What is 8/33 plus 2/8? (Answer: 65/132)

Exact Answer

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Problem: What is 8/33 plus 2/8?
Formula / Expression: 8/33 + 2/8
Final Answer: 65/132
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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 8/33 by 8, and multiply the numerator and denominator of 2/8 by 33 so both fractions share the common base 264.
Working: 8 × 8/33 × 8 = 64/264 and 2 × 33/8 × 33 = 66/264

Step 3: Add the Numerators
Now add the numerators (64 + 66 = 130) and keep the common denominator 264 unchanged.
Working: 64 + 66/264 = 130/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 130 and 264, which is 2. Divide both the numerator and denominator by 2.
Working: 130 ÷ 2/264 ÷ 2 = 65/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 132 produces a repeating decimal (approximately 0.492424, or 49.2424%).
Working: 65 ÷ 132 = 0.492424 (49.2424%)

Key Values:
- Simplified Fraction: 65/132
- Mixed Number Form: 65/132
- Decimal Value: 0.492424
- Percentage: 49.2424%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-33-plus-2-8/
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8/33 + 2/8 = 65/132

Simplified Fraction

65/132

Mixed Number

Proper (65/132)

Decimal Value

0.492424

Percentage

49.2424%

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

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

8 × 8/33 × 8 = 64/264 and 2 × 33/8 × 33 = 66/264

Step 3

Add the Numerators

Now add the numerators (64 + 66 = 130) and keep the common denominator 264 unchanged.

64 + 66/264 = 130/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 130 and 264, which is 2. Divide both the numerator and denominator by 2.

130 ÷ 2/264 ÷ 2 = 65/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 132 produces a repeating decimal (approximately 0.492424, or 49.2424%).

65 ÷ 132 = 0.492424 (49.2424%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/132`
Mixed Number Form	`65/132`
Decimal Form	`0.492424`
Percentage	`49.2424%`

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Frequently Asked Questions

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

8/33 + 2/8 in simplest fraction form is 65/132.

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

8/33 + 2/8 converted to a decimal is 0.492424.

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

8/33 + 2/8 expressed as a percentage is 49.2424%.

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

It results in a repeating decimal (approximately 0.492424...) because the denominator contains prime factors other than 2 and 5.