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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 30 × 4 = 120, keeping the calculation simpler).
Working: LCD(30, 4) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 4/30 by 2, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.
Working: 4 × 2/30 × 2 = 8/60 and 2 × 15/4 × 15 = 30/60

Step 3: Add the Numerators
Now add the numerators (8 + 30 = 38) and keep the common denominator 60 unchanged.
Working: 8 + 30/60 = 38/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 60, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/60 ÷ 2 = 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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4/30 + 2/4 = 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: 4/30 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 30 × 4 = 120, keeping the calculation simpler).

LCD(30, 4) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 4/30 by 2, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.

4 × 2/30 × 2 = 8/60 and 2 × 15/4 × 15 = 30/60

Step 3

Add the Numerators

Now add the numerators (8 + 30 = 38) and keep the common denominator 60 unchanged.

8 + 30/60 = 38/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 60, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/60 ÷ 2 = 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 4/30 plus 2/4 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 4/30 plus 2/4 as a fraction?

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

What is 4/30 plus 2/4 as a decimal?

4/30 + 2/4 converted to a decimal is 0.633333.

What is 4/30 plus 2/4 as a percentage?

4/30 + 2/4 expressed as a percentage is 63.3333%.

Does 4/30 plus 2/4 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.