What is 2/12 plus 9/22? (Answer: 19/33)

Exact Answer

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Problem: What is 2/12 plus 9/22?
Formula / Expression: 2/12 + 9/22
Final Answer: 19/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 132 (which is smaller than their product 12 × 22 = 264, keeping the calculation simpler).
Working: LCD(12, 22) = 132

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 2/12 by 11, and multiply the numerator and denominator of 9/22 by 6 so both fractions share the common base 132.
Working: 2 × 11/12 × 11 = 22/132 and 9 × 6/22 × 6 = 54/132

Step 3: Add the Numerators
Now add the numerators (22 + 54 = 76) and keep the common denominator 132 unchanged.
Working: 22 + 54/132 = 76/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 132, which is 4. Divide both the numerator and denominator by 4.
Working: 76 ÷ 4/132 ÷ 4 = 19/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 33 produces a repeating decimal (approximately 0.575758, or 57.5758%).
Working: 19 ÷ 33 = 0.575758 (57.5758%)

Key Values:
- Simplified Fraction: 19/33
- Mixed Number Form: 19/33
- Decimal Value: 0.575758
- Percentage: 57.5758%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-12-plus-9-22/
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2/12 + 9/22 = 19/33

Simplified Fraction

19/33

Mixed Number

Proper (19/33)

Decimal Value

0.575758

Percentage

57.5758%

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Step-by-Step Solution: 2/12 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 132 (which is smaller than their product 12 × 22 = 264, keeping the calculation simpler).

LCD(12, 22) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 2/12 by 11, and multiply the numerator and denominator of 9/22 by 6 so both fractions share the common base 132.

2 × 11/12 × 11 = 22/132 and 9 × 6/22 × 6 = 54/132

Step 3

Add the Numerators

Now add the numerators (22 + 54 = 76) and keep the common denominator 132 unchanged.

22 + 54/132 = 76/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 132, which is 4. Divide both the numerator and denominator by 4.

76 ÷ 4/132 ÷ 4 = 19/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 33 produces a repeating decimal (approximately 0.575758, or 57.5758%).

19 ÷ 33 = 0.575758 (57.5758%)

Visual Representation

The diagram below illustrates 2/12 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/33`
Mixed Number Form	`19/33`
Decimal Form	`0.575758`
Percentage	`57.5758%`

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Frequently Asked Questions

What is 2/12 plus 9/22 as a fraction?

2/12 + 9/22 in simplest fraction form is 19/33.

What is 2/12 plus 9/22 as a decimal?

2/12 + 9/22 converted to a decimal is 0.575758.

What is 2/12 plus 9/22 as a percentage?

2/12 + 9/22 expressed as a percentage is 57.5758%.

Does 2/12 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.575758...) because the denominator contains prime factors other than 2 and 5.