What is 3/33 plus 2/4? (Answer: 13/22)

Exact Answer

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Problem: What is 3/33 plus 2/4?
Formula / Expression: 3/33 + 2/4
Final Answer: 13/22
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.
Working: LCD(33, 4) = 132

Step 2: Convert to Equivalent Fractions with Common Denominator 132
Multiply the numerator and denominator of 3/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.
Working: 3 × 4/33 × 4 = 12/132 and 2 × 33/4 × 33 = 66/132

Step 3: Add the Numerators
Now add the numerators (12 + 66 = 78) and keep the common denominator 132 unchanged.
Working: 12 + 66/132 = 78/132

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 132, which is 6. Divide both the numerator and denominator by 6.
Working: 78 ÷ 6/132 ÷ 6 = 13/22

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 22 produces a repeating decimal (approximately 0.590909, or 59.0909%).
Working: 13 ÷ 22 = 0.590909 (59.0909%)

Key Values:
- Simplified Fraction: 13/22
- Mixed Number Form: 13/22
- Decimal Value: 0.590909
- Percentage: 59.0909%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-33-plus-2-4/
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3/33 + 2/4 = 13/22

Simplified Fraction

13/22

Mixed Number

Proper (13/22)

Decimal Value

0.590909

Percentage

59.0909%

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Step-by-Step Solution: 3/33 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 4 = 132.

LCD(33, 4) = 132

Step 2

Convert to Equivalent Fractions with Common Denominator 132

Multiply the numerator and denominator of 3/33 by 4, and multiply the numerator and denominator of 2/4 by 33 so both fractions share the common base 132.

3 × 4/33 × 4 = 12/132 and 2 × 33/4 × 33 = 66/132

Step 3

Add the Numerators

Now add the numerators (12 + 66 = 78) and keep the common denominator 132 unchanged.

12 + 66/132 = 78/132

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 132, which is 6. Divide both the numerator and denominator by 6.

78 ÷ 6/132 ÷ 6 = 13/22

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 22 produces a repeating decimal (approximately 0.590909, or 59.0909%).

13 ÷ 22 = 0.590909 (59.0909%)

Visual Representation

The diagram below illustrates 3/33 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/22`
Mixed Number Form	`13/22`
Decimal Form	`0.590909`
Percentage	`59.0909%`

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Frequently Asked Questions

What is 3/33 plus 2/4 as a fraction?

3/33 + 2/4 in simplest fraction form is 13/22.

What is 3/33 plus 2/4 as a decimal?

3/33 + 2/4 converted to a decimal is 0.590909.

What is 3/33 plus 2/4 as a percentage?

3/33 + 2/4 expressed as a percentage is 59.0909%.

Does 3/33 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.590909...) because the denominator contains prime factors other than 2 and 5.