What is 3/19 plus 4/8? (Answer: 25/38)

Exact Answer

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Problem: What is 3/19 plus 4/8?
Formula / Expression: 3/19 + 4/8
Final Answer: 25/38
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.
Working: LCD(19, 8) = 152

Step 2: Convert to Equivalent Fractions with Common Denominator 152
Multiply the numerator and denominator of 3/19 by 8, and multiply the numerator and denominator of 4/8 by 19 so both fractions share the common base 152.
Working: 3 × 8/19 × 8 = 24/152 and 4 × 19/8 × 19 = 76/152

Step 3: Add the Numerators
Now add the numerators (24 + 76 = 100) and keep the common denominator 152 unchanged.
Working: 24 + 76/152 = 100/152

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 100 and 152, which is 4. Divide both the numerator and denominator by 4.
Working: 100 ÷ 4/152 ÷ 4 = 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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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-19-plus-4-8/
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3/19 + 4/8 = 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 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 8 = 152.

LCD(19, 8) = 152

Step 2

Convert to Equivalent Fractions with Common Denominator 152

Multiply the numerator and denominator of 3/19 by 8, and multiply the numerator and denominator of 4/8 by 19 so both fractions share the common base 152.

3 × 8/19 × 8 = 24/152 and 4 × 19/8 × 19 = 76/152

Step 3

Add the Numerators

Now add the numerators (24 + 76 = 100) and keep the common denominator 152 unchanged.

24 + 76/152 = 100/152

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 100 and 152, which is 4. Divide both the numerator and denominator by 4.

100 ÷ 4/152 ÷ 4 = 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 4/8 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 4/8 as a fraction?

3/19 + 4/8 in simplest fraction form is 25/38.

What is 3/19 plus 4/8 as a decimal?

3/19 + 4/8 converted to a decimal is 0.657895.

What is 3/19 plus 4/8 as a percentage?

3/19 + 4/8 expressed as a percentage is 65.7895%.

Does 3/19 plus 4/8 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.