What is 5/33 plus 2/3? (Answer: 9/11)

Exact Answer

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Problem: What is 5/33 plus 2/3?
Formula / Expression: 5/33 + 2/3
Final Answer: 9/11
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.
Working: LCD(33, 3) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 5/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.
Working: 5 × 1/33 × 1 = 5/33 and 2 × 11/3 × 11 = 22/33

Step 3: Add the Numerators
Now add the numerators (5 + 22 = 27) and keep the common denominator 33 unchanged.
Working: 5 + 22/33 = 27/33

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 33, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/33 ÷ 3 = 9/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 11 produces a repeating decimal (approximately 0.818182, or 81.8182%).
Working: 9 ÷ 11 = 0.818182 (81.8182%)

Key Values:
- Simplified Fraction: 9/11
- Mixed Number Form: 9/11
- Decimal Value: 0.818182
- Percentage: 81.8182%

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Solved with FractionsCalc:
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5/33 + 2/3 = 9/11

Simplified Fraction

9/11

Mixed Number

Proper (9/11)

Decimal Value

0.818182

Percentage

81.8182%

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Step-by-Step Solution: 5/33 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 33 is an exact multiple of 3 (3 × 11 = 33). The Least Common Denominator (LCD) is simply 33, meaning we only need to scale one fraction.

LCD(33, 3) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 5/33 by 1, and multiply the numerator and denominator of 2/3 by 11 so both fractions share the common base 33.

5 × 1/33 × 1 = 5/33 and 2 × 11/3 × 11 = 22/33

Step 3

Add the Numerators

Now add the numerators (5 + 22 = 27) and keep the common denominator 33 unchanged.

5 + 22/33 = 27/33

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 33, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/33 ÷ 3 = 9/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 11 produces a repeating decimal (approximately 0.818182, or 81.8182%).

9 ÷ 11 = 0.818182 (81.8182%)

Visual Representation

The diagram below illustrates 5/33 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/11`
Mixed Number Form	`9/11`
Decimal Form	`0.818182`
Percentage	`81.8182%`

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Frequently Asked Questions

What is 5/33 plus 2/3 as a fraction?

5/33 + 2/3 in simplest fraction form is 9/11.

What is 5/33 plus 2/3 as a decimal?

5/33 + 2/3 converted to a decimal is 0.818182.

What is 5/33 plus 2/3 as a percentage?

5/33 + 2/3 expressed as a percentage is 81.8182%.

Does 5/33 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.818182...) because the denominator contains prime factors other than 2 and 5.