What is 1/27 plus 3/21? (Answer: 34/189)

Exact Answer

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Problem: What is 1/27 plus 3/21?
Formula / Expression: 1/27 + 3/21
Final Answer: 34/189
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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 3/21 by 9 so both fractions share the common base 189.
Working: 1 × 7/27 × 7 = 7/189 and 3 × 9/21 × 9 = 27/189

Step 3: Add the Numerators
Now add the numerators (7 + 27 = 34) and keep the common denominator 189 unchanged.
Working: 7 + 27/189 = 34/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 34 and 189 is 1, confirming that 34/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 34/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 189 produces a repeating decimal (approximately 0.179894, or 17.9894%).
Working: 34 ÷ 189 = 0.179894 (17.9894%)

Key Values:
- Simplified Fraction: 34/189
- Mixed Number Form: 34/189
- Decimal Value: 0.179894
- Percentage: 17.9894%

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Solved with FractionsCalc:
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1/27 + 3/21 = 34/189

Simplified Fraction

34/189

Mixed Number

Proper (34/189)

Decimal Value

0.179894

Percentage

17.9894%

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Step-by-Step Solution: 1/27 + 3/21

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 3/21 by 9 so both fractions share the common base 189.

1 × 7/27 × 7 = 7/189 and 3 × 9/21 × 9 = 27/189

Step 3

Add the Numerators

Now add the numerators (7 + 27 = 34) and keep the common denominator 189 unchanged.

7 + 27/189 = 34/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 34 and 189 is 1, confirming that 34/189 cannot be reduced further—it is already in its simplest irreducible form.

34/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 189 produces a repeating decimal (approximately 0.179894, or 17.9894%).

34 ÷ 189 = 0.179894 (17.9894%)

Visual Representation

The diagram below illustrates 1/27 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/189`
Mixed Number Form	`34/189`
Decimal Form	`0.179894`
Percentage	`17.9894%`

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Frequently Asked Questions

What is 1/27 plus 3/21 as a fraction?

1/27 + 3/21 in simplest fraction form is 34/189.

What is 1/27 plus 3/21 as a decimal?

1/27 + 3/21 converted to a decimal is 0.179894.

What is 1/27 plus 3/21 as a percentage?

1/27 + 3/21 expressed as a percentage is 17.9894%.

Does 1/27 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.179894...) because the denominator contains prime factors other than 2 and 5.