What is 2/10 plus 5/22? (Answer: 47/110)

Exact Answer

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Problem: What is 2/10 plus 5/22?
Formula / Expression: 2/10 + 5/22
Final Answer: 47/110
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 110 (which is smaller than their product 10 × 22 = 220, keeping the calculation simpler).
Working: LCD(10, 22) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/10 by 11, and multiply the numerator and denominator of 5/22 by 5 so both fractions share the common base 110.
Working: 2 × 11/10 × 11 = 22/110 and 5 × 5/22 × 5 = 25/110

Step 3: Add the Numerators
Now add the numerators (22 + 25 = 47) and keep the common denominator 110 unchanged.
Working: 22 + 25/110 = 47/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 110 is 1, confirming that 47/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 110 produces a repeating decimal (approximately 0.427273, or 42.7273%).
Working: 47 ÷ 110 = 0.427273 (42.7273%)

Key Values:
- Simplified Fraction: 47/110
- Mixed Number Form: 47/110
- Decimal Value: 0.427273
- Percentage: 42.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-5-22/
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2/10 + 5/22 = 47/110

Simplified Fraction

47/110

Mixed Number

Proper (47/110)

Decimal Value

0.427273

Percentage

42.7273%

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Step-by-Step Solution: 2/10 + 5/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 110 (which is smaller than their product 10 × 22 = 220, keeping the calculation simpler).

LCD(10, 22) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/10 by 11, and multiply the numerator and denominator of 5/22 by 5 so both fractions share the common base 110.

2 × 11/10 × 11 = 22/110 and 5 × 5/22 × 5 = 25/110

Step 3

Add the Numerators

Now add the numerators (22 + 25 = 47) and keep the common denominator 110 unchanged.

22 + 25/110 = 47/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 110 is 1, confirming that 47/110 cannot be reduced further—it is already in its simplest irreducible form.

47/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 110 produces a repeating decimal (approximately 0.427273, or 42.7273%).

47 ÷ 110 = 0.427273 (42.7273%)

Visual Representation

The diagram below illustrates 2/10 plus 5/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/110`
Mixed Number Form	`47/110`
Decimal Form	`0.427273`
Percentage	`42.7273%`

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Frequently Asked Questions

What is 2/10 plus 5/22 as a fraction?

2/10 + 5/22 in simplest fraction form is 47/110.

What is 2/10 plus 5/22 as a decimal?

2/10 + 5/22 converted to a decimal is 0.427273.

What is 2/10 plus 5/22 as a percentage?

2/10 + 5/22 expressed as a percentage is 42.7273%.

Does 2/10 plus 5/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.427273...) because the denominator contains prime factors other than 2 and 5.