What is 2/15 plus 4/8? (Answer: 19/30)

Exact Answer

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Problem: What is 2/15 plus 4/8?
Formula / Expression: 2/15 + 4/8
Final Answer: 19/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 8 = 120.
Working: LCD(15, 8) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/15 by 8, and multiply the numerator and denominator of 4/8 by 15 so both fractions share the common base 120.
Working: 2 × 8/15 × 8 = 16/120 and 4 × 15/8 × 15 = 60/120

Step 3: Add the Numerators
Now add the numerators (16 + 60 = 76) and keep the common denominator 120 unchanged.
Working: 16 + 60/120 = 76/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 120, which is 4. Divide both the numerator and denominator by 4.
Working: 76 ÷ 4/120 ÷ 4 = 19/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).
Working: 19 ÷ 30 = 0.633333 (63.3333%)

Key Values:
- Simplified Fraction: 19/30
- Mixed Number Form: 19/30
- Decimal Value: 0.633333
- Percentage: 63.3333%

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Solved with FractionsCalc:
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2/15 + 4/8 = 19/30

Simplified Fraction

19/30

Mixed Number

Proper (19/30)

Decimal Value

0.633333

Percentage

63.3333%

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Step-by-Step Solution: 2/15 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 8 = 120.

LCD(15, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/15 by 8, and multiply the numerator and denominator of 4/8 by 15 so both fractions share the common base 120.

2 × 8/15 × 8 = 16/120 and 4 × 15/8 × 15 = 60/120

Step 3

Add the Numerators

Now add the numerators (16 + 60 = 76) and keep the common denominator 120 unchanged.

16 + 60/120 = 76/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 120, which is 4. Divide both the numerator and denominator by 4.

76 ÷ 4/120 ÷ 4 = 19/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).

19 ÷ 30 = 0.633333 (63.3333%)

Visual Representation

The diagram below illustrates 2/15 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/30`
Mixed Number Form	`19/30`
Decimal Form	`0.633333`
Percentage	`63.3333%`

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Frequently Asked Questions

What is 2/15 plus 4/8 as a fraction?

2/15 + 4/8 in simplest fraction form is 19/30.

What is 2/15 plus 4/8 as a decimal?

2/15 + 4/8 converted to a decimal is 0.633333.

What is 2/15 plus 4/8 as a percentage?

2/15 + 4/8 expressed as a percentage is 63.3333%.

Does 2/15 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.633333...) because the denominator contains prime factors other than 2 and 5.