What is 3/33 plus 2/21? (Answer: 43/231)

Exact Answer

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Problem: What is 3/33 plus 2/21?
Formula / Expression: 3/33 + 2/21
Final Answer: 43/231
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 3/33 by 7, and multiply the numerator and denominator of 2/21 by 11 so both fractions share the common base 231.
Working: 3 × 7/33 × 7 = 21/231 and 2 × 11/21 × 11 = 22/231

Step 3: Add the Numerators
Now add the numerators (21 + 22 = 43) and keep the common denominator 231 unchanged.
Working: 21 + 22/231 = 43/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 231 is 1, confirming that 43/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 231 produces a repeating decimal (approximately 0.186147, or 18.6147%).
Working: 43 ÷ 231 = 0.186147 (18.6147%)

Key Values:
- Simplified Fraction: 43/231
- Mixed Number Form: 43/231
- Decimal Value: 0.186147
- Percentage: 18.6147%

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3/33 + 2/21 = 43/231

Simplified Fraction

43/231

Mixed Number

Proper (43/231)

Decimal Value

0.186147

Percentage

18.6147%

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Step-by-Step Solution: 3/33 + 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 3/33 by 7, and multiply the numerator and denominator of 2/21 by 11 so both fractions share the common base 231.

3 × 7/33 × 7 = 21/231 and 2 × 11/21 × 11 = 22/231

Step 3

Add the Numerators

Now add the numerators (21 + 22 = 43) and keep the common denominator 231 unchanged.

21 + 22/231 = 43/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 231 is 1, confirming that 43/231 cannot be reduced further—it is already in its simplest irreducible form.

43/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 231 produces a repeating decimal (approximately 0.186147, or 18.6147%).

43 ÷ 231 = 0.186147 (18.6147%)

Visual Representation

The diagram below illustrates 3/33 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/231`
Mixed Number Form	`43/231`
Decimal Form	`0.186147`
Percentage	`18.6147%`

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Frequently Asked Questions

What is 3/33 plus 2/21 as a fraction?

3/33 + 2/21 in simplest fraction form is 43/231.

What is 3/33 plus 2/21 as a decimal?

3/33 + 2/21 converted to a decimal is 0.186147.

What is 3/33 plus 2/21 as a percentage?

3/33 + 2/21 expressed as a percentage is 18.6147%.

Does 3/33 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.186147...) because the denominator contains prime factors other than 2 and 5.