What is 2/27 plus 3/4? (Answer: 89/108)

Exact Answer

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Problem: What is 2/27 plus 3/4?
Formula / Expression: 2/27 + 3/4
Final Answer: 89/108
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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 2/27 by 4, and multiply the numerator and denominator of 3/4 by 27 so both fractions share the common base 108.
Working: 2 × 4/27 × 4 = 8/108 and 3 × 27/4 × 27 = 81/108

Step 3: Add the Numerators
Now add the numerators (8 + 81 = 89) and keep the common denominator 108 unchanged.
Working: 8 + 81/108 = 89/108

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 108 is 1, confirming that 89/108 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/108

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 108 produces a repeating decimal (approximately 0.824074, or 82.4074%).
Working: 89 ÷ 108 = 0.824074 (82.4074%)

Key Values:
- Simplified Fraction: 89/108
- Mixed Number Form: 89/108
- Decimal Value: 0.824074
- Percentage: 82.4074%

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Solved with FractionsCalc:
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2/27 + 3/4 = 89/108

Simplified Fraction

89/108

Mixed Number

Proper (89/108)

Decimal Value

0.824074

Percentage

82.4074%

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Step-by-Step Solution: 2/27 + 3/4

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 2/27 by 4, and multiply the numerator and denominator of 3/4 by 27 so both fractions share the common base 108.

2 × 4/27 × 4 = 8/108 and 3 × 27/4 × 27 = 81/108

Step 3

Add the Numerators

Now add the numerators (8 + 81 = 89) and keep the common denominator 108 unchanged.

8 + 81/108 = 89/108

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 108 is 1, confirming that 89/108 cannot be reduced further—it is already in its simplest irreducible form.

89/108

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 108 produces a repeating decimal (approximately 0.824074, or 82.4074%).

89 ÷ 108 = 0.824074 (82.4074%)

Visual Representation

The diagram below illustrates 2/27 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/108`
Mixed Number Form	`89/108`
Decimal Form	`0.824074`
Percentage	`82.4074%`

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Frequently Asked Questions

What is 2/27 plus 3/4 as a fraction?

2/27 + 3/4 in simplest fraction form is 89/108.

What is 2/27 plus 3/4 as a decimal?

2/27 + 3/4 converted to a decimal is 0.824074.

What is 2/27 plus 3/4 as a percentage?

2/27 + 3/4 expressed as a percentage is 82.4074%.

Does 2/27 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.824074...) because the denominator contains prime factors other than 2 and 5.