What is 2/11 plus 9/22? (Answer: 13/22)

Exact Answer

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Problem: What is 2/11 plus 9/22?
Formula / Expression: 2/11 + 9/22
Final Answer: 13/22
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 22 is an exact multiple of 11 (11 × 2 = 22). The Least Common Denominator (LCD) is simply 22, meaning we only need to scale one fraction.
Working: LCD(11, 22) = 22

Step 2: Convert to Equivalent Fractions with Common Denominator 22
Multiply the numerator and denominator of 2/11 by 2, and multiply the numerator and denominator of 9/22 by 1 so both fractions share the common base 22.
Working: 2 × 2/11 × 2 = 4/22 and 9 × 1/22 × 1 = 9/22

Step 3: Add the Numerators
Now add the numerators (4 + 9 = 13) and keep the common denominator 22 unchanged.
Working: 4 + 9/22 = 13/22

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 22 is 1, confirming that 13/22 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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-2-11-plus-9-22/
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2/11 + 9/22 = 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: 2/11 + 9/22

Step 1

Find the Least Common Denominator (LCD)

Notice that 22 is an exact multiple of 11 (11 × 2 = 22). The Least Common Denominator (LCD) is simply 22, meaning we only need to scale one fraction.

LCD(11, 22) = 22

Step 2

Convert to Equivalent Fractions with Common Denominator 22

Multiply the numerator and denominator of 2/11 by 2, and multiply the numerator and denominator of 9/22 by 1 so both fractions share the common base 22.

2 × 2/11 × 2 = 4/22 and 9 × 1/22 × 1 = 9/22

Step 3

Add the Numerators

Now add the numerators (4 + 9 = 13) and keep the common denominator 22 unchanged.

4 + 9/22 = 13/22

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 22 is 1, confirming that 13/22 cannot be reduced further—it is already in its simplest irreducible form.

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 2/11 plus 9/22 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 2/11 plus 9/22 as a fraction?

2/11 + 9/22 in simplest fraction form is 13/22.

What is 2/11 plus 9/22 as a decimal?

2/11 + 9/22 converted to a decimal is 0.590909.

What is 2/11 plus 9/22 as a percentage?

2/11 + 9/22 expressed as a percentage is 59.0909%.

Does 2/11 plus 9/22 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.