What is 2/18 plus 3/8? (Answer: 35/72)

Exact Answer

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Problem: What is 2/18 plus 3/8?
Formula / Expression: 2/18 + 3/8
Final Answer: 35/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 18 × 8 = 144, keeping the calculation simpler).
Working: LCD(18, 8) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 2/18 by 4, and multiply the numerator and denominator of 3/8 by 9 so both fractions share the common base 72.
Working: 2 × 4/18 × 4 = 8/72 and 3 × 9/8 × 9 = 27/72

Step 3: Add the Numerators
Now add the numerators (8 + 27 = 35) and keep the common denominator 72 unchanged.
Working: 8 + 27/72 = 35/72

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 35 and 72 is 1, confirming that 35/72 cannot be reduced further—it is already in its simplest irreducible form.
Working: 35/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 72 produces a repeating decimal (approximately 0.486111, or 48.6111%).
Working: 35 ÷ 72 = 0.486111 (48.6111%)

Key Values:
- Simplified Fraction: 35/72
- Mixed Number Form: 35/72
- Decimal Value: 0.486111
- Percentage: 48.6111%

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Solved with FractionsCalc:
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2/18 + 3/8 = 35/72

Simplified Fraction

35/72

Mixed Number

Proper (35/72)

Decimal Value

0.486111

Percentage

48.6111%

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Step-by-Step Solution: 2/18 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 72 (which is smaller than their product 18 × 8 = 144, keeping the calculation simpler).

LCD(18, 8) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 2/18 by 4, and multiply the numerator and denominator of 3/8 by 9 so both fractions share the common base 72.

2 × 4/18 × 4 = 8/72 and 3 × 9/8 × 9 = 27/72

Step 3

Add the Numerators

Now add the numerators (8 + 27 = 35) and keep the common denominator 72 unchanged.

8 + 27/72 = 35/72

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 35 and 72 is 1, confirming that 35/72 cannot be reduced further—it is already in its simplest irreducible form.

35/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 72 produces a repeating decimal (approximately 0.486111, or 48.6111%).

35 ÷ 72 = 0.486111 (48.6111%)

Visual Representation

The diagram below illustrates 2/18 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/72`
Mixed Number Form	`35/72`
Decimal Form	`0.486111`
Percentage	`48.6111%`

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Frequently Asked Questions

What is 2/18 plus 3/8 as a fraction?

2/18 + 3/8 in simplest fraction form is 35/72.

What is 2/18 plus 3/8 as a decimal?

2/18 + 3/8 converted to a decimal is 0.486111.

What is 2/18 plus 3/8 as a percentage?

2/18 + 3/8 expressed as a percentage is 48.6111%.

Does 2/18 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.486111...) because the denominator contains prime factors other than 2 and 5.