What is 2/18 plus 3/10? (Answer: 37/90)

Exact Answer

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Problem: What is 2/18 plus 3/10?
Formula / Expression: 2/18 + 3/10
Final Answer: 37/90
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/18 by 5, and multiply the numerator and denominator of 3/10 by 9 so both fractions share the common base 90.
Working: 2 × 5/18 × 5 = 10/90 and 3 × 9/10 × 9 = 27/90

Step 3: Add the Numerators
Now add the numerators (10 + 27 = 37) and keep the common denominator 90 unchanged.
Working: 10 + 27/90 = 37/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 90 is 1, confirming that 37/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 90 produces a repeating decimal (approximately 0.411111, or 41.1111%).
Working: 37 ÷ 90 = 0.411111 (41.1111%)

Key Values:
- Simplified Fraction: 37/90
- Mixed Number Form: 37/90
- Decimal Value: 0.411111
- Percentage: 41.1111%

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Solved with FractionsCalc:
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2/18 + 3/10 = 37/90

Simplified Fraction

37/90

Mixed Number

Proper (37/90)

Decimal Value

0.411111

Percentage

41.1111%

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Step-by-Step Solution: 2/18 + 3/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(18, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/18 by 5, and multiply the numerator and denominator of 3/10 by 9 so both fractions share the common base 90.

2 × 5/18 × 5 = 10/90 and 3 × 9/10 × 9 = 27/90

Step 3

Add the Numerators

Now add the numerators (10 + 27 = 37) and keep the common denominator 90 unchanged.

10 + 27/90 = 37/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 90 is 1, confirming that 37/90 cannot be reduced further—it is already in its simplest irreducible form.

37/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 90 produces a repeating decimal (approximately 0.411111, or 41.1111%).

37 ÷ 90 = 0.411111 (41.1111%)

Visual Representation

The diagram below illustrates 2/18 plus 3/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/90`
Mixed Number Form	`37/90`
Decimal Form	`0.411111`
Percentage	`41.1111%`

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Frequently Asked Questions

What is 2/18 plus 3/10 as a fraction?

2/18 + 3/10 in simplest fraction form is 37/90.

What is 2/18 plus 3/10 as a decimal?

2/18 + 3/10 converted to a decimal is 0.411111.

What is 2/18 plus 3/10 as a percentage?

2/18 + 3/10 expressed as a percentage is 41.1111%.

Does 2/18 plus 3/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.411111...) because the denominator contains prime factors other than 2 and 5.