What is 3/23 plus 11/21? (Answer: 316/483)

Exact Answer

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Problem: What is 3/23 plus 11/21?
Formula / Expression: 3/23 + 11/21
Final Answer: 316/483
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.
Working: LCD(23, 21) = 483

Step 2: Convert to Equivalent Fractions with Common Denominator 483
Multiply the numerator and denominator of 3/23 by 21, and multiply the numerator and denominator of 11/21 by 23 so both fractions share the common base 483.
Working: 3 × 21/23 × 21 = 63/483 and 11 × 23/21 × 23 = 253/483

Step 3: Add the Numerators
Now add the numerators (63 + 253 = 316) and keep the common denominator 483 unchanged.
Working: 63 + 253/483 = 316/483

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 316 and 483 is 1, confirming that 316/483 cannot be reduced further—it is already in its simplest irreducible form.
Working: 316/483

Step 5: Decimal & Percentage Representation
Dividing the numerator 316 by denominator 483 produces a repeating decimal (approximately 0.654244, or 65.4244%).
Working: 316 ÷ 483 = 0.654244 (65.4244%)

Key Values:
- Simplified Fraction: 316/483
- Mixed Number Form: 316/483
- Decimal Value: 0.654244
- Percentage: 65.4244%

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Solved with FractionsCalc:
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3/23 + 11/21 = 316/483

Simplified Fraction

316/483

Mixed Number

Proper (316/483)

Decimal Value

0.654244

Percentage

65.4244%

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Step-by-Step Solution: 3/23 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 21 = 483.

LCD(23, 21) = 483

Step 2

Convert to Equivalent Fractions with Common Denominator 483

Multiply the numerator and denominator of 3/23 by 21, and multiply the numerator and denominator of 11/21 by 23 so both fractions share the common base 483.

3 × 21/23 × 21 = 63/483 and 11 × 23/21 × 23 = 253/483

Step 3

Add the Numerators

Now add the numerators (63 + 253 = 316) and keep the common denominator 483 unchanged.

63 + 253/483 = 316/483

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 316 and 483 is 1, confirming that 316/483 cannot be reduced further—it is already in its simplest irreducible form.

316/483

Step 5

Decimal & Percentage Representation

Dividing the numerator 316 by denominator 483 produces a repeating decimal (approximately 0.654244, or 65.4244%).

316 ÷ 483 = 0.654244 (65.4244%)

Visual Representation

The diagram below illustrates 3/23 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`316/483`
Mixed Number Form	`316/483`
Decimal Form	`0.654244`
Percentage	`65.4244%`

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Frequently Asked Questions

What is 3/23 plus 11/21 as a fraction?

3/23 + 11/21 in simplest fraction form is 316/483.

What is 3/23 plus 11/21 as a decimal?

3/23 + 11/21 converted to a decimal is 0.654244.

What is 3/23 plus 11/21 as a percentage?

3/23 + 11/21 expressed as a percentage is 65.4244%.

Does 3/23 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.654244...) because the denominator contains prime factors other than 2 and 5.