What is 2/33 plus 2/12? (Answer: 5/22)

Exact Answer

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Problem: What is 2/33 plus 2/12?
Formula / Expression: 2/33 + 2/12
Final Answer: 5/22
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 132 (which is smaller than their product 33 × 12 = 396, keeping the calculation simpler).
Working: LCD(33, 12) = 132

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 2/33 by 4, and multiply the numerator and denominator of 2/12 by 11 so both fractions share the common base 132.
Working: 2 × 4/33 × 4 = 8/132 and 2 × 11/12 × 11 = 22/132

Step 3: Add the Numerators
Now add the numerators (8 + 22 = 30) and keep the common denominator 132 unchanged.
Working: 8 + 22/132 = 30/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 132, which is 6. Divide both the numerator and denominator by 6.
Working: 30 ÷ 6/132 ÷ 6 = 5/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 22 produces a repeating decimal (approximately 0.227273, or 22.7273%).
Working: 5 ÷ 22 = 0.227273 (22.7273%)

Key Values:
- Simplified Fraction: 5/22
- Mixed Number Form: 5/22
- Decimal Value: 0.227273
- Percentage: 22.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-12/
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2/33 + 2/12 = 5/22

Simplified Fraction

5/22

Mixed Number

Proper (5/22)

Decimal Value

0.227273

Percentage

22.7273%

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Step-by-Step Solution: 2/33 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 132 (which is smaller than their product 33 × 12 = 396, keeping the calculation simpler).

LCD(33, 12) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 2/33 by 4, and multiply the numerator and denominator of 2/12 by 11 so both fractions share the common base 132.

2 × 4/33 × 4 = 8/132 and 2 × 11/12 × 11 = 22/132

Step 3

Add the Numerators

Now add the numerators (8 + 22 = 30) and keep the common denominator 132 unchanged.

8 + 22/132 = 30/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 132, which is 6. Divide both the numerator and denominator by 6.

30 ÷ 6/132 ÷ 6 = 5/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 22 produces a repeating decimal (approximately 0.227273, or 22.7273%).

5 ÷ 22 = 0.227273 (22.7273%)

Visual Representation

The diagram below illustrates 2/33 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/22`
Mixed Number Form	`5/22`
Decimal Form	`0.227273`
Percentage	`22.7273%`

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Frequently Asked Questions

What is 2/33 plus 2/12 as a fraction?

2/33 + 2/12 in simplest fraction form is 5/22.

What is 2/33 plus 2/12 as a decimal?

2/33 + 2/12 converted to a decimal is 0.227273.

What is 2/33 plus 2/12 as a percentage?

2/33 + 2/12 expressed as a percentage is 22.7273%.

Does 2/33 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.227273...) because the denominator contains prime factors other than 2 and 5.