What is 3/23 plus 2/3? (Answer: 55/69)

Exact Answer

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Problem: What is 3/23 plus 2/3?
Formula / Expression: 3/23 + 2/3
Final Answer: 55/69
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.
Working: LCD(23, 3) = 69

Step 2: Convert to Equivalent Fractions with Common Denominator 69
Multiply the numerator and denominator of 3/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.
Working: 3 × 3/23 × 3 = 9/69 and 2 × 23/3 × 23 = 46/69

Step 3: Add the Numerators
Now add the numerators (9 + 46 = 55) and keep the common denominator 69 unchanged.
Working: 9 + 46/69 = 55/69

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 69 is 1, confirming that 55/69 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/69

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 69 produces a repeating decimal (approximately 0.797101, or 79.7101%).
Working: 55 ÷ 69 = 0.797101 (79.7101%)

Key Values:
- Simplified Fraction: 55/69
- Mixed Number Form: 55/69
- Decimal Value: 0.797101
- Percentage: 79.7101%

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Solved with FractionsCalc:
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3/23 + 2/3 = 55/69

Simplified Fraction

55/69

Mixed Number

Proper (55/69)

Decimal Value

0.797101

Percentage

79.7101%

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Step-by-Step Solution: 3/23 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 3 = 69.

LCD(23, 3) = 69

Step 2

Convert to Equivalent Fractions with Common Denominator 69

Multiply the numerator and denominator of 3/23 by 3, and multiply the numerator and denominator of 2/3 by 23 so both fractions share the common base 69.

3 × 3/23 × 3 = 9/69 and 2 × 23/3 × 23 = 46/69

Step 3

Add the Numerators

Now add the numerators (9 + 46 = 55) and keep the common denominator 69 unchanged.

9 + 46/69 = 55/69

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 69 is 1, confirming that 55/69 cannot be reduced further—it is already in its simplest irreducible form.

55/69

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 69 produces a repeating decimal (approximately 0.797101, or 79.7101%).

55 ÷ 69 = 0.797101 (79.7101%)

Visual Representation

The diagram below illustrates 3/23 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/69`
Mixed Number Form	`55/69`
Decimal Form	`0.797101`
Percentage	`79.7101%`

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Frequently Asked Questions

What is 3/23 plus 2/3 as a fraction?

3/23 + 2/3 in simplest fraction form is 55/69.

What is 3/23 plus 2/3 as a decimal?

3/23 + 2/3 converted to a decimal is 0.797101.

What is 3/23 plus 2/3 as a percentage?

3/23 + 2/3 expressed as a percentage is 79.7101%.

Does 3/23 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.797101...) because the denominator contains prime factors other than 2 and 5.