What is 3/30 plus 2/4? (Answer: 3/5)

Exact Answer

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Problem: What is 3/30 plus 2/4?
Formula / Expression: 3/30 + 2/4
Final Answer: 3/5
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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 3/30 by 2, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.
Working: 3 × 2/30 × 2 = 6/60 and 2 × 15/4 × 15 = 30/60

Step 3: Add the Numerators
Now add the numerators (6 + 30 = 36) and keep the common denominator 60 unchanged.
Working: 6 + 30/60 = 36/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 60, which is 12. Divide both the numerator and denominator by 12.
Working: 36 ÷ 12/60 ÷ 12 = 3/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).
Working: 3 ÷ 5 = 0.6 (60%)

Key Values:
- Simplified Fraction: 3/5
- Mixed Number Form: 3/5
- Decimal Value: 0.6
- Percentage: 60%

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Solved with FractionsCalc:
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3/30 + 2/4 = 3/5

Simplified Fraction

3/5

Mixed Number

Proper (3/5)

Decimal Value

0.6

Percentage

60%

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Step-by-Step Solution: 3/30 + 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 3/30 by 2, and multiply the numerator and denominator of 2/4 by 15 so both fractions share the common base 60.

3 × 2/30 × 2 = 6/60 and 2 × 15/4 × 15 = 30/60

Step 3

Add the Numerators

Now add the numerators (6 + 30 = 36) and keep the common denominator 60 unchanged.

6 + 30/60 = 36/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 60, which is 12. Divide both the numerator and denominator by 12.

36 ÷ 12/60 ÷ 12 = 3/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).

3 ÷ 5 = 0.6 (60%)

Visual Representation

The diagram below illustrates 3/30 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/5`
Mixed Number Form	`3/5`
Decimal Form	`0.6`
Percentage	`60%`

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Frequently Asked Questions

What is 3/30 plus 2/4 as a fraction?

3/30 + 2/4 in simplest fraction form is 3/5.

What is 3/30 plus 2/4 as a decimal?

3/30 + 2/4 converted to a decimal is 0.6.

What is 3/30 plus 2/4 as a percentage?

3/30 + 2/4 expressed as a percentage is 60%.

Does 3/30 plus 2/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.6) because the denominator in simplest terms contains only prime factors 2 and/or 5.