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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.
Working: LCD(18, 9) = 18

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

Step 3: Add the Numerators
Now add the numerators (1 + 8 = 9) and keep the common denominator 18 unchanged.
Working: 1 + 8/18 = 9/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 9 and 18, which is 9. Divide both the numerator and denominator by 9.
Working: 9 ÷ 9/18 ÷ 9 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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1/18 + 4/9 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 1/18 + 4/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 18 is an exact multiple of 9 (9 × 2 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.

LCD(18, 9) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

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

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

Step 3

Add the Numerators

Now add the numerators (1 + 8 = 9) and keep the common denominator 18 unchanged.

1 + 8/18 = 9/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 9 and 18, which is 9. Divide both the numerator and denominator by 9.

9 ÷ 9/18 ÷ 9 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 1/18 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 1/18 plus 4/9 as a fraction?

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

What is 1/18 plus 4/9 as a decimal?

1/18 + 4/9 converted to a decimal is 0.5.

What is 1/18 plus 4/9 as a percentage?

1/18 + 4/9 expressed as a percentage is 50%.

Does 1/18 plus 4/9 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.