What is 2/30 plus 2/5? (Answer: 7/15)

Exact Answer

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Problem: What is 2/30 plus 2/5?
Formula / Expression: 2/30 + 2/5
Final Answer: 7/15
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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 2/5 by 6 so both fractions share the common base 30.
Working: 2 × 1/30 × 1 = 2/30 and 2 × 6/5 × 6 = 12/30

Step 3: Add the Numerators
Now add the numerators (2 + 12 = 14) and keep the common denominator 30 unchanged.
Working: 2 + 12/30 = 14/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/30 ÷ 2 = 7/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
Working: 7 ÷ 15 = 0.466667 (46.6667%)

Key Values:
- Simplified Fraction: 7/15
- Mixed Number Form: 7/15
- Decimal Value: 0.466667
- Percentage: 46.6667%

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Solved with FractionsCalc:
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2/30 + 2/5 = 7/15

Simplified Fraction

7/15

Mixed Number

Proper (7/15)

Decimal Value

0.466667

Percentage

46.6667%

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

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 2/5 by 6 so both fractions share the common base 30.

2 × 1/30 × 1 = 2/30 and 2 × 6/5 × 6 = 12/30

Step 3

Add the Numerators

Now add the numerators (2 + 12 = 14) and keep the common denominator 30 unchanged.

2 + 12/30 = 14/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 30, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/30 ÷ 2 = 7/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).

7 ÷ 15 = 0.466667 (46.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/15`
Mixed Number Form	`7/15`
Decimal Form	`0.466667`
Percentage	`46.6667%`

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Frequently Asked Questions

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

2/30 + 2/5 in simplest fraction form is 7/15.

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

2/30 + 2/5 converted to a decimal is 0.466667.

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

2/30 + 2/5 expressed as a percentage is 46.6667%.

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

It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.