What is 2/10 plus 5/18? (Answer: 43/90)

Exact Answer

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Problem: What is 2/10 plus 5/18?
Formula / Expression: 2/10 + 5/18
Final Answer: 43/90
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 10 × 18 = 180, keeping the calculation simpler).
Working: LCD(10, 18) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/10 by 9, and multiply the numerator and denominator of 5/18 by 5 so both fractions share the common base 90.
Working: 2 × 9/10 × 9 = 18/90 and 5 × 5/18 × 5 = 25/90

Step 3: Add the Numerators
Now add the numerators (18 + 25 = 43) and keep the common denominator 90 unchanged.
Working: 18 + 25/90 = 43/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 90 is 1, confirming that 43/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 90 produces a repeating decimal (approximately 0.477778, or 47.7778%).
Working: 43 ÷ 90 = 0.477778 (47.7778%)

Key Values:
- Simplified Fraction: 43/90
- Mixed Number Form: 43/90
- Decimal Value: 0.477778
- Percentage: 47.7778%

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Solved with FractionsCalc:
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2/10 + 5/18 = 43/90

Simplified Fraction

43/90

Mixed Number

Proper (43/90)

Decimal Value

0.477778

Percentage

47.7778%

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Step-by-Step Solution: 2/10 + 5/18

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 18 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 10 × 18 = 180, keeping the calculation simpler).

LCD(10, 18) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/10 by 9, and multiply the numerator and denominator of 5/18 by 5 so both fractions share the common base 90.

2 × 9/10 × 9 = 18/90 and 5 × 5/18 × 5 = 25/90

Step 3

Add the Numerators

Now add the numerators (18 + 25 = 43) and keep the common denominator 90 unchanged.

18 + 25/90 = 43/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 90 is 1, confirming that 43/90 cannot be reduced further—it is already in its simplest irreducible form.

43/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 90 produces a repeating decimal (approximately 0.477778, or 47.7778%).

43 ÷ 90 = 0.477778 (47.7778%)

Visual Representation

The diagram below illustrates 2/10 plus 5/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/90`
Mixed Number Form	`43/90`
Decimal Form	`0.477778`
Percentage	`47.7778%`

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Frequently Asked Questions

What is 2/10 plus 5/18 as a fraction?

2/10 + 5/18 in simplest fraction form is 43/90.

What is 2/10 plus 5/18 as a decimal?

2/10 + 5/18 converted to a decimal is 0.477778.

What is 2/10 plus 5/18 as a percentage?

2/10 + 5/18 expressed as a percentage is 47.7778%.

Does 2/10 plus 5/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.477778...) because the denominator contains prime factors other than 2 and 5.