118/231

Mixed Number

Proper (118/231)

Decimal Value

0.510823

Percentage

51.0823%

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Step-by-Step Solution: 5/21 + 3/11

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 11) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 5/21 by 11, and multiply the numerator and denominator of 3/11 by 21 so both fractions share the common base 231.

5 × 11/21 × 11 = 55/231 and 3 × 21/11 × 21 = 63/231

Step 3

Add the Numerators

Now add the numerators (55 + 63 = 118) and keep the common denominator 231 unchanged.

55 + 63/231 = 118/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 118 and 231 is 1, confirming that 118/231 cannot be reduced further—it is already in its simplest irreducible form.

118/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 118 by denominator 231 produces a repeating decimal (approximately 0.510823, or 51.0823%).

118 ÷ 231 = 0.510823 (51.0823%)

Visual Representation

The diagram below illustrates 5/21 plus 3/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`118/231`
Mixed Number Form	`118/231`
Decimal Form	`0.510823`
Percentage	`51.0823%`

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Frequently Asked Questions

What is 5/21 plus 3/11 as a fraction?

5/21 + 3/11 in simplest fraction form is 118/231.

What is 5/21 plus 3/11 as a decimal?

5/21 + 3/11 converted to a decimal is 0.510823.

What is 5/21 plus 3/11 as a percentage?

5/21 + 3/11 expressed as a percentage is 51.0823%.

Does 5/21 plus 3/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.510823...) because the denominator contains prime factors other than 2 and 5.