What is 13/27 plus 12/21? (Answer: 199/189)

Exact Answer

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Problem: What is 13/27 plus 12/21?
Formula / Expression: 13/27 + 12/21
Final Answer: 1 10/189 (199/189)
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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 13/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.
Working: 13 × 7/27 × 7 = 91/189 and 12 × 9/21 × 9 = 108/189

Step 3: Add the Numerators
Now add the numerators (91 + 108 = 199) and keep the common denominator 189 unchanged.
Working: 91 + 108/189 = 199/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 199 and 189 is 1, confirming that 199/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 199/189

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (199) is greater than the denominator (189), divide 199 by 189: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/189.
Working: 199/189 = 1 10/189

Step 6: Decimal & Percentage Representation
Dividing the numerator 199 by denominator 189 produces a repeating decimal (approximately 1.05291, or 105.291%).
Working: 199 ÷ 189 = 1.05291 (105.291%)

Key Values:
- Simplified Fraction: 199/189
- Mixed Number Form: 1 10/189
- Decimal Value: 1.05291
- Percentage: 105.291%

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13/27 + 12/21 = 199/189

Simplified Fraction

199/189

Mixed Number

1 10/189

Decimal Value

1.05291

Percentage

105.291%

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Step-by-Step Solution: 13/27 + 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 13/27 by 7, and multiply the numerator and denominator of 12/21 by 9 so both fractions share the common base 189.

13 × 7/27 × 7 = 91/189 and 12 × 9/21 × 9 = 108/189

Step 3

Add the Numerators

Now add the numerators (91 + 108 = 199) and keep the common denominator 189 unchanged.

91 + 108/189 = 199/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 199 and 189 is 1, confirming that 199/189 cannot be reduced further—it is already in its simplest irreducible form.

199/189

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (199) is greater than the denominator (189), divide 199 by 189: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/189.

199/189 = 110/189

Step 6

Decimal & Percentage Representation

Dividing the numerator 199 by denominator 189 produces a repeating decimal (approximately 1.05291, or 105.291%).

199 ÷ 189 = 1.05291 (105.291%)

Visual Representation

The diagram below illustrates 13/27 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`199/189`
Mixed Number Form	`1 10/189`
Decimal Form	`1.05291`
Percentage	`105.291%`

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Frequently Asked Questions

What is 13/27 plus 12/21 as a fraction?

13/27 + 12/21 in simplest fraction form is 199/189 (or 1 10/189 as a mixed number).

What is 13/27 plus 12/21 as a decimal?

13/27 + 12/21 converted to a decimal is 1.05291.

What is 13/27 plus 12/21 as a percentage?

13/27 + 12/21 expressed as a percentage is 105.291%.

How do you write 13/27 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 199/189 can be written as the mixed number 1 10/189.

Does 13/27 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.05291...) because the denominator contains prime factors other than 2 and 5.