What is 2/18 plus 2/17? (Answer: 35/153)

Exact Answer

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Problem: What is 2/18 plus 2/17?
Formula / Expression: 2/18 + 2/17
Final Answer: 35/153
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 17 = 306.
Working: LCD(18, 17) = 306

Step 2: Convert to Equivalent Fractions with Common Denominator 306
Multiply the numerator and denominator of 2/18 by 17, and multiply the numerator and denominator of 2/17 by 18 so both fractions share the common base 306.
Working: 2 × 17/18 × 17 = 34/306 and 2 × 18/17 × 18 = 36/306

Step 3: Add the Numerators
Now add the numerators (34 + 36 = 70) and keep the common denominator 306 unchanged.
Working: 34 + 36/306 = 70/306

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 306, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/306 ÷ 2 = 35/153

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 153 produces a repeating decimal (approximately 0.228758, or 22.8758%).
Working: 35 ÷ 153 = 0.228758 (22.8758%)

Key Values:
- Simplified Fraction: 35/153
- Mixed Number Form: 35/153
- Decimal Value: 0.228758
- Percentage: 22.8758%

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Solved with FractionsCalc:
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2/18 + 2/17 = 35/153

Simplified Fraction

35/153

Mixed Number

Proper (35/153)

Decimal Value

0.228758

Percentage

22.8758%

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Step-by-Step Solution: 2/18 + 2/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 17 = 306.

LCD(18, 17) = 306

Step 2

Convert to Equivalent Fractions with Common Denominator 306

Multiply the numerator and denominator of 2/18 by 17, and multiply the numerator and denominator of 2/17 by 18 so both fractions share the common base 306.

2 × 17/18 × 17 = 34/306 and 2 × 18/17 × 18 = 36/306

Step 3

Add the Numerators

Now add the numerators (34 + 36 = 70) and keep the common denominator 306 unchanged.

34 + 36/306 = 70/306

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 306, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/306 ÷ 2 = 35/153

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 153 produces a repeating decimal (approximately 0.228758, or 22.8758%).

35 ÷ 153 = 0.228758 (22.8758%)

Visual Representation

The diagram below illustrates 2/18 plus 2/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/153`
Mixed Number Form	`35/153`
Decimal Form	`0.228758`
Percentage	`22.8758%`

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Frequently Asked Questions

What is 2/18 plus 2/17 as a fraction?

2/18 + 2/17 in simplest fraction form is 35/153.

What is 2/18 plus 2/17 as a decimal?

2/18 + 2/17 converted to a decimal is 0.228758.

What is 2/18 plus 2/17 as a percentage?

2/18 + 2/17 expressed as a percentage is 22.8758%.

Does 2/18 plus 2/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.228758...) because the denominator contains prime factors other than 2 and 5.