What is 4/33 plus 5/21? (Answer: 83/231)

Exact Answer

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Problem: What is 4/33 plus 5/21?
Formula / Expression: 4/33 + 5/21
Final Answer: 83/231
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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 4/33 by 7, and multiply the numerator and denominator of 5/21 by 11 so both fractions share the common base 231.
Working: 4 × 7/33 × 7 = 28/231 and 5 × 11/21 × 11 = 55/231

Step 3: Add the Numerators
Now add the numerators (28 + 55 = 83) and keep the common denominator 231 unchanged.
Working: 28 + 55/231 = 83/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 83 and 231 is 1, confirming that 83/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 83/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 231 produces a repeating decimal (approximately 0.359307, or 35.9307%).
Working: 83 ÷ 231 = 0.359307 (35.9307%)

Key Values:
- Simplified Fraction: 83/231
- Mixed Number Form: 83/231
- Decimal Value: 0.359307
- Percentage: 35.9307%

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Solved with FractionsCalc:
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4/33 + 5/21 = 83/231

Simplified Fraction

83/231

Mixed Number

Proper (83/231)

Decimal Value

0.359307

Percentage

35.9307%

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Step-by-Step Solution: 4/33 + 5/21

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 4/33 by 7, and multiply the numerator and denominator of 5/21 by 11 so both fractions share the common base 231.

4 × 7/33 × 7 = 28/231 and 5 × 11/21 × 11 = 55/231

Step 3

Add the Numerators

Now add the numerators (28 + 55 = 83) and keep the common denominator 231 unchanged.

28 + 55/231 = 83/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 83 and 231 is 1, confirming that 83/231 cannot be reduced further—it is already in its simplest irreducible form.

83/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 231 produces a repeating decimal (approximately 0.359307, or 35.9307%).

83 ÷ 231 = 0.359307 (35.9307%)

Visual Representation

The diagram below illustrates 4/33 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/231`
Mixed Number Form	`83/231`
Decimal Form	`0.359307`
Percentage	`35.9307%`

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Frequently Asked Questions

What is 4/33 plus 5/21 as a fraction?

4/33 + 5/21 in simplest fraction form is 83/231.

What is 4/33 plus 5/21 as a decimal?

4/33 + 5/21 converted to a decimal is 0.359307.

What is 4/33 plus 5/21 as a percentage?

4/33 + 5/21 expressed as a percentage is 35.9307%.

Does 4/33 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.359307...) because the denominator contains prime factors other than 2 and 5.