What is 6/21 plus 8/27? (Answer: 110/189)

Exact Answer

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Problem: What is 6/21 plus 8/27?
Formula / Expression: 6/21 + 8/27
Final Answer: 110/189
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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 6/21 by 9, and multiply the numerator and denominator of 8/27 by 7 so both fractions share the common base 189.
Working: 6 × 9/21 × 9 = 54/189 and 8 × 7/27 × 7 = 56/189

Step 3: Add the Numerators
Now add the numerators (54 + 56 = 110) and keep the common denominator 189 unchanged.
Working: 54 + 56/189 = 110/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 110 and 189 is 1, confirming that 110/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 110/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 110 by denominator 189 produces a repeating decimal (approximately 0.582011, or 58.2011%).
Working: 110 ÷ 189 = 0.582011 (58.2011%)

Key Values:
- Simplified Fraction: 110/189
- Mixed Number Form: 110/189
- Decimal Value: 0.582011
- Percentage: 58.2011%

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Solved with FractionsCalc:
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6/21 + 8/27 = 110/189

Simplified Fraction

110/189

Mixed Number

Proper (110/189)

Decimal Value

0.582011

Percentage

58.2011%

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Step-by-Step Solution: 6/21 + 8/27

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 6/21 by 9, and multiply the numerator and denominator of 8/27 by 7 so both fractions share the common base 189.

6 × 9/21 × 9 = 54/189 and 8 × 7/27 × 7 = 56/189

Step 3

Add the Numerators

Now add the numerators (54 + 56 = 110) and keep the common denominator 189 unchanged.

54 + 56/189 = 110/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 110 and 189 is 1, confirming that 110/189 cannot be reduced further—it is already in its simplest irreducible form.

110/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 110 by denominator 189 produces a repeating decimal (approximately 0.582011, or 58.2011%).

110 ÷ 189 = 0.582011 (58.2011%)

Visual Representation

The diagram below illustrates 6/21 plus 8/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`110/189`
Mixed Number Form	`110/189`
Decimal Form	`0.582011`
Percentage	`58.2011%`

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Frequently Asked Questions

What is 6/21 plus 8/27 as a fraction?

6/21 + 8/27 in simplest fraction form is 110/189.

What is 6/21 plus 8/27 as a decimal?

6/21 + 8/27 converted to a decimal is 0.582011.

What is 6/21 plus 8/27 as a percentage?

6/21 + 8/27 expressed as a percentage is 58.2011%.

Does 6/21 plus 8/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.582011...) because the denominator contains prime factors other than 2 and 5.