What is 2/30 plus 2/8? (Answer: 19/60)

Exact Answer

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Problem: What is 2/30 plus 2/8?
Formula / Expression: 2/30 + 2/8
Final Answer: 19/60
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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 2/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.
Working: 2 × 4/30 × 4 = 8/120 and 2 × 15/8 × 15 = 30/120

Step 3: Add the Numerators
Now add the numerators (8 + 30 = 38) and keep the common denominator 120 unchanged.
Working: 8 + 30/120 = 38/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/120 ÷ 2 = 19/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 60 produces a repeating decimal (approximately 0.316667, or 31.6667%).
Working: 19 ÷ 60 = 0.316667 (31.6667%)

Key Values:
- Simplified Fraction: 19/60
- Mixed Number Form: 19/60
- Decimal Value: 0.316667
- Percentage: 31.6667%

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2/30 + 2/8 = 19/60

Simplified Fraction

19/60

Mixed Number

Proper (19/60)

Decimal Value

0.316667

Percentage

31.6667%

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Step-by-Step Solution: 2/30 + 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 2/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.

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

Step 3

Add the Numerators

Now add the numerators (8 + 30 = 38) and keep the common denominator 120 unchanged.

8 + 30/120 = 38/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 120, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/120 ÷ 2 = 19/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 60 produces a repeating decimal (approximately 0.316667, or 31.6667%).

19 ÷ 60 = 0.316667 (31.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/60`
Mixed Number Form	`19/60`
Decimal Form	`0.316667`
Percentage	`31.6667%`

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Frequently Asked Questions

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

2/30 + 2/8 in simplest fraction form is 19/60.

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

2/30 + 2/8 converted to a decimal is 0.316667.

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

2/30 + 2/8 expressed as a percentage is 31.6667%.

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

It results in a repeating decimal (approximately 0.316667...) because the denominator contains prime factors other than 2 and 5.