What is 12/27 plus 12/21? (Answer: 64/63)

Exact Answer

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Problem: What is 12/27 plus 12/21?
Formula / Expression: 12/27 + 12/21
Final Answer: 1 1/63 (64/63)
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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 12/21 by 9 so both fractions share the common base 189.
Working: 12 × 7/27 × 7 = 84/189 and 12 × 9/21 × 9 = 108/189

Step 3: Add the Numerators
Now add the numerators (84 + 108 = 192) and keep the common denominator 189 unchanged.
Working: 84 + 108/189 = 192/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 192 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 192 ÷ 3/189 ÷ 3 = 64/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (64) is greater than the denominator (63), divide 64 by 63: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/63.
Working: 64/63 = 1 1/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 63 produces a repeating decimal (approximately 1.015873, or 101.5873%).
Working: 64 ÷ 63 = 1.015873 (101.5873%)

Key Values:
- Simplified Fraction: 64/63
- Mixed Number Form: 1 1/63
- Decimal Value: 1.015873
- Percentage: 101.5873%

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Solved with FractionsCalc:
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12/27 + 12/21 = 64/63

Simplified Fraction

64/63

Mixed Number

1 1/63

Decimal Value

1.015873

Percentage

101.5873%

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

12 × 7/27 × 7 = 84/189 and 12 × 9/21 × 9 = 108/189

Step 3

Add the Numerators

Now add the numerators (84 + 108 = 192) and keep the common denominator 189 unchanged.

84 + 108/189 = 192/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 192 and 189, which is 3. Divide both the numerator and denominator by 3.

192 ÷ 3/189 ÷ 3 = 64/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (64) is greater than the denominator (63), divide 64 by 63: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/63.

64/63 = 11/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 63 produces a repeating decimal (approximately 1.015873, or 101.5873%).

64 ÷ 63 = 1.015873 (101.5873%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/63`
Mixed Number Form	`1 1/63`
Decimal Form	`1.015873`
Percentage	`101.5873%`

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Frequently Asked Questions

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

12/27 + 12/21 in simplest fraction form is 64/63 (or 1 1/63 as a mixed number).

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

12/27 + 12/21 converted to a decimal is 1.015873.

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

12/27 + 12/21 expressed as a percentage is 101.5873%.

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

Because the numerator is greater than the denominator, the improper fraction 64/63 can be written as the mixed number 1 1/63.

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

It results in a repeating decimal (approximately 1.015873...) because the denominator contains prime factors other than 2 and 5.