What is 2/18 plus 9/39? (Answer: 40/117)

Exact Answer

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Problem: What is 2/18 plus 9/39?
Formula / Expression: 2/18 + 9/39
Final Answer: 40/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 234 (which is smaller than their product 18 × 39 = 702, keeping the calculation simpler).
Working: LCD(18, 39) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 2/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.
Working: 2 × 13/18 × 13 = 26/234 and 9 × 6/39 × 6 = 54/234

Step 3: Add the Numerators
Now add the numerators (26 + 54 = 80) and keep the common denominator 234 unchanged.
Working: 26 + 54/234 = 80/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 80 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 80 ÷ 2/234 ÷ 2 = 40/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 117 produces a repeating decimal (approximately 0.34188, or 34.188%).
Working: 40 ÷ 117 = 0.34188 (34.188%)

Key Values:
- Simplified Fraction: 40/117
- Mixed Number Form: 40/117
- Decimal Value: 0.34188
- Percentage: 34.188%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-9-39/
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2/18 + 9/39 = 40/117

Simplified Fraction

40/117

Mixed Number

Proper (40/117)

Decimal Value

0.34188

Percentage

34.188%

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Step-by-Step Solution: 2/18 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 234 (which is smaller than their product 18 × 39 = 702, keeping the calculation simpler).

LCD(18, 39) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 2/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.

2 × 13/18 × 13 = 26/234 and 9 × 6/39 × 6 = 54/234

Step 3

Add the Numerators

Now add the numerators (26 + 54 = 80) and keep the common denominator 234 unchanged.

26 + 54/234 = 80/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 80 and 234, which is 2. Divide both the numerator and denominator by 2.

80 ÷ 2/234 ÷ 2 = 40/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 117 produces a repeating decimal (approximately 0.34188, or 34.188%).

40 ÷ 117 = 0.34188 (34.188%)

Visual Representation

The diagram below illustrates 2/18 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/117`
Mixed Number Form	`40/117`
Decimal Form	`0.34188`
Percentage	`34.188%`

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Frequently Asked Questions

What is 2/18 plus 9/39 as a fraction?

2/18 + 9/39 in simplest fraction form is 40/117.

What is 2/18 plus 9/39 as a decimal?

2/18 + 9/39 converted to a decimal is 0.34188.

What is 2/18 plus 9/39 as a percentage?

2/18 + 9/39 expressed as a percentage is 34.188%.

Does 2/18 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.34188...) because the denominator contains prime factors other than 2 and 5.