What is 4/15 plus 4/9? (Answer: 32/45)

Exact Answer

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Problem: What is 4/15 plus 4/9?
Formula / Expression: 4/15 + 4/9
Final Answer: 32/45
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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 4/9 by 5 so both fractions share the common base 45.
Working: 4 × 3/15 × 3 = 12/45 and 4 × 5/9 × 5 = 20/45

Step 3: Add the Numerators
Now add the numerators (12 + 20 = 32) and keep the common denominator 45 unchanged.
Working: 12 + 20/45 = 32/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 45 is 1, confirming that 32/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 45 produces a repeating decimal (approximately 0.711111, or 71.1111%).
Working: 32 ÷ 45 = 0.711111 (71.1111%)

Key Values:
- Simplified Fraction: 32/45
- Mixed Number Form: 32/45
- Decimal Value: 0.711111
- Percentage: 71.1111%

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Solved with FractionsCalc:
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4/15 + 4/9 = 32/45

Simplified Fraction

32/45

Mixed Number

Proper (32/45)

Decimal Value

0.711111

Percentage

71.1111%

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

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 4/9 by 5 so both fractions share the common base 45.

4 × 3/15 × 3 = 12/45 and 4 × 5/9 × 5 = 20/45

Step 3

Add the Numerators

Now add the numerators (12 + 20 = 32) and keep the common denominator 45 unchanged.

12 + 20/45 = 32/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 45 is 1, confirming that 32/45 cannot be reduced further—it is already in its simplest irreducible form.

32/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 45 produces a repeating decimal (approximately 0.711111, or 71.1111%).

32 ÷ 45 = 0.711111 (71.1111%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/45`
Mixed Number Form	`32/45`
Decimal Form	`0.711111`
Percentage	`71.1111%`

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Frequently Asked Questions

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

4/15 + 4/9 in simplest fraction form is 32/45.

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

4/15 + 4/9 converted to a decimal is 0.711111.

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

4/15 + 4/9 expressed as a percentage is 71.1111%.

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

It results in a repeating decimal (approximately 0.711111...) because the denominator contains prime factors other than 2 and 5.