What is 3/22 plus 2/12? (Answer: 10/33)

Exact Answer

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Problem: What is 3/22 plus 2/12?
Formula / Expression: 3/22 + 2/12
Final Answer: 10/33
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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 3/22 by 6, and multiply the numerator and denominator of 2/12 by 11 so both fractions share the common base 132.
Working: 3 × 6/22 × 6 = 18/132 and 2 × 11/12 × 11 = 22/132

Step 3: Add the Numerators
Now add the numerators (18 + 22 = 40) and keep the common denominator 132 unchanged.
Working: 18 + 22/132 = 40/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 132, which is 4. Divide both the numerator and denominator by 4.
Working: 40 ÷ 4/132 ÷ 4 = 10/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 33 produces a repeating decimal (approximately 0.30303, or 30.303%).
Working: 10 ÷ 33 = 0.30303 (30.303%)

Key Values:
- Simplified Fraction: 10/33
- Mixed Number Form: 10/33
- Decimal Value: 0.30303
- Percentage: 30.303%

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Solved with FractionsCalc:
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3/22 + 2/12 = 10/33

Simplified Fraction

10/33

Mixed Number

Proper (10/33)

Decimal Value

0.30303

Percentage

30.303%

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

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

3 × 6/22 × 6 = 18/132 and 2 × 11/12 × 11 = 22/132

Step 3

Add the Numerators

Now add the numerators (18 + 22 = 40) and keep the common denominator 132 unchanged.

18 + 22/132 = 40/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 132, which is 4. Divide both the numerator and denominator by 4.

40 ÷ 4/132 ÷ 4 = 10/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 33 produces a repeating decimal (approximately 0.30303, or 30.303%).

10 ÷ 33 = 0.30303 (30.303%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/33`
Mixed Number Form	`10/33`
Decimal Form	`0.30303`
Percentage	`30.303%`

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Frequently Asked Questions

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

3/22 + 2/12 in simplest fraction form is 10/33.

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

3/22 + 2/12 converted to a decimal is 0.30303.

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

3/22 + 2/12 expressed as a percentage is 30.303%.

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

It results in a repeating decimal (approximately 0.30303...) because the denominator contains prime factors other than 2 and 5.