What is 2/30 plus 3/9? (Answer: 2/5)

Exact Answer

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Problem: What is 2/30 plus 3/9?
Formula / Expression: 2/30 + 3/9
Final Answer: 2/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 30 × 9 = 270, keeping the calculation simpler).
Working: LCD(30, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/30 by 3, and multiply the numerator and denominator of 3/9 by 10 so both fractions share the common base 90.
Working: 2 × 3/30 × 3 = 6/90 and 3 × 10/9 × 10 = 30/90

Step 3: Add the Numerators
Now add the numerators (6 + 30 = 36) and keep the common denominator 90 unchanged.
Working: 6 + 30/90 = 36/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 90, which is 18. Divide both the numerator and denominator by 18.
Working: 36 ÷ 18/90 ÷ 18 = 2/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).
Working: 2 ÷ 5 = 0.4 (40%)

Key Values:
- Simplified Fraction: 2/5
- Mixed Number Form: 2/5
- Decimal Value: 0.4
- Percentage: 40%

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2/30 + 3/9 = 2/5

Simplified Fraction

2/5

Mixed Number

Proper (2/5)

Decimal Value

0.4

Percentage

40%

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Step-by-Step Solution: 2/30 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 30 × 9 = 270, keeping the calculation simpler).

LCD(30, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/30 by 3, and multiply the numerator and denominator of 3/9 by 10 so both fractions share the common base 90.

2 × 3/30 × 3 = 6/90 and 3 × 10/9 × 10 = 30/90

Step 3

Add the Numerators

Now add the numerators (6 + 30 = 36) and keep the common denominator 90 unchanged.

6 + 30/90 = 36/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 90, which is 18. Divide both the numerator and denominator by 18.

36 ÷ 18/90 ÷ 18 = 2/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).

2 ÷ 5 = 0.4 (40%)

Visual Representation

The diagram below illustrates 2/30 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/5`
Mixed Number Form	`2/5`
Decimal Form	`0.4`
Percentage	`40%`

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Frequently Asked Questions

What is 2/30 plus 3/9 as a fraction?

2/30 + 3/9 in simplest fraction form is 2/5.

What is 2/30 plus 3/9 as a decimal?

2/30 + 3/9 converted to a decimal is 0.4.

What is 2/30 plus 3/9 as a percentage?

2/30 + 3/9 expressed as a percentage is 40%.

Does 2/30 plus 3/9 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.