What is 2/22 plus 3/10? (Answer: 43/110)

Exact Answer

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Problem: What is 2/22 plus 3/10?
Formula / Expression: 2/22 + 3/10
Final Answer: 43/110
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 110 (which is smaller than their product 22 × 10 = 220, keeping the calculation simpler).
Working: LCD(22, 10) = 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 3/10 by 11 so both fractions share the common base 110.
Working: 2 × 5/22 × 5 = 10/110 and 3 × 11/10 × 11 = 33/110

Step 3: Add the Numerators
Now add the numerators (10 + 33 = 43) and keep the common denominator 110 unchanged.
Working: 10 + 33/110 = 43/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 110 is 1, confirming that 43/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 110 produces a repeating decimal (approximately 0.390909, or 39.0909%).
Working: 43 ÷ 110 = 0.390909 (39.0909%)

Key Values:
- Simplified Fraction: 43/110
- Mixed Number Form: 43/110
- Decimal Value: 0.390909
- Percentage: 39.0909%

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Solved with FractionsCalc:
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2/22 + 3/10 = 43/110

Simplified Fraction

43/110

Mixed Number

Proper (43/110)

Decimal Value

0.390909

Percentage

39.0909%

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Step-by-Step Solution: 2/22 + 3/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 10) = 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 3/10 by 11 so both fractions share the common base 110.

2 × 5/22 × 5 = 10/110 and 3 × 11/10 × 11 = 33/110

Step 3

Add the Numerators

Now add the numerators (10 + 33 = 43) and keep the common denominator 110 unchanged.

10 + 33/110 = 43/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 110 is 1, confirming that 43/110 cannot be reduced further—it is already in its simplest irreducible form.

43/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 110 produces a repeating decimal (approximately 0.390909, or 39.0909%).

43 ÷ 110 = 0.390909 (39.0909%)

Visual Representation

The diagram below illustrates 2/22 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/110`
Mixed Number Form	`43/110`
Decimal Form	`0.390909`
Percentage	`39.0909%`

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Frequently Asked Questions

What is 2/22 plus 3/10 as a fraction?

2/22 + 3/10 in simplest fraction form is 43/110.

What is 2/22 plus 3/10 as a decimal?

2/22 + 3/10 converted to a decimal is 0.390909.

What is 2/22 plus 3/10 as a percentage?

2/22 + 3/10 expressed as a percentage is 39.0909%.

Does 2/22 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.390909...) because the denominator contains prime factors other than 2 and 5.