What is 3/23 plus 2/5? (Answer: 61/115)

Exact Answer

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Problem: What is 3/23 plus 2/5?
Formula / Expression: 3/23 + 2/5
Final Answer: 61/115
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 5 = 115.
Working: LCD(23, 5) = 115

Step 2: Convert to Equivalent Fractions with Common Denominator 115
Multiply the numerator and denominator of 3/23 by 5, and multiply the numerator and denominator of 2/5 by 23 so both fractions share the common base 115.
Working: 3 × 5/23 × 5 = 15/115 and 2 × 23/5 × 23 = 46/115

Step 3: Add the Numerators
Now add the numerators (15 + 46 = 61) and keep the common denominator 115 unchanged.
Working: 15 + 46/115 = 61/115

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 115 is 1, confirming that 61/115 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/115

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 115 produces a repeating decimal (approximately 0.530435, or 53.0435%).
Working: 61 ÷ 115 = 0.530435 (53.0435%)

Key Values:
- Simplified Fraction: 61/115
- Mixed Number Form: 61/115
- Decimal Value: 0.530435
- Percentage: 53.0435%

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Solved with FractionsCalc:
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3/23 + 2/5 = 61/115

Simplified Fraction

61/115

Mixed Number

Proper (61/115)

Decimal Value

0.530435

Percentage

53.0435%

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Step-by-Step Solution: 3/23 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 5 = 115.

LCD(23, 5) = 115

Step 2

Convert to Equivalent Fractions with Common Denominator 115

Multiply the numerator and denominator of 3/23 by 5, and multiply the numerator and denominator of 2/5 by 23 so both fractions share the common base 115.

3 × 5/23 × 5 = 15/115 and 2 × 23/5 × 23 = 46/115

Step 3

Add the Numerators

Now add the numerators (15 + 46 = 61) and keep the common denominator 115 unchanged.

15 + 46/115 = 61/115

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 115 is 1, confirming that 61/115 cannot be reduced further—it is already in its simplest irreducible form.

61/115

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 115 produces a repeating decimal (approximately 0.530435, or 53.0435%).

61 ÷ 115 = 0.530435 (53.0435%)

Visual Representation

The diagram below illustrates 3/23 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/115`
Mixed Number Form	`61/115`
Decimal Form	`0.530435`
Percentage	`53.0435%`

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Frequently Asked Questions

What is 3/23 plus 2/5 as a fraction?

3/23 + 2/5 in simplest fraction form is 61/115.

What is 3/23 plus 2/5 as a decimal?

3/23 + 2/5 converted to a decimal is 0.530435.

What is 3/23 plus 2/5 as a percentage?

3/23 + 2/5 expressed as a percentage is 53.0435%.

Does 3/23 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.530435...) because the denominator contains prime factors other than 2 and 5.