What is 2/23 plus 2/18? (Answer: 41/207)

Exact Answer

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Problem: What is 2/23 plus 2/18?
Formula / Expression: 2/23 + 2/18
Final Answer: 41/207
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 18 = 414.
Working: LCD(23, 18) = 414

Step 2: Convert to Equivalent Fractions with Common Denominator 414
Multiply the numerator and denominator of 2/23 by 18, and multiply the numerator and denominator of 2/18 by 23 so both fractions share the common base 414.
Working: 2 × 18/23 × 18 = 36/414 and 2 × 23/18 × 23 = 46/414

Step 3: Add the Numerators
Now add the numerators (36 + 46 = 82) and keep the common denominator 414 unchanged.
Working: 36 + 46/414 = 82/414

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 414, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/414 ÷ 2 = 41/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 207 produces a repeating decimal (approximately 0.198068, or 19.8068%).
Working: 41 ÷ 207 = 0.198068 (19.8068%)

Key Values:
- Simplified Fraction: 41/207
- Mixed Number Form: 41/207
- Decimal Value: 0.198068
- Percentage: 19.8068%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-2-18/
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2/23 + 2/18 = 41/207

Simplified Fraction

41/207

Mixed Number

Proper (41/207)

Decimal Value

0.198068

Percentage

19.8068%

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Step-by-Step Solution: 2/23 + 2/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 18 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 18 = 414.

LCD(23, 18) = 414

Step 2

Convert to Equivalent Fractions with Common Denominator 414

Multiply the numerator and denominator of 2/23 by 18, and multiply the numerator and denominator of 2/18 by 23 so both fractions share the common base 414.

2 × 18/23 × 18 = 36/414 and 2 × 23/18 × 23 = 46/414

Step 3

Add the Numerators

Now add the numerators (36 + 46 = 82) and keep the common denominator 414 unchanged.

36 + 46/414 = 82/414

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 414, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/414 ÷ 2 = 41/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 207 produces a repeating decimal (approximately 0.198068, or 19.8068%).

41 ÷ 207 = 0.198068 (19.8068%)

Visual Representation

The diagram below illustrates 2/23 plus 2/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/207`
Mixed Number Form	`41/207`
Decimal Form	`0.198068`
Percentage	`19.8068%`

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Frequently Asked Questions

What is 2/23 plus 2/18 as a fraction?

2/23 + 2/18 in simplest fraction form is 41/207.

What is 2/23 plus 2/18 as a decimal?

2/23 + 2/18 converted to a decimal is 0.198068.

What is 2/23 plus 2/18 as a percentage?

2/23 + 2/18 expressed as a percentage is 19.8068%.

Does 2/23 plus 2/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.198068...) because the denominator contains prime factors other than 2 and 5.