What is 12/27 plus 15/21? (Answer: 73/63)

Exact Answer

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Problem: What is 12/27 plus 15/21?
Formula / Expression: 12/27 + 15/21
Final Answer: 1 10/63 (73/63)
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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 12/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
Working: 12 × 7/27 × 7 = 84/189 and 15 × 9/21 × 9 = 135/189

Step 3: Add the Numerators
Now add the numerators (84 + 135 = 219) and keep the common denominator 189 unchanged.
Working: 84 + 135/189 = 219/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 219 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 219 ÷ 3/189 ÷ 3 = 73/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (73) is greater than the denominator (63), divide 73 by 63: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/63.
Working: 73/63 = 1 10/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 63 produces a repeating decimal (approximately 1.15873, or 115.873%).
Working: 73 ÷ 63 = 1.15873 (115.873%)

Key Values:
- Simplified Fraction: 73/63
- Mixed Number Form: 1 10/63
- Decimal Value: 1.15873
- Percentage: 115.873%

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12/27 + 15/21 = 73/63

Simplified Fraction

73/63

Mixed Number

1 10/63

Decimal Value

1.15873

Percentage

115.873%

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Step-by-Step Solution: 12/27 + 15/21

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 12/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.

12 × 7/27 × 7 = 84/189 and 15 × 9/21 × 9 = 135/189

Step 3

Add the Numerators

Now add the numerators (84 + 135 = 219) and keep the common denominator 189 unchanged.

84 + 135/189 = 219/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 219 and 189, which is 3. Divide both the numerator and denominator by 3.

219 ÷ 3/189 ÷ 3 = 73/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (73) is greater than the denominator (63), divide 73 by 63: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/63.

73/63 = 110/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 63 produces a repeating decimal (approximately 1.15873, or 115.873%).

73 ÷ 63 = 1.15873 (115.873%)

Visual Representation

The diagram below illustrates 12/27 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/63`
Mixed Number Form	`1 10/63`
Decimal Form	`1.15873`
Percentage	`115.873%`

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Frequently Asked Questions

What is 12/27 plus 15/21 as a fraction?

12/27 + 15/21 in simplest fraction form is 73/63 (or 1 10/63 as a mixed number).

What is 12/27 plus 15/21 as a decimal?

12/27 + 15/21 converted to a decimal is 1.15873.

What is 12/27 plus 15/21 as a percentage?

12/27 + 15/21 expressed as a percentage is 115.873%.

How do you write 12/27 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 73/63 can be written as the mixed number 1 10/63.

Does 12/27 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.15873...) because the denominator contains prime factors other than 2 and 5.