What is 5/33 plus 6/21? (Answer: 101/231)

Exact Answer

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Problem: What is 5/33 plus 6/21?
Formula / Expression: 5/33 + 6/21
Final Answer: 101/231
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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 5/33 by 7, and multiply the numerator and denominator of 6/21 by 11 so both fractions share the common base 231.
Working: 5 × 7/33 × 7 = 35/231 and 6 × 11/21 × 11 = 66/231

Step 3: Add the Numerators
Now add the numerators (35 + 66 = 101) and keep the common denominator 231 unchanged.
Working: 35 + 66/231 = 101/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 231 is 1, confirming that 101/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 231 produces a repeating decimal (approximately 0.437229, or 43.7229%).
Working: 101 ÷ 231 = 0.437229 (43.7229%)

Key Values:
- Simplified Fraction: 101/231
- Mixed Number Form: 101/231
- Decimal Value: 0.437229
- Percentage: 43.7229%

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Solved with FractionsCalc:
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5/33 + 6/21 = 101/231

Simplified Fraction

101/231

Mixed Number

Proper (101/231)

Decimal Value

0.437229

Percentage

43.7229%

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Step-by-Step Solution: 5/33 + 6/21

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 5/33 by 7, and multiply the numerator and denominator of 6/21 by 11 so both fractions share the common base 231.

5 × 7/33 × 7 = 35/231 and 6 × 11/21 × 11 = 66/231

Step 3

Add the Numerators

Now add the numerators (35 + 66 = 101) and keep the common denominator 231 unchanged.

35 + 66/231 = 101/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 231 is 1, confirming that 101/231 cannot be reduced further—it is already in its simplest irreducible form.

101/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 231 produces a repeating decimal (approximately 0.437229, or 43.7229%).

101 ÷ 231 = 0.437229 (43.7229%)

Visual Representation

The diagram below illustrates 5/33 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/231`
Mixed Number Form	`101/231`
Decimal Form	`0.437229`
Percentage	`43.7229%`

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Frequently Asked Questions

What is 5/33 plus 6/21 as a fraction?

5/33 + 6/21 in simplest fraction form is 101/231.

What is 5/33 plus 6/21 as a decimal?

5/33 + 6/21 converted to a decimal is 0.437229.

What is 5/33 plus 6/21 as a percentage?

5/33 + 6/21 expressed as a percentage is 43.7229%.

Does 5/33 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.437229...) because the denominator contains prime factors other than 2 and 5.