What is 2/33 plus 3/10? (Answer: 119/330)

Exact Answer

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Problem: What is 2/33 plus 3/10?
Formula / Expression: 2/33 + 3/10
Final Answer: 119/330
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 10 = 330.
Working: LCD(33, 10) = 330

Step 2: Convert to Equivalent Fractions with Common Denominator 330
Multiply the numerator and denominator of 2/33 by 10, and multiply the numerator and denominator of 3/10 by 33 so both fractions share the common base 330.
Working: 2 × 10/33 × 10 = 20/330 and 3 × 33/10 × 33 = 99/330

Step 3: Add the Numerators
Now add the numerators (20 + 99 = 119) and keep the common denominator 330 unchanged.
Working: 20 + 99/330 = 119/330

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 119 and 330 is 1, confirming that 119/330 cannot be reduced further—it is already in its simplest irreducible form.
Working: 119/330

Step 5: Decimal & Percentage Representation
Dividing the numerator 119 by denominator 330 produces a repeating decimal (approximately 0.360606, or 36.0606%).
Working: 119 ÷ 330 = 0.360606 (36.0606%)

Key Values:
- Simplified Fraction: 119/330
- Mixed Number Form: 119/330
- Decimal Value: 0.360606
- Percentage: 36.0606%

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2/33 + 3/10 = 119/330

Simplified Fraction

119/330

Mixed Number

Proper (119/330)

Decimal Value

0.360606

Percentage

36.0606%

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Step-by-Step Solution: 2/33 + 3/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 10 = 330.

LCD(33, 10) = 330

Step 2

Convert to Equivalent Fractions with Common Denominator 330

Multiply the numerator and denominator of 2/33 by 10, and multiply the numerator and denominator of 3/10 by 33 so both fractions share the common base 330.

2 × 10/33 × 10 = 20/330 and 3 × 33/10 × 33 = 99/330

Step 3

Add the Numerators

Now add the numerators (20 + 99 = 119) and keep the common denominator 330 unchanged.

20 + 99/330 = 119/330

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 119 and 330 is 1, confirming that 119/330 cannot be reduced further—it is already in its simplest irreducible form.

119/330

Step 5

Decimal & Percentage Representation

Dividing the numerator 119 by denominator 330 produces a repeating decimal (approximately 0.360606, or 36.0606%).

119 ÷ 330 = 0.360606 (36.0606%)

Visual Representation

The diagram below illustrates 2/33 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`119/330`
Mixed Number Form	`119/330`
Decimal Form	`0.360606`
Percentage	`36.0606%`

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Frequently Asked Questions

What is 2/33 plus 3/10 as a fraction?

2/33 + 3/10 in simplest fraction form is 119/330.

What is 2/33 plus 3/10 as a decimal?

2/33 + 3/10 converted to a decimal is 0.360606.

What is 2/33 plus 3/10 as a percentage?

2/33 + 3/10 expressed as a percentage is 36.0606%.

Does 2/33 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.360606...) because the denominator contains prime factors other than 2 and 5.