What is 2/23 plus 3/10? (Answer: 89/230)

Exact Answer

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Problem: What is 2/23 plus 3/10?
Formula / Expression: 2/23 + 3/10
Final Answer: 89/230
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 10 = 230.
Working: LCD(23, 10) = 230

Step 2: Convert to Equivalent Fractions with Common Denominator 230
Multiply the numerator and denominator of 2/23 by 10, and multiply the numerator and denominator of 3/10 by 23 so both fractions share the common base 230.
Working: 2 × 10/23 × 10 = 20/230 and 3 × 23/10 × 23 = 69/230

Step 3: Add the Numerators
Now add the numerators (20 + 69 = 89) and keep the common denominator 230 unchanged.
Working: 20 + 69/230 = 89/230

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 230 is 1, confirming that 89/230 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/230

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 230 produces a repeating decimal (approximately 0.386957, or 38.6957%).
Working: 89 ÷ 230 = 0.386957 (38.6957%)

Key Values:
- Simplified Fraction: 89/230
- Mixed Number Form: 89/230
- Decimal Value: 0.386957
- Percentage: 38.6957%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-3-10/
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2/23 + 3/10 = 89/230

Simplified Fraction

89/230

Mixed Number

Proper (89/230)

Decimal Value

0.386957

Percentage

38.6957%

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Step-by-Step Solution: 2/23 + 3/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 10 = 230.

LCD(23, 10) = 230

Step 2

Convert to Equivalent Fractions with Common Denominator 230

Multiply the numerator and denominator of 2/23 by 10, and multiply the numerator and denominator of 3/10 by 23 so both fractions share the common base 230.

2 × 10/23 × 10 = 20/230 and 3 × 23/10 × 23 = 69/230

Step 3

Add the Numerators

Now add the numerators (20 + 69 = 89) and keep the common denominator 230 unchanged.

20 + 69/230 = 89/230

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 230 is 1, confirming that 89/230 cannot be reduced further—it is already in its simplest irreducible form.

89/230

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 230 produces a repeating decimal (approximately 0.386957, or 38.6957%).

89 ÷ 230 = 0.386957 (38.6957%)

Visual Representation

The diagram below illustrates 2/23 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/230`
Mixed Number Form	`89/230`
Decimal Form	`0.386957`
Percentage	`38.6957%`

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Frequently Asked Questions

What is 2/23 plus 3/10 as a fraction?

2/23 + 3/10 in simplest fraction form is 89/230.

What is 2/23 plus 3/10 as a decimal?

2/23 + 3/10 converted to a decimal is 0.386957.

What is 2/23 plus 3/10 as a percentage?

2/23 + 3/10 expressed as a percentage is 38.6957%.

Does 2/23 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.386957...) because the denominator contains prime factors other than 2 and 5.