What is 5/18 plus 2/5? (Answer: 61/90)

Exact Answer

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Problem: What is 5/18 plus 2/5?
Formula / Expression: 5/18 + 2/5
Final Answer: 61/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 5 = 90.
Working: LCD(18, 5) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 5/18 by 5, and multiply the numerator and denominator of 2/5 by 18 so both fractions share the common base 90.
Working: 5 × 5/18 × 5 = 25/90 and 2 × 18/5 × 18 = 36/90

Step 3: Add the Numerators
Now add the numerators (25 + 36 = 61) and keep the common denominator 90 unchanged.
Working: 25 + 36/90 = 61/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 90 is 1, confirming that 61/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 90 produces a repeating decimal (approximately 0.677778, or 67.7778%).
Working: 61 ÷ 90 = 0.677778 (67.7778%)

Key Values:
- Simplified Fraction: 61/90
- Mixed Number Form: 61/90
- Decimal Value: 0.677778
- Percentage: 67.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-18-plus-2-5/
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5/18 + 2/5 = 61/90

Simplified Fraction

61/90

Mixed Number

Proper (61/90)

Decimal Value

0.677778

Percentage

67.7778%

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Step-by-Step Solution: 5/18 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 5 = 90.

LCD(18, 5) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 5/18 by 5, and multiply the numerator and denominator of 2/5 by 18 so both fractions share the common base 90.

5 × 5/18 × 5 = 25/90 and 2 × 18/5 × 18 = 36/90

Step 3

Add the Numerators

Now add the numerators (25 + 36 = 61) and keep the common denominator 90 unchanged.

25 + 36/90 = 61/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 90 is 1, confirming that 61/90 cannot be reduced further—it is already in its simplest irreducible form.

61/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 90 produces a repeating decimal (approximately 0.677778, or 67.7778%).

61 ÷ 90 = 0.677778 (67.7778%)

Visual Representation

The diagram below illustrates 5/18 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/90`
Mixed Number Form	`61/90`
Decimal Form	`0.677778`
Percentage	`67.7778%`

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Frequently Asked Questions

What is 5/18 plus 2/5 as a fraction?

5/18 + 2/5 in simplest fraction form is 61/90.

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

5/18 + 2/5 converted to a decimal is 0.677778.

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

5/18 + 2/5 expressed as a percentage is 67.7778%.

Does 5/18 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.677778...) because the denominator contains prime factors other than 2 and 5.