What is 2/27 plus 4/7? (Answer: 122/189)

Exact Answer

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Problem: What is 2/27 plus 4/7?
Formula / Expression: 2/27 + 4/7
Final Answer: 122/189
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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 2/27 by 7, and multiply the numerator and denominator of 4/7 by 27 so both fractions share the common base 189.
Working: 2 × 7/27 × 7 = 14/189 and 4 × 27/7 × 27 = 108/189

Step 3: Add the Numerators
Now add the numerators (14 + 108 = 122) and keep the common denominator 189 unchanged.
Working: 14 + 108/189 = 122/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 189 is 1, confirming that 122/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 122/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 189 produces a repeating decimal (approximately 0.645503, or 64.5503%).
Working: 122 ÷ 189 = 0.645503 (64.5503%)

Key Values:
- Simplified Fraction: 122/189
- Mixed Number Form: 122/189
- Decimal Value: 0.645503
- Percentage: 64.5503%

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Solved with FractionsCalc:
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2/27 + 4/7 = 122/189

Simplified Fraction

122/189

Mixed Number

Proper (122/189)

Decimal Value

0.645503

Percentage

64.5503%

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Step-by-Step Solution: 2/27 + 4/7

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 2/27 by 7, and multiply the numerator and denominator of 4/7 by 27 so both fractions share the common base 189.

2 × 7/27 × 7 = 14/189 and 4 × 27/7 × 27 = 108/189

Step 3

Add the Numerators

Now add the numerators (14 + 108 = 122) and keep the common denominator 189 unchanged.

14 + 108/189 = 122/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 122 and 189 is 1, confirming that 122/189 cannot be reduced further—it is already in its simplest irreducible form.

122/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 189 produces a repeating decimal (approximately 0.645503, or 64.5503%).

122 ÷ 189 = 0.645503 (64.5503%)

Visual Representation

The diagram below illustrates 2/27 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/189`
Mixed Number Form	`122/189`
Decimal Form	`0.645503`
Percentage	`64.5503%`

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Frequently Asked Questions

What is 2/27 plus 4/7 as a fraction?

2/27 + 4/7 in simplest fraction form is 122/189.

What is 2/27 plus 4/7 as a decimal?

2/27 + 4/7 converted to a decimal is 0.645503.

What is 2/27 plus 4/7 as a percentage?

2/27 + 4/7 expressed as a percentage is 64.5503%.

Does 2/27 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.645503...) because the denominator contains prime factors other than 2 and 5.