What is 1/9 plus 4/18? (Answer: 1/3)

Exact Answer

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Problem: What is 1/9 plus 4/18?
Formula / Expression: 1/9 + 4/18
Final Answer: 1/3
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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(9, 18) = 18

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

Step 3: Add the Numerators
Now add the numerators (2 + 4 = 6) and keep the common denominator 18 unchanged.
Working: 2 + 4/18 = 6/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 18, which is 6. Divide both the numerator and denominator by 6.
Working: 6 ÷ 6/18 ÷ 6 = 1/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).
Working: 1 ÷ 3 = 0.333333 (33.3333%)

Key Values:
- Simplified Fraction: 1/3
- Mixed Number Form: 1/3
- Decimal Value: 0.333333
- Percentage: 33.3333%

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Solved with FractionsCalc:
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1/9 + 4/18 = 1/3

Simplified Fraction

1/3

Mixed Number

Proper (1/3)

Decimal Value

0.333333

Percentage

33.3333%

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

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(9, 18) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

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

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

Step 3

Add the Numerators

Now add the numerators (2 + 4 = 6) and keep the common denominator 18 unchanged.

2 + 4/18 = 6/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 18, which is 6. Divide both the numerator and denominator by 6.

6 ÷ 6/18 ÷ 6 = 1/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 3 produces a repeating decimal (approximately 0.333333, or 33.3333%).

1 ÷ 3 = 0.333333 (33.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/3`
Mixed Number Form	`1/3`
Decimal Form	`0.333333`
Percentage	`33.3333%`

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Frequently Asked Questions

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

1/9 + 4/18 in simplest fraction form is 1/3.

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

1/9 + 4/18 converted to a decimal is 0.333333.

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

1/9 + 4/18 expressed as a percentage is 33.3333%.

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

It results in a repeating decimal (approximately 0.333333...) because the denominator contains prime factors other than 2 and 5.