What is 1/27 plus 2/7? (Answer: 61/189)

Exact Answer

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Problem: What is 1/27 plus 2/7?
Formula / Expression: 1/27 + 2/7
Final Answer: 61/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 7 = 189.
Working: LCD(27, 7) = 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 2/7 by 27 so both fractions share the common base 189.
Working: 1 × 7/27 × 7 = 7/189 and 2 × 27/7 × 27 = 54/189

Step 3: Add the Numerators
Now add the numerators (7 + 54 = 61) and keep the common denominator 189 unchanged.
Working: 7 + 54/189 = 61/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 189 is 1, confirming that 61/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 189 produces a repeating decimal (approximately 0.322751, or 32.2751%).
Working: 61 ÷ 189 = 0.322751 (32.2751%)

Key Values:
- Simplified Fraction: 61/189
- Mixed Number Form: 61/189
- Decimal Value: 0.322751
- Percentage: 32.2751%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-27-plus-2-7/
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1/27 + 2/7 = 61/189

Simplified Fraction

61/189

Mixed Number

Proper (61/189)

Decimal Value

0.322751

Percentage

32.2751%

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Step-by-Step Solution: 1/27 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 7 = 189.

LCD(27, 7) = 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 2/7 by 27 so both fractions share the common base 189.

1 × 7/27 × 7 = 7/189 and 2 × 27/7 × 27 = 54/189

Step 3

Add the Numerators

Now add the numerators (7 + 54 = 61) and keep the common denominator 189 unchanged.

7 + 54/189 = 61/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 189 is 1, confirming that 61/189 cannot be reduced further—it is already in its simplest irreducible form.

61/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 189 produces a repeating decimal (approximately 0.322751, or 32.2751%).

61 ÷ 189 = 0.322751 (32.2751%)

Visual Representation

The diagram below illustrates 1/27 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/189`
Mixed Number Form	`61/189`
Decimal Form	`0.322751`
Percentage	`32.2751%`

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Frequently Asked Questions

What is 1/27 plus 2/7 as a fraction?

1/27 + 2/7 in simplest fraction form is 61/189.

What is 1/27 plus 2/7 as a decimal?

1/27 + 2/7 converted to a decimal is 0.322751.

What is 1/27 plus 2/7 as a percentage?

1/27 + 2/7 expressed as a percentage is 32.2751%.

Does 1/27 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.322751...) because the denominator contains prime factors other than 2 and 5.