What is 2/22 plus 3/18? (Answer: 17/66)

Exact Answer

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Problem: What is 2/22 plus 3/18?
Formula / Expression: 2/22 + 3/18
Final Answer: 17/66
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 198 (which is smaller than their product 22 × 18 = 396, keeping the calculation simpler).
Working: LCD(22, 18) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 3/18 by 11 so both fractions share the common base 198.
Working: 2 × 9/22 × 9 = 18/198 and 3 × 11/18 × 11 = 33/198

Step 3: Add the Numerators
Now add the numerators (18 + 33 = 51) and keep the common denominator 198 unchanged.
Working: 18 + 33/198 = 51/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 51 and 198, which is 3. Divide both the numerator and denominator by 3.
Working: 51 ÷ 3/198 ÷ 3 = 17/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 66 produces a repeating decimal (approximately 0.257576, or 25.7576%).
Working: 17 ÷ 66 = 0.257576 (25.7576%)

Key Values:
- Simplified Fraction: 17/66
- Mixed Number Form: 17/66
- Decimal Value: 0.257576
- Percentage: 25.7576%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-3-18/
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2/22 + 3/18 = 17/66

Simplified Fraction

17/66

Mixed Number

Proper (17/66)

Decimal Value

0.257576

Percentage

25.7576%

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Step-by-Step Solution: 2/22 + 3/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 198 (which is smaller than their product 22 × 18 = 396, keeping the calculation simpler).

LCD(22, 18) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 2/22 by 9, and multiply the numerator and denominator of 3/18 by 11 so both fractions share the common base 198.

2 × 9/22 × 9 = 18/198 and 3 × 11/18 × 11 = 33/198

Step 3

Add the Numerators

Now add the numerators (18 + 33 = 51) and keep the common denominator 198 unchanged.

18 + 33/198 = 51/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 51 and 198, which is 3. Divide both the numerator and denominator by 3.

51 ÷ 3/198 ÷ 3 = 17/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 66 produces a repeating decimal (approximately 0.257576, or 25.7576%).

17 ÷ 66 = 0.257576 (25.7576%)

Visual Representation

The diagram below illustrates 2/22 plus 3/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/66`
Mixed Number Form	`17/66`
Decimal Form	`0.257576`
Percentage	`25.7576%`

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Frequently Asked Questions

What is 2/22 plus 3/18 as a fraction?

2/22 + 3/18 in simplest fraction form is 17/66.

What is 2/22 plus 3/18 as a decimal?

2/22 + 3/18 converted to a decimal is 0.257576.

What is 2/22 plus 3/18 as a percentage?

2/22 + 3/18 expressed as a percentage is 25.7576%.

Does 2/22 plus 3/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.257576...) because the denominator contains prime factors other than 2 and 5.