What is 2/22 plus 5/10? (Answer: 13/22)

Exact Answer

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Problem: What is 2/22 plus 5/10?
Formula / Expression: 2/22 + 5/10
Final Answer: 13/22
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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 5/10 by 11 so both fractions share the common base 110.
Working: 2 × 5/22 × 5 = 10/110 and 5 × 11/10 × 11 = 55/110

Step 3: Add the Numerators
Now add the numerators (10 + 55 = 65) and keep the common denominator 110 unchanged.
Working: 10 + 55/110 = 65/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 65 and 110, which is 5. Divide both the numerator and denominator by 5.
Working: 65 ÷ 5/110 ÷ 5 = 13/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 22 produces a repeating decimal (approximately 0.590909, or 59.0909%).
Working: 13 ÷ 22 = 0.590909 (59.0909%)

Key Values:
- Simplified Fraction: 13/22
- Mixed Number Form: 13/22
- Decimal Value: 0.590909
- Percentage: 59.0909%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-5-10/
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2/22 + 5/10 = 13/22

Simplified Fraction

13/22

Mixed Number

Proper (13/22)

Decimal Value

0.590909

Percentage

59.0909%

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

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 5/10 by 11 so both fractions share the common base 110.

2 × 5/22 × 5 = 10/110 and 5 × 11/10 × 11 = 55/110

Step 3

Add the Numerators

Now add the numerators (10 + 55 = 65) and keep the common denominator 110 unchanged.

10 + 55/110 = 65/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 65 and 110, which is 5. Divide both the numerator and denominator by 5.

65 ÷ 5/110 ÷ 5 = 13/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 22 produces a repeating decimal (approximately 0.590909, or 59.0909%).

13 ÷ 22 = 0.590909 (59.0909%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/22`
Mixed Number Form	`13/22`
Decimal Form	`0.590909`
Percentage	`59.0909%`

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Frequently Asked Questions

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

2/22 + 5/10 in simplest fraction form is 13/22.

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

2/22 + 5/10 converted to a decimal is 0.590909.

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

2/22 + 5/10 expressed as a percentage is 59.0909%.

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

It results in a repeating decimal (approximately 0.590909...) because the denominator contains prime factors other than 2 and 5.