What is 14/33 plus 12/21? (Answer: 230/231)

Exact Answer

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Problem: What is 14/33 plus 12/21?
Formula / Expression: 14/33 + 12/21
Final Answer: 230/231
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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 14/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.
Working: 14 × 7/33 × 7 = 98/231 and 12 × 11/21 × 11 = 132/231

Step 3: Add the Numerators
Now add the numerators (98 + 132 = 230) and keep the common denominator 231 unchanged.
Working: 98 + 132/231 = 230/231

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 230 and 231 is 1, confirming that 230/231 cannot be reduced further—it is already in its simplest irreducible form.
Working: 230/231

Step 5: Decimal & Percentage Representation
Dividing the numerator 230 by denominator 231 produces a repeating decimal (approximately 0.995671, or 99.5671%).
Working: 230 ÷ 231 = 0.995671 (99.5671%)

Key Values:
- Simplified Fraction: 230/231
- Mixed Number Form: 230/231
- Decimal Value: 0.995671
- Percentage: 99.5671%

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Solved with FractionsCalc:
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14/33 + 12/21 = 230/231

Simplified Fraction

230/231

Mixed Number

Proper (230/231)

Decimal Value

0.995671

Percentage

99.5671%

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Step-by-Step Solution: 14/33 + 12/21

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 14/33 by 7, and multiply the numerator and denominator of 12/21 by 11 so both fractions share the common base 231.

14 × 7/33 × 7 = 98/231 and 12 × 11/21 × 11 = 132/231

Step 3

Add the Numerators

Now add the numerators (98 + 132 = 230) and keep the common denominator 231 unchanged.

98 + 132/231 = 230/231

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 230 and 231 is 1, confirming that 230/231 cannot be reduced further—it is already in its simplest irreducible form.

230/231

Step 5

Decimal & Percentage Representation

Dividing the numerator 230 by denominator 231 produces a repeating decimal (approximately 0.995671, or 99.5671%).

230 ÷ 231 = 0.995671 (99.5671%)

Visual Representation

The diagram below illustrates 14/33 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`230/231`
Mixed Number Form	`230/231`
Decimal Form	`0.995671`
Percentage	`99.5671%`

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Frequently Asked Questions

What is 14/33 plus 12/21 as a fraction?

14/33 + 12/21 in simplest fraction form is 230/231.

What is 14/33 plus 12/21 as a decimal?

14/33 + 12/21 converted to a decimal is 0.995671.

What is 14/33 plus 12/21 as a percentage?

14/33 + 12/21 expressed as a percentage is 99.5671%.

Does 14/33 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.995671...) because the denominator contains prime factors other than 2 and 5.