What is 3/19 plus 1/2? (Answer: 25/38)

Exact Answer

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Problem: What is 3/19 plus 1/2?
Formula / Expression: 3/19 + 1/2
Final Answer: 25/38
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 2 = 38.
Working: LCD(19, 2) = 38

Step 2: Convert to Equivalent Fractions with Common Denominator 38
Multiply the numerator and denominator of 3/19 by 2, and multiply the numerator and denominator of 1/2 by 19 so both fractions share the common base 38.
Working: 3 × 2/19 × 2 = 6/38 and 1 × 19/2 × 19 = 19/38

Step 3: Add the Numerators
Now add the numerators (6 + 19 = 25) and keep the common denominator 38 unchanged.
Working: 6 + 19/38 = 25/38

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 38 is 1, confirming that 25/38 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/38

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 38 produces a repeating decimal (approximately 0.657895, or 65.7895%).
Working: 25 ÷ 38 = 0.657895 (65.7895%)

Key Values:
- Simplified Fraction: 25/38
- Mixed Number Form: 25/38
- Decimal Value: 0.657895
- Percentage: 65.7895%

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3/19 + 1/2 = 25/38

Simplified Fraction

25/38

Mixed Number

Proper (25/38)

Decimal Value

0.657895

Percentage

65.7895%

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Step-by-Step Solution: 3/19 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 2 = 38.

LCD(19, 2) = 38

Step 2

Convert to Equivalent Fractions with Common Denominator 38

Multiply the numerator and denominator of 3/19 by 2, and multiply the numerator and denominator of 1/2 by 19 so both fractions share the common base 38.

3 × 2/19 × 2 = 6/38 and 1 × 19/2 × 19 = 19/38

Step 3

Add the Numerators

Now add the numerators (6 + 19 = 25) and keep the common denominator 38 unchanged.

6 + 19/38 = 25/38

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 38 is 1, confirming that 25/38 cannot be reduced further—it is already in its simplest irreducible form.

25/38

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 38 produces a repeating decimal (approximately 0.657895, or 65.7895%).

25 ÷ 38 = 0.657895 (65.7895%)

Visual Representation

The diagram below illustrates 3/19 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/38`
Mixed Number Form	`25/38`
Decimal Form	`0.657895`
Percentage	`65.7895%`

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Frequently Asked Questions

What is 3/19 plus 1/2 as a fraction?

3/19 + 1/2 in simplest fraction form is 25/38.

What is 3/19 plus 1/2 as a decimal?

3/19 + 1/2 converted to a decimal is 0.657895.

What is 3/19 plus 1/2 as a percentage?

3/19 + 1/2 expressed as a percentage is 65.7895%.

Does 3/19 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.657895...) because the denominator contains prime factors other than 2 and 5.