What is 2/30 plus 3/8? (Answer: 53/120)

Exact Answer

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Problem: What is 2/30 plus 3/8?
Formula / Expression: 2/30 + 3/8
Final Answer: 53/120
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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 3/8 by 15 so both fractions share the common base 120.
Working: 2 × 4/30 × 4 = 8/120 and 3 × 15/8 × 15 = 45/120

Step 3: Add the Numerators
Now add the numerators (8 + 45 = 53) and keep the common denominator 120 unchanged.
Working: 8 + 45/120 = 53/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 120 is 1, confirming that 53/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 120 produces a repeating decimal (approximately 0.441667, or 44.1667%).
Working: 53 ÷ 120 = 0.441667 (44.1667%)

Key Values:
- Simplified Fraction: 53/120
- Mixed Number Form: 53/120
- Decimal Value: 0.441667
- Percentage: 44.1667%

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2/30 + 3/8 = 53/120

Simplified Fraction

53/120

Mixed Number

Proper (53/120)

Decimal Value

0.441667

Percentage

44.1667%

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Step-by-Step Solution: 2/30 + 3/8

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 3/8 by 15 so both fractions share the common base 120.

2 × 4/30 × 4 = 8/120 and 3 × 15/8 × 15 = 45/120

Step 3

Add the Numerators

Now add the numerators (8 + 45 = 53) and keep the common denominator 120 unchanged.

8 + 45/120 = 53/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 120 is 1, confirming that 53/120 cannot be reduced further—it is already in its simplest irreducible form.

53/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 120 produces a repeating decimal (approximately 0.441667, or 44.1667%).

53 ÷ 120 = 0.441667 (44.1667%)

Visual Representation

The diagram below illustrates 2/30 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/120`
Mixed Number Form	`53/120`
Decimal Form	`0.441667`
Percentage	`44.1667%`

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Frequently Asked Questions

What is 2/30 plus 3/8 as a fraction?

2/30 + 3/8 in simplest fraction form is 53/120.

What is 2/30 plus 3/8 as a decimal?

2/30 + 3/8 converted to a decimal is 0.441667.

What is 2/30 plus 3/8 as a percentage?

2/30 + 3/8 expressed as a percentage is 44.1667%.

Does 2/30 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.441667...) because the denominator contains prime factors other than 2 and 5.