What is 4/15 plus 2/4? (Answer: 23/30)

Exact Answer

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Problem: What is 4/15 plus 2/4?
Formula / Expression: 4/15 + 2/4
Final Answer: 23/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 4 = 60.
Working: LCD(15, 4) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 4/15 by 4, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.
Working: 4 × 4/15 × 4 = 16/60 and 2 × 15/4 × 15 = 30/60

Step 3: Add the Numerators
Now add the numerators (16 + 30 = 46) and keep the common denominator 60 unchanged.
Working: 16 + 30/60 = 46/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 60, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/60 ÷ 2 = 23/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 30 produces a repeating decimal (approximately 0.766667, or 76.6667%).
Working: 23 ÷ 30 = 0.766667 (76.6667%)

Key Values:
- Simplified Fraction: 23/30
- Mixed Number Form: 23/30
- Decimal Value: 0.766667
- Percentage: 76.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-15-plus-2-4/
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4/15 + 2/4 = 23/30

Simplified Fraction

23/30

Mixed Number

Proper (23/30)

Decimal Value

0.766667

Percentage

76.6667%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 15 × 4 = 60.

LCD(15, 4) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 4/15 by 4, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.

4 × 4/15 × 4 = 16/60 and 2 × 15/4 × 15 = 30/60

Step 3

Add the Numerators

Now add the numerators (16 + 30 = 46) and keep the common denominator 60 unchanged.

16 + 30/60 = 46/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 60, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/60 ÷ 2 = 23/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 30 produces a repeating decimal (approximately 0.766667, or 76.6667%).

23 ÷ 30 = 0.766667 (76.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/30`
Mixed Number Form	`23/30`
Decimal Form	`0.766667`
Percentage	`76.6667%`

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Frequently Asked Questions

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

4/15 + 2/4 in simplest fraction form is 23/30.

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

4/15 + 2/4 converted to a decimal is 0.766667.

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

4/15 + 2/4 expressed as a percentage is 76.6667%.

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

It results in a repeating decimal (approximately 0.766667...) because the denominator contains prime factors other than 2 and 5.