What is 2/10 plus 8/22? (Answer: 31/55)

Exact Answer

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Problem: What is 2/10 plus 8/22?
Formula / Expression: 2/10 + 8/22
Final Answer: 31/55
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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 8/22 by 5 so both fractions share the common base 110.
Working: 2 × 11/10 × 11 = 22/110 and 8 × 5/22 × 5 = 40/110

Step 3: Add the Numerators
Now add the numerators (22 + 40 = 62) and keep the common denominator 110 unchanged.
Working: 22 + 40/110 = 62/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/110 ÷ 2 = 31/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 55 produces a repeating decimal (approximately 0.563636, or 56.3636%).
Working: 31 ÷ 55 = 0.563636 (56.3636%)

Key Values:
- Simplified Fraction: 31/55
- Mixed Number Form: 31/55
- Decimal Value: 0.563636
- Percentage: 56.3636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-8-22/
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2/10 + 8/22 = 31/55

Simplified Fraction

31/55

Mixed Number

Proper (31/55)

Decimal Value

0.563636

Percentage

56.3636%

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Step-by-Step Solution: 2/10 + 8/22

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 8/22 by 5 so both fractions share the common base 110.

2 × 11/10 × 11 = 22/110 and 8 × 5/22 × 5 = 40/110

Step 3

Add the Numerators

Now add the numerators (22 + 40 = 62) and keep the common denominator 110 unchanged.

22 + 40/110 = 62/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 110, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/110 ÷ 2 = 31/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 55 produces a repeating decimal (approximately 0.563636, or 56.3636%).

31 ÷ 55 = 0.563636 (56.3636%)

Visual Representation

The diagram below illustrates 2/10 plus 8/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/55`
Mixed Number Form	`31/55`
Decimal Form	`0.563636`
Percentage	`56.3636%`

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Frequently Asked Questions

What is 2/10 plus 8/22 as a fraction?

2/10 + 8/22 in simplest fraction form is 31/55.

What is 2/10 plus 8/22 as a decimal?

2/10 + 8/22 converted to a decimal is 0.563636.

What is 2/10 plus 8/22 as a percentage?

2/10 + 8/22 expressed as a percentage is 56.3636%.

Does 2/10 plus 8/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.563636...) because the denominator contains prime factors other than 2 and 5.