What is 9/21 plus 12/27? (Answer: 55/63)

Exact Answer

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Problem: What is 9/21 plus 12/27?
Formula / Expression: 9/21 + 12/27
Final Answer: 55/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 9/21 by 9, and multiply the numerator and denominator of 12/27 by 7 so both fractions share the common base 189.
Working: 9 × 9/21 × 9 = 81/189 and 12 × 7/27 × 7 = 84/189

Step 3: Add the Numerators
Now add the numerators (81 + 84 = 165) and keep the common denominator 189 unchanged.
Working: 81 + 84/189 = 165/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 165 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 165 ÷ 3/189 ÷ 3 = 55/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 63 produces a repeating decimal (approximately 0.873016, or 87.3016%).
Working: 55 ÷ 63 = 0.873016 (87.3016%)

Key Values:
- Simplified Fraction: 55/63
- Mixed Number Form: 55/63
- Decimal Value: 0.873016
- Percentage: 87.3016%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-12-27/
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9/21 + 12/27 = 55/63

Simplified Fraction

55/63

Mixed Number

Proper (55/63)

Decimal Value

0.873016

Percentage

87.3016%

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Step-by-Step Solution: 9/21 + 12/27

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

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

9 × 9/21 × 9 = 81/189 and 12 × 7/27 × 7 = 84/189

Step 3

Add the Numerators

Now add the numerators (81 + 84 = 165) and keep the common denominator 189 unchanged.

81 + 84/189 = 165/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 165 and 189, which is 3. Divide both the numerator and denominator by 3.

165 ÷ 3/189 ÷ 3 = 55/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 63 produces a repeating decimal (approximately 0.873016, or 87.3016%).

55 ÷ 63 = 0.873016 (87.3016%)

Visual Representation

The diagram below illustrates 9/21 plus 12/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/63`
Mixed Number Form	`55/63`
Decimal Form	`0.873016`
Percentage	`87.3016%`

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Frequently Asked Questions

What is 9/21 plus 12/27 as a fraction?

9/21 + 12/27 in simplest fraction form is 55/63.

What is 9/21 plus 12/27 as a decimal?

9/21 + 12/27 converted to a decimal is 0.873016.

What is 9/21 plus 12/27 as a percentage?

9/21 + 12/27 expressed as a percentage is 87.3016%.

Does 9/21 plus 12/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.873016...) because the denominator contains prime factors other than 2 and 5.