What is 3/11 plus 10/21? (Answer: 173/231)

Exact Answer

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Problem: What is 3/11 plus 10/21?
Formula / Expression: 3/11 + 10/21
Final Answer: 173/231
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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 3/11 by 21, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 3 × 21/11 × 21 = 63/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (63 + 110 = 173) and keep the common denominator 231 unchanged.
Working: 63 + 110/231 = 173/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 173 and 231 is 1, confirming that 173/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 173/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 231 produces a repeating decimal (approximately 0.748918, or 74.8918%).
Working: 173 ÷ 231 = 0.748918 (74.8918%)

Key Values:
- Simplified Fraction: 173/231
- Mixed Number Form: 173/231
- Decimal Value: 0.748918
- Percentage: 74.8918%

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3/11 + 10/21 = 173/231

Simplified Fraction

173/231

Mixed Number

Proper (173/231)

Decimal Value

0.748918

Percentage

74.8918%

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Step-by-Step Solution: 3/11 + 10/21

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 3/11 by 21, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.

3 × 21/11 × 21 = 63/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (63 + 110 = 173) and keep the common denominator 231 unchanged.

63 + 110/231 = 173/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 173 and 231 is 1, confirming that 173/231 cannot be reduced further—it is already in its simplest irreducible form.

173/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 231 produces a repeating decimal (approximately 0.748918, or 74.8918%).

173 ÷ 231 = 0.748918 (74.8918%)

Visual Representation

The diagram below illustrates 3/11 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/231`
Mixed Number Form	`173/231`
Decimal Form	`0.748918`
Percentage	`74.8918%`

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Frequently Asked Questions

What is 3/11 plus 10/21 as a fraction?

3/11 + 10/21 in simplest fraction form is 173/231.

What is 3/11 plus 10/21 as a decimal?

3/11 + 10/21 converted to a decimal is 0.748918.

What is 3/11 plus 10/21 as a percentage?

3/11 + 10/21 expressed as a percentage is 74.8918%.

Does 3/11 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.748918...) because the denominator contains prime factors other than 2 and 5.