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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 22 share a common factor (GCD = 11). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 33 × 22 = 726, keeping the calculation simpler).
Working: LCD(33, 22) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 2/33 by 2, and multiply the numerator and denominator of 2/22 by 3 so both fractions share the common base 66.
Working: 2 × 2/33 × 2 = 4/66 and 2 × 3/22 × 3 = 6/66

Step 3: Add the Numerators
Now add the numerators (4 + 6 = 10) and keep the common denominator 66 unchanged.
Working: 4 + 6/66 = 10/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 10 ÷ 2/66 ÷ 2 = 5/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 33 produces a repeating decimal (approximately 0.151515, or 15.1515%).
Working: 5 ÷ 33 = 0.151515 (15.1515%)

Key Values:
- Simplified Fraction: 5/33
- Mixed Number Form: 5/33
- Decimal Value: 0.151515
- Percentage: 15.1515%

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

Simplified Fraction

5/33

Mixed Number

Proper (5/33)

Decimal Value

0.151515

Percentage

15.1515%

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Step-by-Step Solution: 2/33 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 22 share a common factor (GCD = 11). Finding their Least Common Multiple gives an LCD of 66 (which is smaller than their product 33 × 22 = 726, keeping the calculation simpler).

LCD(33, 22) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 2/33 by 2, and multiply the numerator and denominator of 2/22 by 3 so both fractions share the common base 66.

2 × 2/33 × 2 = 4/66 and 2 × 3/22 × 3 = 6/66

Step 3

Add the Numerators

Now add the numerators (4 + 6 = 10) and keep the common denominator 66 unchanged.

4 + 6/66 = 10/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 66, which is 2. Divide both the numerator and denominator by 2.

10 ÷ 2/66 ÷ 2 = 5/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 33 produces a repeating decimal (approximately 0.151515, or 15.1515%).

5 ÷ 33 = 0.151515 (15.1515%)

Visual Representation

The diagram below illustrates 2/33 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/33`
Mixed Number Form	`5/33`
Decimal Form	`0.151515`
Percentage	`15.1515%`

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Frequently Asked Questions

What is 2/33 plus 2/22 as a fraction?

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

What is 2/33 plus 2/22 as a decimal?

2/33 + 2/22 converted to a decimal is 0.151515.

What is 2/33 plus 2/22 as a percentage?

2/33 + 2/22 expressed as a percentage is 15.1515%.

Does 2/33 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.151515...) because the denominator contains prime factors other than 2 and 5.