What is 1/22 plus 2/5? (Answer: 49/110)

Exact Answer

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Problem: What is 1/22 plus 2/5?
Formula / Expression: 1/22 + 2/5
Final Answer: 49/110
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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 1/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.
Working: 1 × 5/22 × 5 = 5/110 and 2 × 22/5 × 22 = 44/110

Step 3: Add the Numerators
Now add the numerators (5 + 44 = 49) and keep the common denominator 110 unchanged.
Working: 5 + 44/110 = 49/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 110 is 1, confirming that 49/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 110 produces a repeating decimal (approximately 0.445455, or 44.5455%).
Working: 49 ÷ 110 = 0.445455 (44.5455%)

Key Values:
- Simplified Fraction: 49/110
- Mixed Number Form: 49/110
- Decimal Value: 0.445455
- Percentage: 44.5455%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-22-plus-2-5/
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1/22 + 2/5 = 49/110

Simplified Fraction

49/110

Mixed Number

Proper (49/110)

Decimal Value

0.445455

Percentage

44.5455%

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Step-by-Step Solution: 1/22 + 2/5

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 1/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.

1 × 5/22 × 5 = 5/110 and 2 × 22/5 × 22 = 44/110

Step 3

Add the Numerators

Now add the numerators (5 + 44 = 49) and keep the common denominator 110 unchanged.

5 + 44/110 = 49/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 110 is 1, confirming that 49/110 cannot be reduced further—it is already in its simplest irreducible form.

49/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 110 produces a repeating decimal (approximately 0.445455, or 44.5455%).

49 ÷ 110 = 0.445455 (44.5455%)

Visual Representation

The diagram below illustrates 1/22 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/110`
Mixed Number Form	`49/110`
Decimal Form	`0.445455`
Percentage	`44.5455%`

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Frequently Asked Questions

What is 1/22 plus 2/5 as a fraction?

1/22 + 2/5 in simplest fraction form is 49/110.

What is 1/22 plus 2/5 as a decimal?

1/22 + 2/5 converted to a decimal is 0.445455.

What is 1/22 plus 2/5 as a percentage?

1/22 + 2/5 expressed as a percentage is 44.5455%.

Does 1/22 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.445455...) because the denominator contains prime factors other than 2 and 5.