What is 5/18 plus 2/3? (Answer: 17/18)

Exact Answer

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Problem: What is 5/18 plus 2/3?
Formula / Expression: 5/18 + 2/3
Final Answer: 17/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 18 is an exact multiple of 3 (3 × 6 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.
Working: LCD(18, 3) = 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 2/3 by 6 so both fractions share the common base 18.
Working: 5 × 1/18 × 1 = 5/18 and 2 × 6/3 × 6 = 12/18

Step 3: Add the Numerators
Now add the numerators (5 + 12 = 17) and keep the common denominator 18 unchanged.
Working: 5 + 12/18 = 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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Solved with FractionsCalc:
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5/18 + 2/3 = 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: 5/18 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 18 is an exact multiple of 3 (3 × 6 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.

LCD(18, 3) = 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 2/3 by 6 so both fractions share the common base 18.

5 × 1/18 × 1 = 5/18 and 2 × 6/3 × 6 = 12/18

Step 3

Add the Numerators

Now add the numerators (5 + 12 = 17) and keep the common denominator 18 unchanged.

5 + 12/18 = 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 5/18 plus 2/3 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 5/18 plus 2/3 as a fraction?

5/18 + 2/3 in simplest fraction form is 17/18.

What is 5/18 plus 2/3 as a decimal?

5/18 + 2/3 converted to a decimal is 0.944444.

What is 5/18 plus 2/3 as a percentage?

5/18 + 2/3 expressed as a percentage is 94.4444%.

Does 5/18 plus 2/3 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.