What is 3/23 plus 2/8? (Answer: 35/92)

Exact Answer

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Problem: What is 3/23 plus 2/8?
Formula / Expression: 3/23 + 2/8
Final Answer: 35/92
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 8 = 184.
Working: LCD(23, 8) = 184

Step 2: Convert to Equivalent Fractions with Common Denominator 184
Multiply the numerator and denominator of 3/23 by 8, and multiply the numerator and denominator of 2/8 by 23 so both fractions share the common base 184.
Working: 3 × 8/23 × 8 = 24/184 and 2 × 23/8 × 23 = 46/184

Step 3: Add the Numerators
Now add the numerators (24 + 46 = 70) and keep the common denominator 184 unchanged.
Working: 24 + 46/184 = 70/184

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 184, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/184 ÷ 2 = 35/92

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 92 produces a repeating decimal (approximately 0.380435, or 38.0435%).
Working: 35 ÷ 92 = 0.380435 (38.0435%)

Key Values:
- Simplified Fraction: 35/92
- Mixed Number Form: 35/92
- Decimal Value: 0.380435
- Percentage: 38.0435%

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Solved with FractionsCalc:
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3/23 + 2/8 = 35/92

Simplified Fraction

35/92

Mixed Number

Proper (35/92)

Decimal Value

0.380435

Percentage

38.0435%

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Step-by-Step Solution: 3/23 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 8 = 184.

LCD(23, 8) = 184

Step 2

Convert to Equivalent Fractions with Common Denominator 184

Multiply the numerator and denominator of 3/23 by 8, and multiply the numerator and denominator of 2/8 by 23 so both fractions share the common base 184.

3 × 8/23 × 8 = 24/184 and 2 × 23/8 × 23 = 46/184

Step 3

Add the Numerators

Now add the numerators (24 + 46 = 70) and keep the common denominator 184 unchanged.

24 + 46/184 = 70/184

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 184, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/184 ÷ 2 = 35/92

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 92 produces a repeating decimal (approximately 0.380435, or 38.0435%).

35 ÷ 92 = 0.380435 (38.0435%)

Visual Representation

The diagram below illustrates 3/23 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/92`
Mixed Number Form	`35/92`
Decimal Form	`0.380435`
Percentage	`38.0435%`

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Frequently Asked Questions

What is 3/23 plus 2/8 as a fraction?

3/23 + 2/8 in simplest fraction form is 35/92.

What is 3/23 plus 2/8 as a decimal?

3/23 + 2/8 converted to a decimal is 0.380435.

What is 3/23 plus 2/8 as a percentage?

3/23 + 2/8 expressed as a percentage is 38.0435%.

Does 3/23 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.380435...) because the denominator contains prime factors other than 2 and 5.