What is 7/27 plus 2/4? (Answer: 41/54)

Exact Answer

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Problem: What is 7/27 plus 2/4?
Formula / Expression: 7/27 + 2/4
Final Answer: 41/54
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 4 = 108.
Working: LCD(27, 4) = 108

Step 2: Convert to Equivalent Fractions with Common Denominator 108
Multiply the numerator and denominator of 7/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.
Working: 7 × 4/27 × 4 = 28/108 and 2 × 27/4 × 27 = 54/108

Step 3: Add the Numerators
Now add the numerators (28 + 54 = 82) and keep the common denominator 108 unchanged.
Working: 28 + 54/108 = 82/108

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 108, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/108 ÷ 2 = 41/54

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 54 produces a repeating decimal (approximately 0.759259, or 75.9259%).
Working: 41 ÷ 54 = 0.759259 (75.9259%)

Key Values:
- Simplified Fraction: 41/54
- Mixed Number Form: 41/54
- Decimal Value: 0.759259
- Percentage: 75.9259%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-27-plus-2-4/
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7/27 + 2/4 = 41/54

Simplified Fraction

41/54

Mixed Number

Proper (41/54)

Decimal Value

0.759259

Percentage

75.9259%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 4 = 108.

LCD(27, 4) = 108

Step 2

Convert to Equivalent Fractions with Common Denominator 108

Multiply the numerator and denominator of 7/27 by 4, and multiply the numerator and denominator of 2/4 by 27 so both fractions share the common base 108.

7 × 4/27 × 4 = 28/108 and 2 × 27/4 × 27 = 54/108

Step 3

Add the Numerators

Now add the numerators (28 + 54 = 82) and keep the common denominator 108 unchanged.

28 + 54/108 = 82/108

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 108, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/108 ÷ 2 = 41/54

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 54 produces a repeating decimal (approximately 0.759259, or 75.9259%).

41 ÷ 54 = 0.759259 (75.9259%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/54`
Mixed Number Form	`41/54`
Decimal Form	`0.759259`
Percentage	`75.9259%`

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Frequently Asked Questions

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

7/27 + 2/4 in simplest fraction form is 41/54.

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

7/27 + 2/4 converted to a decimal is 0.759259.

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

7/27 + 2/4 expressed as a percentage is 75.9259%.

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

It results in a repeating decimal (approximately 0.759259...) because the denominator contains prime factors other than 2 and 5.