What is 2/21 plus 4/33? (Answer: 50/231)

Exact Answer

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Problem: What is 2/21 plus 4/33?
Formula / Expression: 2/21 + 4/33
Final Answer: 50/231
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 2/21 by 11, and multiply the numerator and denominator of 4/33 by 7 so both fractions share the common base 231.
Working: 2 × 11/21 × 11 = 22/231 and 4 × 7/33 × 7 = 28/231

Step 3: Add the Numerators
Now add the numerators (22 + 28 = 50) and keep the common denominator 231 unchanged.
Working: 22 + 28/231 = 50/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 50 and 231 is 1, confirming that 50/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 50/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 231 produces a repeating decimal (approximately 0.21645, or 21.645%).
Working: 50 ÷ 231 = 0.21645 (21.645%)

Key Values:
- Simplified Fraction: 50/231
- Mixed Number Form: 50/231
- Decimal Value: 0.21645
- Percentage: 21.645%

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Solved with FractionsCalc:
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2/21 + 4/33 = 50/231

Simplified Fraction

50/231

Mixed Number

Proper (50/231)

Decimal Value

0.21645

Percentage

21.645%

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Step-by-Step Solution: 2/21 + 4/33

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 2/21 by 11, and multiply the numerator and denominator of 4/33 by 7 so both fractions share the common base 231.

2 × 11/21 × 11 = 22/231 and 4 × 7/33 × 7 = 28/231

Step 3

Add the Numerators

Now add the numerators (22 + 28 = 50) and keep the common denominator 231 unchanged.

22 + 28/231 = 50/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 50 and 231 is 1, confirming that 50/231 cannot be reduced further—it is already in its simplest irreducible form.

50/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 231 produces a repeating decimal (approximately 0.21645, or 21.645%).

50 ÷ 231 = 0.21645 (21.645%)

Visual Representation

The diagram below illustrates 2/21 plus 4/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/231`
Mixed Number Form	`50/231`
Decimal Form	`0.21645`
Percentage	`21.645%`

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Frequently Asked Questions

What is 2/21 plus 4/33 as a fraction?

2/21 + 4/33 in simplest fraction form is 50/231.

What is 2/21 plus 4/33 as a decimal?

2/21 + 4/33 converted to a decimal is 0.21645.

What is 2/21 plus 4/33 as a percentage?

2/21 + 4/33 expressed as a percentage is 21.645%.

Does 2/21 plus 4/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.21645...) because the denominator contains prime factors other than 2 and 5.