What is 2/8 plus 3/12? (Answer: 1/2)

Exact Answer

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Problem: What is 2/8 plus 3/12?
Formula / Expression: 2/8 + 3/12
Final Answer: 1/2
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 2/8 by 3, and multiply the numerator and denominator of 3/12 by 2 so both fractions share the common base 24.
Working: 2 × 3/8 × 3 = 6/24 and 3 × 2/12 × 2 = 6/24

Step 3: Add the Numerators
Now add the numerators (6 + 6 = 12) and keep the common denominator 24 unchanged.
Working: 6 + 6/24 = 12/24

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 24, which is 12. Divide both the numerator and denominator by 12.
Working: 12 ÷ 12/24 ÷ 12 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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2/8 + 3/12 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 12) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

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

2 × 3/8 × 3 = 6/24 and 3 × 2/12 × 2 = 6/24

Step 3

Add the Numerators

Now add the numerators (6 + 6 = 12) and keep the common denominator 24 unchanged.

6 + 6/24 = 12/24

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 24, which is 12. Divide both the numerator and denominator by 12.

12 ÷ 12/24 ÷ 12 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

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

2/8 + 3/12 in simplest fraction form is 1/2.

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

2/8 + 3/12 converted to a decimal is 0.5.

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

2/8 + 3/12 expressed as a percentage is 50%.

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

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.