What is 3/21 plus 5/33? (Answer: 68/231)

Exact Answer

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Problem: What is 3/21 plus 5/33?
Formula / Expression: 3/21 + 5/33
Final Answer: 68/231
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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 3/21 by 11, and multiply the numerator and denominator of 5/33 by 7 so both fractions share the common base 231.
Working: 3 × 11/21 × 11 = 33/231 and 5 × 7/33 × 7 = 35/231

Step 3: Add the Numerators
Now add the numerators (33 + 35 = 68) and keep the common denominator 231 unchanged.
Working: 33 + 35/231 = 68/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 68 and 231 is 1, confirming that 68/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 68/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 231 produces a repeating decimal (approximately 0.294372, or 29.4372%).
Working: 68 ÷ 231 = 0.294372 (29.4372%)

Key Values:
- Simplified Fraction: 68/231
- Mixed Number Form: 68/231
- Decimal Value: 0.294372
- Percentage: 29.4372%

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Solved with FractionsCalc:
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3/21 + 5/33 = 68/231

Simplified Fraction

68/231

Mixed Number

Proper (68/231)

Decimal Value

0.294372

Percentage

29.4372%

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Step-by-Step Solution: 3/21 + 5/33

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 3/21 by 11, and multiply the numerator and denominator of 5/33 by 7 so both fractions share the common base 231.

3 × 11/21 × 11 = 33/231 and 5 × 7/33 × 7 = 35/231

Step 3

Add the Numerators

Now add the numerators (33 + 35 = 68) and keep the common denominator 231 unchanged.

33 + 35/231 = 68/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 68 and 231 is 1, confirming that 68/231 cannot be reduced further—it is already in its simplest irreducible form.

68/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 231 produces a repeating decimal (approximately 0.294372, or 29.4372%).

68 ÷ 231 = 0.294372 (29.4372%)

Visual Representation

The diagram below illustrates 3/21 plus 5/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/231`
Mixed Number Form	`68/231`
Decimal Form	`0.294372`
Percentage	`29.4372%`

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Frequently Asked Questions

What is 3/21 plus 5/33 as a fraction?

3/21 + 5/33 in simplest fraction form is 68/231.

What is 3/21 plus 5/33 as a decimal?

3/21 + 5/33 converted to a decimal is 0.294372.

What is 3/21 plus 5/33 as a percentage?

3/21 + 5/33 expressed as a percentage is 29.4372%.

Does 3/21 plus 5/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.294372...) because the denominator contains prime factors other than 2 and 5.