What is 2/22 plus 2/10? (Answer: 16/55)

Exact Answer

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Problem: What is 2/22 plus 2/10?
Formula / Expression: 2/22 + 2/10
Final Answer: 16/55
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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 2/10 by 11 so both fractions share the common base 110.
Working: 2 × 5/22 × 5 = 10/110 and 2 × 11/10 × 11 = 22/110

Step 3: Add the Numerators
Now add the numerators (10 + 22 = 32) and keep the common denominator 110 unchanged.
Working: 10 + 22/110 = 32/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 32 ÷ 2/110 ÷ 2 = 16/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 55 produces a repeating decimal (approximately 0.290909, or 29.0909%).
Working: 16 ÷ 55 = 0.290909 (29.0909%)

Key Values:
- Simplified Fraction: 16/55
- Mixed Number Form: 16/55
- Decimal Value: 0.290909
- Percentage: 29.0909%

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Solved with FractionsCalc:
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2/22 + 2/10 = 16/55

Simplified Fraction

16/55

Mixed Number

Proper (16/55)

Decimal Value

0.290909

Percentage

29.0909%

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

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 2/10 by 11 so both fractions share the common base 110.

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

Step 3

Add the Numerators

Now add the numerators (10 + 22 = 32) and keep the common denominator 110 unchanged.

10 + 22/110 = 32/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 110, which is 2. Divide both the numerator and denominator by 2.

32 ÷ 2/110 ÷ 2 = 16/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 55 produces a repeating decimal (approximately 0.290909, or 29.0909%).

16 ÷ 55 = 0.290909 (29.0909%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/55`
Mixed Number Form	`16/55`
Decimal Form	`0.290909`
Percentage	`29.0909%`

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Frequently Asked Questions

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

2/22 + 2/10 in simplest fraction form is 16/55.

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

2/22 + 2/10 converted to a decimal is 0.290909.

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

2/22 + 2/10 expressed as a percentage is 29.0909%.

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

It results in a repeating decimal (approximately 0.290909...) because the denominator contains prime factors other than 2 and 5.