What is 2/30 plus 2/10? (Answer: 4/15)

Exact Answer

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Problem: What is 2/30 plus 2/10?
Formula / Expression: 2/30 + 2/10
Final Answer: 4/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 30 is an exact multiple of 10 (10 × 3 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.
Working: LCD(30, 10) = 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 2/10 by 3 so both fractions share the common base 30.
Working: 2 × 1/30 × 1 = 2/30 and 2 × 3/10 × 3 = 6/30

Step 3: Add the Numerators
Now add the numerators (2 + 6 = 8) and keep the common denominator 30 unchanged.
Working: 2 + 6/30 = 8/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 8 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 8 ÷ 2/30 ÷ 2 = 4/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 15 produces a repeating decimal (approximately 0.266667, or 26.6667%).
Working: 4 ÷ 15 = 0.266667 (26.6667%)

Key Values:
- Simplified Fraction: 4/15
- Mixed Number Form: 4/15
- Decimal Value: 0.266667
- Percentage: 26.6667%

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Solved with FractionsCalc:
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2/30 + 2/10 = 4/15

Simplified Fraction

4/15

Mixed Number

Proper (4/15)

Decimal Value

0.266667

Percentage

26.6667%

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Step-by-Step Solution: 2/30 + 2/10

Step 1

Find the Least Common Denominator (LCD)

Notice that 30 is an exact multiple of 10 (10 × 3 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.

LCD(30, 10) = 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 2/10 by 3 so both fractions share the common base 30.

2 × 1/30 × 1 = 2/30 and 2 × 3/10 × 3 = 6/30

Step 3

Add the Numerators

Now add the numerators (2 + 6 = 8) and keep the common denominator 30 unchanged.

2 + 6/30 = 8/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 8 and 30, which is 2. Divide both the numerator and denominator by 2.

8 ÷ 2/30 ÷ 2 = 4/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 15 produces a repeating decimal (approximately 0.266667, or 26.6667%).

4 ÷ 15 = 0.266667 (26.6667%)

Visual Representation

The diagram below illustrates 2/30 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/15`
Mixed Number Form	`4/15`
Decimal Form	`0.266667`
Percentage	`26.6667%`

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Frequently Asked Questions

What is 2/30 plus 2/10 as a fraction?

2/30 + 2/10 in simplest fraction form is 4/15.

What is 2/30 plus 2/10 as a decimal?

2/30 + 2/10 converted to a decimal is 0.266667.

What is 2/30 plus 2/10 as a percentage?

2/30 + 2/10 expressed as a percentage is 26.6667%.

Does 2/30 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.266667...) because the denominator contains prime factors other than 2 and 5.