What is 4/27 plus 2/5? (Answer: 74/135)

Exact Answer

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Problem: What is 4/27 plus 2/5?
Formula / Expression: 4/27 + 2/5
Final Answer: 74/135
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 5 = 135.
Working: LCD(27, 5) = 135

Step 2: Convert to Equivalent Fractions with Common Denominator 135
Multiply the numerator and denominator of 4/27 by 5, and multiply the numerator and denominator of 2/5 by 27 so both fractions share the common base 135.
Working: 4 × 5/27 × 5 = 20/135 and 2 × 27/5 × 27 = 54/135

Step 3: Add the Numerators
Now add the numerators (20 + 54 = 74) and keep the common denominator 135 unchanged.
Working: 20 + 54/135 = 74/135

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 135 is 1, confirming that 74/135 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/135

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 135 produces a repeating decimal (approximately 0.548148, or 54.8148%).
Working: 74 ÷ 135 = 0.548148 (54.8148%)

Key Values:
- Simplified Fraction: 74/135
- Mixed Number Form: 74/135
- Decimal Value: 0.548148
- Percentage: 54.8148%

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Solved with FractionsCalc:
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4/27 + 2/5 = 74/135

Simplified Fraction

74/135

Mixed Number

Proper (74/135)

Decimal Value

0.548148

Percentage

54.8148%

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Step-by-Step Solution: 4/27 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 5 = 135.

LCD(27, 5) = 135

Step 2

Convert to Equivalent Fractions with Common Denominator 135

Multiply the numerator and denominator of 4/27 by 5, and multiply the numerator and denominator of 2/5 by 27 so both fractions share the common base 135.

4 × 5/27 × 5 = 20/135 and 2 × 27/5 × 27 = 54/135

Step 3

Add the Numerators

Now add the numerators (20 + 54 = 74) and keep the common denominator 135 unchanged.

20 + 54/135 = 74/135

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 135 is 1, confirming that 74/135 cannot be reduced further—it is already in its simplest irreducible form.

74/135

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 135 produces a repeating decimal (approximately 0.548148, or 54.8148%).

74 ÷ 135 = 0.548148 (54.8148%)

Visual Representation

The diagram below illustrates 4/27 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/135`
Mixed Number Form	`74/135`
Decimal Form	`0.548148`
Percentage	`54.8148%`

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Frequently Asked Questions

What is 4/27 plus 2/5 as a fraction?

4/27 + 2/5 in simplest fraction form is 74/135.

What is 4/27 plus 2/5 as a decimal?

4/27 + 2/5 converted to a decimal is 0.548148.

What is 4/27 plus 2/5 as a percentage?

4/27 + 2/5 expressed as a percentage is 54.8148%.

Does 4/27 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.548148...) because the denominator contains prime factors other than 2 and 5.