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

Exact Answer

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Problem: What is 2/30 plus 3/5?
Formula / Expression: 2/30 + 3/5
Final Answer: 2/3
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 30 is an exact multiple of 5 (5 × 6 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.
Working: LCD(30, 5) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/30 by 1, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.
Working: 2 × 1/30 × 1 = 2/30 and 3 × 6/5 × 6 = 18/30

Step 3: Add the Numerators
Now add the numerators (2 + 18 = 20) and keep the common denominator 30 unchanged.
Working: 2 + 18/30 = 20/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 30, which is 10. Divide both the numerator and denominator by 10.
Working: 20 ÷ 10/30 ÷ 10 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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2/30 + 3/5 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 2/30 + 3/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 30 is an exact multiple of 5 (5 × 6 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.

LCD(30, 5) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 2/30 by 1, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.

2 × 1/30 × 1 = 2/30 and 3 × 6/5 × 6 = 18/30

Step 3

Add the Numerators

Now add the numerators (2 + 18 = 20) and keep the common denominator 30 unchanged.

2 + 18/30 = 20/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 30, which is 10. Divide both the numerator and denominator by 10.

20 ÷ 10/30 ÷ 10 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 2/30 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 2/30 plus 3/5 as a fraction?

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

What is 2/30 plus 3/5 as a decimal?

2/30 + 3/5 converted to a decimal is 0.666667.

What is 2/30 plus 3/5 as a percentage?

2/30 + 3/5 expressed as a percentage is 66.6667%.

Does 2/30 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.