What is 2/5 plus 12/22? (Answer: 52/55)

Exact Answer

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Problem: What is 2/5 plus 12/22?
Formula / Expression: 2/5 + 12/22
Final Answer: 52/55
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/5 by 22, and multiply the numerator and denominator of 12/22 by 5 so both fractions share the common base 110.
Working: 2 × 22/5 × 22 = 44/110 and 12 × 5/22 × 5 = 60/110

Step 3: Add the Numerators
Now add the numerators (44 + 60 = 104) and keep the common denominator 110 unchanged.
Working: 44 + 60/110 = 104/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 104 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 104 ÷ 2/110 ÷ 2 = 52/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 55 produces a repeating decimal (approximately 0.945455, or 94.5455%).
Working: 52 ÷ 55 = 0.945455 (94.5455%)

Key Values:
- Simplified Fraction: 52/55
- Mixed Number Form: 52/55
- Decimal Value: 0.945455
- Percentage: 94.5455%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-plus-12-22/
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2/5 + 12/22 = 52/55

Simplified Fraction

52/55

Mixed Number

Proper (52/55)

Decimal Value

0.945455

Percentage

94.5455%

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Step-by-Step Solution: 2/5 + 12/22

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 22) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/5 by 22, and multiply the numerator and denominator of 12/22 by 5 so both fractions share the common base 110.

2 × 22/5 × 22 = 44/110 and 12 × 5/22 × 5 = 60/110

Step 3

Add the Numerators

Now add the numerators (44 + 60 = 104) and keep the common denominator 110 unchanged.

44 + 60/110 = 104/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 104 and 110, which is 2. Divide both the numerator and denominator by 2.

104 ÷ 2/110 ÷ 2 = 52/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 55 produces a repeating decimal (approximately 0.945455, or 94.5455%).

52 ÷ 55 = 0.945455 (94.5455%)

Visual Representation

The diagram below illustrates 2/5 plus 12/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/55`
Mixed Number Form	`52/55`
Decimal Form	`0.945455`
Percentage	`94.5455%`

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Frequently Asked Questions

What is 2/5 plus 12/22 as a fraction?

2/5 + 12/22 in simplest fraction form is 52/55.

What is 2/5 plus 12/22 as a decimal?

2/5 + 12/22 converted to a decimal is 0.945455.

What is 2/5 plus 12/22 as a percentage?

2/5 + 12/22 expressed as a percentage is 94.5455%.

Does 2/5 plus 12/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.945455...) because the denominator contains prime factors other than 2 and 5.