What is 5/18 plus 5/9? (Answer: 5/6)

Exact Answer

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Problem: What is 5/18 plus 5/9?
Formula / Expression: 5/18 + 5/9
Final Answer: 5/6
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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 5/18 by 1, and multiply the numerator and denominator of 5/9 by 2 so both fractions share the common base 18.
Working: 5 × 1/18 × 1 = 5/18 and 5 × 2/9 × 2 = 10/18

Step 3: Add the Numerators
Now add the numerators (5 + 10 = 15) and keep the common denominator 18 unchanged.
Working: 5 + 10/18 = 15/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 18, which is 3. Divide both the numerator and denominator by 3.
Working: 15 ÷ 3/18 ÷ 3 = 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-18-plus-5-9/
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5/18 + 5/9 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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Step-by-Step Solution: 5/18 + 5/9

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 5/18 by 1, and multiply the numerator and denominator of 5/9 by 2 so both fractions share the common base 18.

5 × 1/18 × 1 = 5/18 and 5 × 2/9 × 2 = 10/18

Step 3

Add the Numerators

Now add the numerators (5 + 10 = 15) and keep the common denominator 18 unchanged.

5 + 10/18 = 15/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 18, which is 3. Divide both the numerator and denominator by 3.

15 ÷ 3/18 ÷ 3 = 5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

The diagram below illustrates 5/18 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

What is 5/18 plus 5/9 as a fraction?

5/18 + 5/9 in simplest fraction form is 5/6.

What is 5/18 plus 5/9 as a decimal?

5/18 + 5/9 converted to a decimal is 0.833333.

What is 5/18 plus 5/9 as a percentage?

5/18 + 5/9 expressed as a percentage is 83.3333%.

Does 5/18 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.