What is 5/30 plus 2/8? (Answer: 5/12)

Exact Answer

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Problem: What is 5/30 plus 2/8?
Formula / Expression: 5/30 + 2/8
Final Answer: 5/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).
Working: LCD(30, 8) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 5/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.
Working: 5 × 4/30 × 4 = 20/120 and 2 × 15/8 × 15 = 30/120

Step 3: Add the Numerators
Now add the numerators (20 + 30 = 50) and keep the common denominator 120 unchanged.
Working: 20 + 30/120 = 50/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 50 and 120, which is 10. Divide both the numerator and denominator by 10.
Working: 50 ÷ 10/120 ÷ 10 = 5/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).
Working: 5 ÷ 12 = 0.416667 (41.6667%)

Key Values:
- Simplified Fraction: 5/12
- Mixed Number Form: 5/12
- Decimal Value: 0.416667
- Percentage: 41.6667%

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Solved with FractionsCalc:
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5/30 + 2/8 = 5/12

Simplified Fraction

5/12

Mixed Number

Proper (5/12)

Decimal Value

0.416667

Percentage

41.6667%

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Step-by-Step Solution: 5/30 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).

LCD(30, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 5/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.

5 × 4/30 × 4 = 20/120 and 2 × 15/8 × 15 = 30/120

Step 3

Add the Numerators

Now add the numerators (20 + 30 = 50) and keep the common denominator 120 unchanged.

20 + 30/120 = 50/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 50 and 120, which is 10. Divide both the numerator and denominator by 10.

50 ÷ 10/120 ÷ 10 = 5/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).

5 ÷ 12 = 0.416667 (41.6667%)

Visual Representation

The diagram below illustrates 5/30 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/12`
Mixed Number Form	`5/12`
Decimal Form	`0.416667`
Percentage	`41.6667%`

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Frequently Asked Questions

What is 5/30 plus 2/8 as a fraction?

5/30 + 2/8 in simplest fraction form is 5/12.

What is 5/30 plus 2/8 as a decimal?

5/30 + 2/8 converted to a decimal is 0.416667.

What is 5/30 plus 2/8 as a percentage?

5/30 + 2/8 expressed as a percentage is 41.6667%.

Does 5/30 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.416667...) because the denominator contains prime factors other than 2 and 5.