What is 2/23 plus 3/5? (Answer: 79/115)

Exact Answer

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Problem: What is 2/23 plus 3/5?
Formula / Expression: 2/23 + 3/5
Final Answer: 79/115
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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 2/23 by 5, and multiply the numerator and denominator of 3/5 by 23 so both fractions share the common base 115.
Working: 2 × 5/23 × 5 = 10/115 and 3 × 23/5 × 23 = 69/115

Step 3: Add the Numerators
Now add the numerators (10 + 69 = 79) and keep the common denominator 115 unchanged.
Working: 10 + 69/115 = 79/115

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 115 is 1, confirming that 79/115 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/115

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 115 produces a repeating decimal (approximately 0.686957, or 68.6957%).
Working: 79 ÷ 115 = 0.686957 (68.6957%)

Key Values:
- Simplified Fraction: 79/115
- Mixed Number Form: 79/115
- Decimal Value: 0.686957
- Percentage: 68.6957%

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2/23 + 3/5 = 79/115

Simplified Fraction

79/115

Mixed Number

Proper (79/115)

Decimal Value

0.686957

Percentage

68.6957%

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

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

2 × 5/23 × 5 = 10/115 and 3 × 23/5 × 23 = 69/115

Step 3

Add the Numerators

Now add the numerators (10 + 69 = 79) and keep the common denominator 115 unchanged.

10 + 69/115 = 79/115

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 115 is 1, confirming that 79/115 cannot be reduced further—it is already in its simplest irreducible form.

79/115

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 115 produces a repeating decimal (approximately 0.686957, or 68.6957%).

79 ÷ 115 = 0.686957 (68.6957%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/115`
Mixed Number Form	`79/115`
Decimal Form	`0.686957`
Percentage	`68.6957%`

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Frequently Asked Questions

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

2/23 + 3/5 in simplest fraction form is 79/115.

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

2/23 + 3/5 converted to a decimal is 0.686957.

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

2/23 + 3/5 expressed as a percentage is 68.6957%.

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

It results in a repeating decimal (approximately 0.686957...) because the denominator contains prime factors other than 2 and 5.