What is 2/23 plus 2/15? (Answer: 76/345)

Exact Answer

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Problem: What is 2/23 plus 2/15?
Formula / Expression: 2/23 + 2/15
Final Answer: 76/345
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 15 = 345.
Working: LCD(23, 15) = 345

Step 2: Convert to Equivalent Fractions with Common Denominator 345
Multiply the numerator and denominator of 2/23 by 15, and multiply the numerator and denominator of 2/15 by 23 so both fractions share the common base 345.
Working: 2 × 15/23 × 15 = 30/345 and 2 × 23/15 × 23 = 46/345

Step 3: Add the Numerators
Now add the numerators (30 + 46 = 76) and keep the common denominator 345 unchanged.
Working: 30 + 46/345 = 76/345

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 345 is 1, confirming that 76/345 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/345

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 345 produces a repeating decimal (approximately 0.22029, or 22.029%).
Working: 76 ÷ 345 = 0.22029 (22.029%)

Key Values:
- Simplified Fraction: 76/345
- Mixed Number Form: 76/345
- Decimal Value: 0.22029
- Percentage: 22.029%

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Solved with FractionsCalc:
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2/23 + 2/15 = 76/345

Simplified Fraction

76/345

Mixed Number

Proper (76/345)

Decimal Value

0.22029

Percentage

22.029%

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Step-by-Step Solution: 2/23 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 15 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 15 = 345.

LCD(23, 15) = 345

Step 2

Convert to Equivalent Fractions with Common Denominator 345

Multiply the numerator and denominator of 2/23 by 15, and multiply the numerator and denominator of 2/15 by 23 so both fractions share the common base 345.

2 × 15/23 × 15 = 30/345 and 2 × 23/15 × 23 = 46/345

Step 3

Add the Numerators

Now add the numerators (30 + 46 = 76) and keep the common denominator 345 unchanged.

30 + 46/345 = 76/345

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 345 is 1, confirming that 76/345 cannot be reduced further—it is already in its simplest irreducible form.

76/345

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 345 produces a repeating decimal (approximately 0.22029, or 22.029%).

76 ÷ 345 = 0.22029 (22.029%)

Visual Representation

The diagram below illustrates 2/23 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/345`
Mixed Number Form	`76/345`
Decimal Form	`0.22029`
Percentage	`22.029%`

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Frequently Asked Questions

What is 2/23 plus 2/15 as a fraction?

2/23 + 2/15 in simplest fraction form is 76/345.

What is 2/23 plus 2/15 as a decimal?

2/23 + 2/15 converted to a decimal is 0.22029.

What is 2/23 plus 2/15 as a percentage?

2/23 + 2/15 expressed as a percentage is 22.029%.

Does 2/23 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.22029...) because the denominator contains prime factors other than 2 and 5.