What is 2/22 plus 3/12? (Answer: 15/44)

Exact Answer

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Problem: What is 2/22 plus 3/12?
Formula / Expression: 2/22 + 3/12
Final Answer: 15/44
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 2/22 by 6, and multiply the numerator and denominator of 3/12 by 11 so both fractions share the common base 132.
Working: 2 × 6/22 × 6 = 12/132 and 3 × 11/12 × 11 = 33/132

Step 3: Add the Numerators
Now add the numerators (12 + 33 = 45) and keep the common denominator 132 unchanged.
Working: 12 + 33/132 = 45/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 132, which is 3. Divide both the numerator and denominator by 3.
Working: 45 ÷ 3/132 ÷ 3 = 15/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 44 produces a repeating decimal (approximately 0.340909, or 34.0909%).
Working: 15 ÷ 44 = 0.340909 (34.0909%)

Key Values:
- Simplified Fraction: 15/44
- Mixed Number Form: 15/44
- Decimal Value: 0.340909
- Percentage: 34.0909%

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Solved with FractionsCalc:
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2/22 + 3/12 = 15/44

Simplified Fraction

15/44

Mixed Number

Proper (15/44)

Decimal Value

0.340909

Percentage

34.0909%

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Step-by-Step Solution: 2/22 + 3/12

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 12) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 2/22 by 6, and multiply the numerator and denominator of 3/12 by 11 so both fractions share the common base 132.

2 × 6/22 × 6 = 12/132 and 3 × 11/12 × 11 = 33/132

Step 3

Add the Numerators

Now add the numerators (12 + 33 = 45) and keep the common denominator 132 unchanged.

12 + 33/132 = 45/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 45 and 132, which is 3. Divide both the numerator and denominator by 3.

45 ÷ 3/132 ÷ 3 = 15/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 44 produces a repeating decimal (approximately 0.340909, or 34.0909%).

15 ÷ 44 = 0.340909 (34.0909%)

Visual Representation

The diagram below illustrates 2/22 plus 3/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/44`
Mixed Number Form	`15/44`
Decimal Form	`0.340909`
Percentage	`34.0909%`

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Frequently Asked Questions

What is 2/22 plus 3/12 as a fraction?

2/22 + 3/12 in simplest fraction form is 15/44.

What is 2/22 plus 3/12 as a decimal?

2/22 + 3/12 converted to a decimal is 0.340909.

What is 2/22 plus 3/12 as a percentage?

2/22 + 3/12 expressed as a percentage is 34.0909%.

Does 2/22 plus 3/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.340909...) because the denominator contains prime factors other than 2 and 5.