What is 3/9 plus 3/5? (Answer: 14/15)

Exact Answer

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Problem: What is 3/9 plus 3/5?
Formula / Expression: 3/9 + 3/5
Final Answer: 14/15
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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 3/5 by 9 so both fractions share the common base 45.
Working: 3 × 5/9 × 5 = 15/45 and 3 × 9/5 × 9 = 27/45

Step 3: Add the Numerators
Now add the numerators (15 + 27 = 42) and keep the common denominator 45 unchanged.
Working: 15 + 27/45 = 42/45

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 45, which is 3. Divide both the numerator and denominator by 3.
Working: 42 ÷ 3/45 ÷ 3 = 14/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).
Working: 14 ÷ 15 = 0.933333 (93.3333%)

Key Values:
- Simplified Fraction: 14/15
- Mixed Number Form: 14/15
- Decimal Value: 0.933333
- Percentage: 93.3333%

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3/9 + 3/5 = 14/15

Simplified Fraction

14/15

Mixed Number

Proper (14/15)

Decimal Value

0.933333

Percentage

93.3333%

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

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 3/5 by 9 so both fractions share the common base 45.

3 × 5/9 × 5 = 15/45 and 3 × 9/5 × 9 = 27/45

Step 3

Add the Numerators

Now add the numerators (15 + 27 = 42) and keep the common denominator 45 unchanged.

15 + 27/45 = 42/45

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 45, which is 3. Divide both the numerator and denominator by 3.

42 ÷ 3/45 ÷ 3 = 14/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 15 produces a repeating decimal (approximately 0.933333, or 93.3333%).

14 ÷ 15 = 0.933333 (93.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/15`
Mixed Number Form	`14/15`
Decimal Form	`0.933333`
Percentage	`93.3333%`

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Frequently Asked Questions

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

3/9 + 3/5 in simplest fraction form is 14/15.

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

3/9 + 3/5 converted to a decimal is 0.933333.

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

3/9 + 3/5 expressed as a percentage is 93.3333%.

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

It results in a repeating decimal (approximately 0.933333...) because the denominator contains prime factors other than 2 and 5.