What is 5/22 plus 2/5? (Answer: 69/110)

Exact Answer

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Problem: What is 5/22 plus 2/5?
Formula / Expression: 5/22 + 2/5
Final Answer: 69/110
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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 5/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.
Working: 5 × 5/22 × 5 = 25/110 and 2 × 22/5 × 22 = 44/110

Step 3: Add the Numerators
Now add the numerators (25 + 44 = 69) and keep the common denominator 110 unchanged.
Working: 25 + 44/110 = 69/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 110 is 1, confirming that 69/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 110 produces a repeating decimal (approximately 0.627273, or 62.7273%).
Working: 69 ÷ 110 = 0.627273 (62.7273%)

Key Values:
- Simplified Fraction: 69/110
- Mixed Number Form: 69/110
- Decimal Value: 0.627273
- Percentage: 62.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-2-5/
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5/22 + 2/5 = 69/110

Simplified Fraction

69/110

Mixed Number

Proper (69/110)

Decimal Value

0.627273

Percentage

62.7273%

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Step-by-Step Solution: 5/22 + 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 5/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.

5 × 5/22 × 5 = 25/110 and 2 × 22/5 × 22 = 44/110

Step 3

Add the Numerators

Now add the numerators (25 + 44 = 69) and keep the common denominator 110 unchanged.

25 + 44/110 = 69/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 110 is 1, confirming that 69/110 cannot be reduced further—it is already in its simplest irreducible form.

69/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 110 produces a repeating decimal (approximately 0.627273, or 62.7273%).

69 ÷ 110 = 0.627273 (62.7273%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/110`
Mixed Number Form	`69/110`
Decimal Form	`0.627273`
Percentage	`62.7273%`

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Frequently Asked Questions

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

5/22 + 2/5 in simplest fraction form is 69/110.

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

5/22 + 2/5 converted to a decimal is 0.627273.

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

5/22 + 2/5 expressed as a percentage is 62.7273%.

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

It results in a repeating decimal (approximately 0.627273...) because the denominator contains prime factors other than 2 and 5.