What is 3/9 plus 8/15? (Answer: 13/15)

Exact Answer

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Problem: What is 3/9 plus 8/15?
Formula / Expression: 3/9 + 8/15
Final Answer: 13/15
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).
Working: LCD(9, 15) = 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 8/15 by 3 so both fractions share the common base 45.
Working: 3 × 5/9 × 5 = 15/45 and 8 × 3/15 × 3 = 24/45

Step 3: Add the Numerators
Now add the numerators (15 + 24 = 39) and keep the common denominator 45 unchanged.
Working: 15 + 24/45 = 39/45

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 45, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/45 ÷ 3 = 13/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).
Working: 13 ÷ 15 = 0.866667 (86.6667%)

Key Values:
- Simplified Fraction: 13/15
- Mixed Number Form: 13/15
- Decimal Value: 0.866667
- Percentage: 86.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-8-15/
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3/9 + 8/15 = 13/15

Simplified Fraction

13/15

Mixed Number

Proper (13/15)

Decimal Value

0.866667

Percentage

86.6667%

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Step-by-Step Solution: 3/9 + 8/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 45 (which is smaller than their product 9 × 15 = 135, keeping the calculation simpler).

LCD(9, 15) = 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 8/15 by 3 so both fractions share the common base 45.

3 × 5/9 × 5 = 15/45 and 8 × 3/15 × 3 = 24/45

Step 3

Add the Numerators

Now add the numerators (15 + 24 = 39) and keep the common denominator 45 unchanged.

15 + 24/45 = 39/45

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 45, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/45 ÷ 3 = 13/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).

13 ÷ 15 = 0.866667 (86.6667%)

Visual Representation

The diagram below illustrates 3/9 plus 8/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/15`
Mixed Number Form	`13/15`
Decimal Form	`0.866667`
Percentage	`86.6667%`

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Frequently Asked Questions

What is 3/9 plus 8/15 as a fraction?

3/9 + 8/15 in simplest fraction form is 13/15.

What is 3/9 plus 8/15 as a decimal?

3/9 + 8/15 converted to a decimal is 0.866667.

What is 3/9 plus 8/15 as a percentage?

3/9 + 8/15 expressed as a percentage is 86.6667%.

Does 3/9 plus 8/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866667...) because the denominator contains prime factors other than 2 and 5.