What is 4/9 plus 1/2? (Answer: 17/18)

Exact Answer

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Problem: What is 4/9 plus 1/2?
Formula / Expression: 4/9 + 1/2
Final Answer: 17/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 2 = 18.
Working: LCD(9, 2) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 4/9 by 2, and multiply the numerator and denominator of 1/2 by 9 so both fractions share the common base 18.
Working: 4 × 2/9 × 2 = 8/18 and 1 × 9/2 × 9 = 9/18

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 18 unchanged.
Working: 8 + 9/18 = 17/18

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 18 is 1, confirming that 17/18 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 18 produces a repeating decimal (approximately 0.944444, or 94.4444%).
Working: 17 ÷ 18 = 0.944444 (94.4444%)

Key Values:
- Simplified Fraction: 17/18
- Mixed Number Form: 17/18
- Decimal Value: 0.944444
- Percentage: 94.4444%

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4/9 + 1/2 = 17/18

Simplified Fraction

17/18

Mixed Number

Proper (17/18)

Decimal Value

0.944444

Percentage

94.4444%

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Step-by-Step Solution: 4/9 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 2 = 18.

LCD(9, 2) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 4/9 by 2, and multiply the numerator and denominator of 1/2 by 9 so both fractions share the common base 18.

4 × 2/9 × 2 = 8/18 and 1 × 9/2 × 9 = 9/18

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 18 unchanged.

8 + 9/18 = 17/18

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 18 is 1, confirming that 17/18 cannot be reduced further—it is already in its simplest irreducible form.

17/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 18 produces a repeating decimal (approximately 0.944444, or 94.4444%).

17 ÷ 18 = 0.944444 (94.4444%)

Visual Representation

The diagram below illustrates 4/9 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/18`
Mixed Number Form	`17/18`
Decimal Form	`0.944444`
Percentage	`94.4444%`

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Frequently Asked Questions

What is 4/9 plus 1/2 as a fraction?

4/9 + 1/2 in simplest fraction form is 17/18.

What is 4/9 plus 1/2 as a decimal?

4/9 + 1/2 converted to a decimal is 0.944444.

What is 4/9 plus 1/2 as a percentage?

4/9 + 1/2 expressed as a percentage is 94.4444%.

Does 4/9 plus 1/2 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.944444...) because the denominator contains prime factors other than 2 and 5.