What is 4/15 plus 3/9? (Answer: 3/5)

Exact Answer

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Problem: What is 4/15 plus 3/9?
Formula / Expression: 4/15 + 3/9
Final Answer: 3/5
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/15 by 3, and multiply the numerator and denominator of 3/9 by 5 so both fractions share the common base 45.
Working: 4 × 3/15 × 3 = 12/45 and 3 × 5/9 × 5 = 15/45

Step 3: Add the Numerators
Now add the numerators (12 + 15 = 27) and keep the common denominator 45 unchanged.
Working: 12 + 15/45 = 27/45

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 45, which is 9. Divide both the numerator and denominator by 9.
Working: 27 ÷ 9/45 ÷ 9 = 3/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).
Working: 3 ÷ 5 = 0.6 (60%)

Key Values:
- Simplified Fraction: 3/5
- Mixed Number Form: 3/5
- Decimal Value: 0.6
- Percentage: 60%

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Solved with FractionsCalc:
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4/15 + 3/9 = 3/5

Simplified Fraction

3/5

Mixed Number

Proper (3/5)

Decimal Value

0.6

Percentage

60%

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Step-by-Step Solution: 4/15 + 3/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(15, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 4/15 by 3, and multiply the numerator and denominator of 3/9 by 5 so both fractions share the common base 45.

4 × 3/15 × 3 = 12/45 and 3 × 5/9 × 5 = 15/45

Step 3

Add the Numerators

Now add the numerators (12 + 15 = 27) and keep the common denominator 45 unchanged.

12 + 15/45 = 27/45

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 45, which is 9. Divide both the numerator and denominator by 9.

27 ÷ 9/45 ÷ 9 = 3/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).

3 ÷ 5 = 0.6 (60%)

Visual Representation

The diagram below illustrates 4/15 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/5`
Mixed Number Form	`3/5`
Decimal Form	`0.6`
Percentage	`60%`

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Frequently Asked Questions

What is 4/15 plus 3/9 as a fraction?

4/15 + 3/9 in simplest fraction form is 3/5.

What is 4/15 plus 3/9 as a decimal?

4/15 + 3/9 converted to a decimal is 0.6.

What is 4/15 plus 3/9 as a percentage?

4/15 + 3/9 expressed as a percentage is 60%.

Does 4/15 plus 3/9 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.6) because the denominator in simplest terms contains only prime factors 2 and/or 5.