What is 2/33 plus 4/8? (Answer: 37/66)

Exact Answer

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Problem: What is 2/33 plus 4/8?
Formula / Expression: 2/33 + 4/8
Final Answer: 37/66
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.
Working: LCD(33, 8) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 4/8 by 33 so both fractions share the common base 264.
Working: 2 × 8/33 × 8 = 16/264 and 4 × 33/8 × 33 = 132/264

Step 3: Add the Numerators
Now add the numerators (16 + 132 = 148) and keep the common denominator 264 unchanged.
Working: 16 + 132/264 = 148/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 148 and 264, which is 4. Divide both the numerator and denominator by 4.
Working: 148 ÷ 4/264 ÷ 4 = 37/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 66 produces a repeating decimal (approximately 0.560606, or 56.0606%).
Working: 37 ÷ 66 = 0.560606 (56.0606%)

Key Values:
- Simplified Fraction: 37/66
- Mixed Number Form: 37/66
- Decimal Value: 0.560606
- Percentage: 56.0606%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-4-8/
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2/33 + 4/8 = 37/66

Simplified Fraction

37/66

Mixed Number

Proper (37/66)

Decimal Value

0.560606

Percentage

56.0606%

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Step-by-Step Solution: 2/33 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 8 = 264.

LCD(33, 8) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 4/8 by 33 so both fractions share the common base 264.

2 × 8/33 × 8 = 16/264 and 4 × 33/8 × 33 = 132/264

Step 3

Add the Numerators

Now add the numerators (16 + 132 = 148) and keep the common denominator 264 unchanged.

16 + 132/264 = 148/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 148 and 264, which is 4. Divide both the numerator and denominator by 4.

148 ÷ 4/264 ÷ 4 = 37/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 66 produces a repeating decimal (approximately 0.560606, or 56.0606%).

37 ÷ 66 = 0.560606 (56.0606%)

Visual Representation

The diagram below illustrates 2/33 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/66`
Mixed Number Form	`37/66`
Decimal Form	`0.560606`
Percentage	`56.0606%`

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Frequently Asked Questions

What is 2/33 plus 4/8 as a fraction?

2/33 + 4/8 in simplest fraction form is 37/66.

What is 2/33 plus 4/8 as a decimal?

2/33 + 4/8 converted to a decimal is 0.560606.

What is 2/33 plus 4/8 as a percentage?

2/33 + 4/8 expressed as a percentage is 56.0606%.

Does 2/33 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.560606...) because the denominator contains prime factors other than 2 and 5.