What is 2/8 plus 9/33? (Answer: 23/44)

Exact Answer

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Problem: What is 2/8 plus 9/33?
Formula / Expression: 2/8 + 9/33
Final Answer: 23/44
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/8 by 33, and multiply the numerator and denominator of 9/33 by 8 so both fractions share the common base 264.
Working: 2 × 33/8 × 33 = 66/264 and 9 × 8/33 × 8 = 72/264

Step 3: Add the Numerators
Now add the numerators (66 + 72 = 138) and keep the common denominator 264 unchanged.
Working: 66 + 72/264 = 138/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 138 and 264, which is 6. Divide both the numerator and denominator by 6.
Working: 138 ÷ 6/264 ÷ 6 = 23/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 44 produces a repeating decimal (approximately 0.522727, or 52.2727%).
Working: 23 ÷ 44 = 0.522727 (52.2727%)

Key Values:
- Simplified Fraction: 23/44
- Mixed Number Form: 23/44
- Decimal Value: 0.522727
- Percentage: 52.2727%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-9-33/
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2/8 + 9/33 = 23/44

Simplified Fraction

23/44

Mixed Number

Proper (23/44)

Decimal Value

0.522727

Percentage

52.2727%

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Step-by-Step Solution: 2/8 + 9/33

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 33) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/8 by 33, and multiply the numerator and denominator of 9/33 by 8 so both fractions share the common base 264.

2 × 33/8 × 33 = 66/264 and 9 × 8/33 × 8 = 72/264

Step 3

Add the Numerators

Now add the numerators (66 + 72 = 138) and keep the common denominator 264 unchanged.

66 + 72/264 = 138/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 138 and 264, which is 6. Divide both the numerator and denominator by 6.

138 ÷ 6/264 ÷ 6 = 23/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 44 produces a repeating decimal (approximately 0.522727, or 52.2727%).

23 ÷ 44 = 0.522727 (52.2727%)

Visual Representation

The diagram below illustrates 2/8 plus 9/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/44`
Mixed Number Form	`23/44`
Decimal Form	`0.522727`
Percentage	`52.2727%`

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Frequently Asked Questions

What is 2/8 plus 9/33 as a fraction?

2/8 + 9/33 in simplest fraction form is 23/44.

What is 2/8 plus 9/33 as a decimal?

2/8 + 9/33 converted to a decimal is 0.522727.

What is 2/8 plus 9/33 as a percentage?

2/8 + 9/33 expressed as a percentage is 52.2727%.

Does 2/8 plus 9/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.522727...) because the denominator contains prime factors other than 2 and 5.