What is 2/12 plus 3/8? (Answer: 13/24)

Exact Answer

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Problem: What is 2/12 plus 3/8?
Formula / Expression: 2/12 + 3/8
Final Answer: 13/24
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 12 × 8 = 96, keeping the calculation simpler).
Working: LCD(12, 8) = 24

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 2/12 by 2, and multiply the numerator and denominator of 3/8 by 3 so both fractions share the common base 24.
Working: 2 × 2/12 × 2 = 4/24 and 3 × 3/8 × 3 = 9/24

Step 3: Add the Numerators
Now add the numerators (4 + 9 = 13) and keep the common denominator 24 unchanged.
Working: 4 + 9/24 = 13/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 24 is 1, confirming that 13/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 24 produces a repeating decimal (approximately 0.541667, or 54.1667%).
Working: 13 ÷ 24 = 0.541667 (54.1667%)

Key Values:
- Simplified Fraction: 13/24
- Mixed Number Form: 13/24
- Decimal Value: 0.541667
- Percentage: 54.1667%

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Solved with FractionsCalc:
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2/12 + 3/8 = 13/24

Simplified Fraction

13/24

Mixed Number

Proper (13/24)

Decimal Value

0.541667

Percentage

54.1667%

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Step-by-Step Solution: 2/12 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 24 (which is smaller than their product 12 × 8 = 96, keeping the calculation simpler).

LCD(12, 8) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

Multiply the numerator and denominator of 2/12 by 2, and multiply the numerator and denominator of 3/8 by 3 so both fractions share the common base 24.

2 × 2/12 × 2 = 4/24 and 3 × 3/8 × 3 = 9/24

Step 3

Add the Numerators

Now add the numerators (4 + 9 = 13) and keep the common denominator 24 unchanged.

4 + 9/24 = 13/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 24 is 1, confirming that 13/24 cannot be reduced further—it is already in its simplest irreducible form.

13/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 24 produces a repeating decimal (approximately 0.541667, or 54.1667%).

13 ÷ 24 = 0.541667 (54.1667%)

Visual Representation

The diagram below illustrates 2/12 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/24`
Mixed Number Form	`13/24`
Decimal Form	`0.541667`
Percentage	`54.1667%`

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Frequently Asked Questions

What is 2/12 plus 3/8 as a fraction?

2/12 + 3/8 in simplest fraction form is 13/24.

What is 2/12 plus 3/8 as a decimal?

2/12 + 3/8 converted to a decimal is 0.541667.

What is 2/12 plus 3/8 as a percentage?

2/12 + 3/8 expressed as a percentage is 54.1667%.

Does 2/12 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.541667...) because the denominator contains prime factors other than 2 and 5.