What is 12/27 plus 11/21? (Answer: 61/63)

Exact Answer

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Problem: What is 12/27 plus 11/21?
Formula / Expression: 12/27 + 11/21
Final Answer: 61/63
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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 11/21 by 9 so both fractions share the common base 189.
Working: 12 × 7/27 × 7 = 84/189 and 11 × 9/21 × 9 = 99/189

Step 3: Add the Numerators
Now add the numerators (84 + 99 = 183) and keep the common denominator 189 unchanged.
Working: 84 + 99/189 = 183/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 183 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 183 ÷ 3/189 ÷ 3 = 61/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 63 produces a repeating decimal (approximately 0.968254, or 96.8254%).
Working: 61 ÷ 63 = 0.968254 (96.8254%)

Key Values:
- Simplified Fraction: 61/63
- Mixed Number Form: 61/63
- Decimal Value: 0.968254
- Percentage: 96.8254%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-27-plus-11-21/
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12/27 + 11/21 = 61/63

Simplified Fraction

61/63

Mixed Number

Proper (61/63)

Decimal Value

0.968254

Percentage

96.8254%

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Step-by-Step Solution: 12/27 + 11/21

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 11/21 by 9 so both fractions share the common base 189.

12 × 7/27 × 7 = 84/189 and 11 × 9/21 × 9 = 99/189

Step 3

Add the Numerators

Now add the numerators (84 + 99 = 183) and keep the common denominator 189 unchanged.

84 + 99/189 = 183/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 183 and 189, which is 3. Divide both the numerator and denominator by 3.

183 ÷ 3/189 ÷ 3 = 61/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 63 produces a repeating decimal (approximately 0.968254, or 96.8254%).

61 ÷ 63 = 0.968254 (96.8254%)

Visual Representation

The diagram below illustrates 12/27 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/63`
Mixed Number Form	`61/63`
Decimal Form	`0.968254`
Percentage	`96.8254%`

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Frequently Asked Questions

What is 12/27 plus 11/21 as a fraction?

12/27 + 11/21 in simplest fraction form is 61/63.

What is 12/27 plus 11/21 as a decimal?

12/27 + 11/21 converted to a decimal is 0.968254.

What is 12/27 plus 11/21 as a percentage?

12/27 + 11/21 expressed as a percentage is 96.8254%.

Does 12/27 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.968254...) because the denominator contains prime factors other than 2 and 5.