What is 2/22 plus 3/5? (Answer: 38/55)

Exact Answer

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Problem: What is 2/22 plus 3/5?
Formula / Expression: 2/22 + 3/5
Final Answer: 38/55
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 5 = 110.
Working: LCD(22, 5) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/22 by 5, and multiply the numerator and denominator of 3/5 by 22 so both fractions share the common base 110.
Working: 2 × 5/22 × 5 = 10/110 and 3 × 22/5 × 22 = 66/110

Step 3: Add the Numerators
Now add the numerators (10 + 66 = 76) and keep the common denominator 110 unchanged.
Working: 10 + 66/110 = 76/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 76 ÷ 2/110 ÷ 2 = 38/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 55 produces a repeating decimal (approximately 0.690909, or 69.0909%).
Working: 38 ÷ 55 = 0.690909 (69.0909%)

Key Values:
- Simplified Fraction: 38/55
- Mixed Number Form: 38/55
- Decimal Value: 0.690909
- Percentage: 69.0909%

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Solved with FractionsCalc:
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2/22 + 3/5 = 38/55

Simplified Fraction

38/55

Mixed Number

Proper (38/55)

Decimal Value

0.690909

Percentage

69.0909%

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Step-by-Step Solution: 2/22 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 5 = 110.

LCD(22, 5) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/22 by 5, and multiply the numerator and denominator of 3/5 by 22 so both fractions share the common base 110.

2 × 5/22 × 5 = 10/110 and 3 × 22/5 × 22 = 66/110

Step 3

Add the Numerators

Now add the numerators (10 + 66 = 76) and keep the common denominator 110 unchanged.

10 + 66/110 = 76/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 110, which is 2. Divide both the numerator and denominator by 2.

76 ÷ 2/110 ÷ 2 = 38/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 55 produces a repeating decimal (approximately 0.690909, or 69.0909%).

38 ÷ 55 = 0.690909 (69.0909%)

Visual Representation

The diagram below illustrates 2/22 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/55`
Mixed Number Form	`38/55`
Decimal Form	`0.690909`
Percentage	`69.0909%`

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Frequently Asked Questions

What is 2/22 plus 3/5 as a fraction?

2/22 + 3/5 in simplest fraction form is 38/55.

What is 2/22 plus 3/5 as a decimal?

2/22 + 3/5 converted to a decimal is 0.690909.

What is 2/22 plus 3/5 as a percentage?

2/22 + 3/5 expressed as a percentage is 69.0909%.

Does 2/22 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.690909...) because the denominator contains prime factors other than 2 and 5.