What is 3/23 plus 2/10? (Answer: 38/115)

Exact Answer

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Problem: What is 3/23 plus 2/10?
Formula / Expression: 3/23 + 2/10
Final Answer: 38/115
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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 3/23 by 10, and multiply the numerator and denominator of 2/10 by 23 so both fractions share the common base 230.
Working: 3 × 10/23 × 10 = 30/230 and 2 × 23/10 × 23 = 46/230

Step 3: Add the Numerators
Now add the numerators (30 + 46 = 76) and keep the common denominator 230 unchanged.
Working: 30 + 46/230 = 76/230

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 230, which is 2. Divide both the numerator and denominator by 2.
Working: 76 ÷ 2/230 ÷ 2 = 38/115

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 115 produces a repeating decimal (approximately 0.330435, or 33.0435%).
Working: 38 ÷ 115 = 0.330435 (33.0435%)

Key Values:
- Simplified Fraction: 38/115
- Mixed Number Form: 38/115
- Decimal Value: 0.330435
- Percentage: 33.0435%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-23-plus-2-10/
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3/23 + 2/10 = 38/115

Simplified Fraction

38/115

Mixed Number

Proper (38/115)

Decimal Value

0.330435

Percentage

33.0435%

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

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

3 × 10/23 × 10 = 30/230 and 2 × 23/10 × 23 = 46/230

Step 3

Add the Numerators

Now add the numerators (30 + 46 = 76) and keep the common denominator 230 unchanged.

30 + 46/230 = 76/230

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 230, which is 2. Divide both the numerator and denominator by 2.

76 ÷ 2/230 ÷ 2 = 38/115

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 115 produces a repeating decimal (approximately 0.330435, or 33.0435%).

38 ÷ 115 = 0.330435 (33.0435%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/115`
Mixed Number Form	`38/115`
Decimal Form	`0.330435`
Percentage	`33.0435%`

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Frequently Asked Questions

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

3/23 + 2/10 in simplest fraction form is 38/115.

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

3/23 + 2/10 converted to a decimal is 0.330435.

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

3/23 + 2/10 expressed as a percentage is 33.0435%.

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

It results in a repeating decimal (approximately 0.330435...) because the denominator contains prime factors other than 2 and 5.