What is 2/27 plus 3/8? (Answer: 97/216)

Exact Answer

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Problem: What is 2/27 plus 3/8?
Formula / Expression: 2/27 + 3/8
Final Answer: 97/216
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 8 = 216.
Working: LCD(27, 8) = 216

Step 2: Convert to Equivalent Fractions with Common Denominator 216
Multiply the numerator and denominator of 2/27 by 8, and multiply the numerator and denominator of 3/8 by 27 so both fractions share the common base 216.
Working: 2 × 8/27 × 8 = 16/216 and 3 × 27/8 × 27 = 81/216

Step 3: Add the Numerators
Now add the numerators (16 + 81 = 97) and keep the common denominator 216 unchanged.
Working: 16 + 81/216 = 97/216

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 216 is 1, confirming that 97/216 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/216

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 216 produces a repeating decimal (approximately 0.449074, or 44.9074%).
Working: 97 ÷ 216 = 0.449074 (44.9074%)

Key Values:
- Simplified Fraction: 97/216
- Mixed Number Form: 97/216
- Decimal Value: 0.449074
- Percentage: 44.9074%

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Solved with FractionsCalc:
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2/27 + 3/8 = 97/216

Simplified Fraction

97/216

Mixed Number

Proper (97/216)

Decimal Value

0.449074

Percentage

44.9074%

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Step-by-Step Solution: 2/27 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 8 = 216.

LCD(27, 8) = 216

Step 2

Convert to Equivalent Fractions with Common Denominator 216

Multiply the numerator and denominator of 2/27 by 8, and multiply the numerator and denominator of 3/8 by 27 so both fractions share the common base 216.

2 × 8/27 × 8 = 16/216 and 3 × 27/8 × 27 = 81/216

Step 3

Add the Numerators

Now add the numerators (16 + 81 = 97) and keep the common denominator 216 unchanged.

16 + 81/216 = 97/216

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 216 is 1, confirming that 97/216 cannot be reduced further—it is already in its simplest irreducible form.

97/216

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 216 produces a repeating decimal (approximately 0.449074, or 44.9074%).

97 ÷ 216 = 0.449074 (44.9074%)

Visual Representation

The diagram below illustrates 2/27 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/216`
Mixed Number Form	`97/216`
Decimal Form	`0.449074`
Percentage	`44.9074%`

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Frequently Asked Questions

What is 2/27 plus 3/8 as a fraction?

2/27 + 3/8 in simplest fraction form is 97/216.

What is 2/27 plus 3/8 as a decimal?

2/27 + 3/8 converted to a decimal is 0.449074.

What is 2/27 plus 3/8 as a percentage?

2/27 + 3/8 expressed as a percentage is 44.9074%.

Does 2/27 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.449074...) because the denominator contains prime factors other than 2 and 5.