What is 1/27 plus 11/21? (Answer: 106/189)

Exact Answer

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Problem: What is 1/27 plus 11/21?
Formula / Expression: 1/27 + 11/21
Final Answer: 106/189
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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 1/27 by 7, and multiply the numerator and denominator of 11/21 by 9 so both fractions share the common base 189.
Working: 1 × 7/27 × 7 = 7/189 and 11 × 9/21 × 9 = 99/189

Step 3: Add the Numerators
Now add the numerators (7 + 99 = 106) and keep the common denominator 189 unchanged.
Working: 7 + 99/189 = 106/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 189 is 1, confirming that 106/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 106/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 189 produces a repeating decimal (approximately 0.560847, or 56.0847%).
Working: 106 ÷ 189 = 0.560847 (56.0847%)

Key Values:
- Simplified Fraction: 106/189
- Mixed Number Form: 106/189
- Decimal Value: 0.560847
- Percentage: 56.0847%

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Solved with FractionsCalc:
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1/27 + 11/21 = 106/189

Simplified Fraction

106/189

Mixed Number

Proper (106/189)

Decimal Value

0.560847

Percentage

56.0847%

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Step-by-Step Solution: 1/27 + 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 1/27 by 7, and multiply the numerator and denominator of 11/21 by 9 so both fractions share the common base 189.

1 × 7/27 × 7 = 7/189 and 11 × 9/21 × 9 = 99/189

Step 3

Add the Numerators

Now add the numerators (7 + 99 = 106) and keep the common denominator 189 unchanged.

7 + 99/189 = 106/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 106 and 189 is 1, confirming that 106/189 cannot be reduced further—it is already in its simplest irreducible form.

106/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 189 produces a repeating decimal (approximately 0.560847, or 56.0847%).

106 ÷ 189 = 0.560847 (56.0847%)

Visual Representation

The diagram below illustrates 1/27 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/189`
Mixed Number Form	`106/189`
Decimal Form	`0.560847`
Percentage	`56.0847%`

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Frequently Asked Questions

What is 1/27 plus 11/21 as a fraction?

1/27 + 11/21 in simplest fraction form is 106/189.

What is 1/27 plus 11/21 as a decimal?

1/27 + 11/21 converted to a decimal is 0.560847.

What is 1/27 plus 11/21 as a percentage?

1/27 + 11/21 expressed as a percentage is 56.0847%.

Does 1/27 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.560847...) because the denominator contains prime factors other than 2 and 5.