What is 14/27 plus 12/21? (Answer: 206/189)

Exact Answer

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Problem: What is 14/27 plus 12/21?
Formula / Expression: 14/27 + 12/21
Final Answer: 1 17/189 (206/189)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 14/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.
Working: 14 × 7/27 × 7 = 98/189 and 12 × 9/21 × 9 = 108/189

Step 3: Add the Numerators
Now add the numerators (98 + 108 = 206) and keep the common denominator 189 unchanged.
Working: 98 + 108/189 = 206/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 206 and 189 is 1, confirming that 206/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 206/189

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (206) is greater than the denominator (189), divide 206 by 189: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/189.
Working: 206/189 = 1 17/189

Step 6: Decimal & Percentage Representation
Dividing the numerator 206 by denominator 189 produces a repeating decimal (approximately 1.089947, or 108.9947%).
Working: 206 ÷ 189 = 1.089947 (108.9947%)

Key Values:
- Simplified Fraction: 206/189
- Mixed Number Form: 1 17/189
- Decimal Value: 1.089947
- Percentage: 108.9947%

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Solved with FractionsCalc:
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14/27 + 12/21 = 206/189

Simplified Fraction

206/189

Mixed Number

1 17/189

Decimal Value

1.089947

Percentage

108.9947%

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Step-by-Step Solution: 14/27 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 14/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.

14 × 7/27 × 7 = 98/189 and 12 × 9/21 × 9 = 108/189

Step 3

Add the Numerators

Now add the numerators (98 + 108 = 206) and keep the common denominator 189 unchanged.

98 + 108/189 = 206/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 206 and 189 is 1, confirming that 206/189 cannot be reduced further—it is already in its simplest irreducible form.

206/189

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (206) is greater than the denominator (189), divide 206 by 189: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/189.

206/189 = 117/189

Step 6

Decimal & Percentage Representation

Dividing the numerator 206 by denominator 189 produces a repeating decimal (approximately 1.089947, or 108.9947%).

206 ÷ 189 = 1.089947 (108.9947%)

Visual Representation

The diagram below illustrates 14/27 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`206/189`
Mixed Number Form	`1 17/189`
Decimal Form	`1.089947`
Percentage	`108.9947%`

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Frequently Asked Questions

What is 14/27 plus 12/21 as a fraction?

14/27 + 12/21 in simplest fraction form is 206/189 (or 1 17/189 as a mixed number).

What is 14/27 plus 12/21 as a decimal?

14/27 + 12/21 converted to a decimal is 1.089947.

What is 14/27 plus 12/21 as a percentage?

14/27 + 12/21 expressed as a percentage is 108.9947%.

How do you write 14/27 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 206/189 can be written as the mixed number 1 17/189.

Does 14/27 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.089947...) because the denominator contains prime factors other than 2 and 5.