What is 3/9 plus 2/5? (Answer: 11/15)

Exact Answer

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Problem: What is 3/9 plus 2/5?
Formula / Expression: 3/9 + 2/5
Final Answer: 11/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 5 = 45.
Working: LCD(9, 5) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 3/9 by 5, and multiply the numerator and denominator of 2/5 by 9 so both fractions share the common base 45.
Working: 3 × 5/9 × 5 = 15/45 and 2 × 9/5 × 9 = 18/45

Step 3: Add the Numerators
Now add the numerators (15 + 18 = 33) and keep the common denominator 45 unchanged.
Working: 15 + 18/45 = 33/45

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 45, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/45 ÷ 3 = 11/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).
Working: 11 ÷ 15 = 0.733333 (73.3333%)

Key Values:
- Simplified Fraction: 11/15
- Mixed Number Form: 11/15
- Decimal Value: 0.733333
- Percentage: 73.3333%

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Solved with FractionsCalc:
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3/9 + 2/5 = 11/15

Simplified Fraction

11/15

Mixed Number

Proper (11/15)

Decimal Value

0.733333

Percentage

73.3333%

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Step-by-Step Solution: 3/9 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 5 = 45.

LCD(9, 5) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 3/9 by 5, and multiply the numerator and denominator of 2/5 by 9 so both fractions share the common base 45.

3 × 5/9 × 5 = 15/45 and 2 × 9/5 × 9 = 18/45

Step 3

Add the Numerators

Now add the numerators (15 + 18 = 33) and keep the common denominator 45 unchanged.

15 + 18/45 = 33/45

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 45, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/45 ÷ 3 = 11/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).

11 ÷ 15 = 0.733333 (73.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/15`
Mixed Number Form	`11/15`
Decimal Form	`0.733333`
Percentage	`73.3333%`

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Frequently Asked Questions

What is 3/9 plus 2/5 as a fraction?

3/9 + 2/5 in simplest fraction form is 11/15.

What is 3/9 plus 2/5 as a decimal?

3/9 + 2/5 converted to a decimal is 0.733333.

What is 3/9 plus 2/5 as a percentage?

3/9 + 2/5 expressed as a percentage is 73.3333%.

Does 3/9 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.733333...) because the denominator contains prime factors other than 2 and 5.