What is 2/18 plus 7/39? (Answer: 34/117)

Exact Answer

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Problem: What is 2/18 plus 7/39?
Formula / Expression: 2/18 + 7/39
Final Answer: 34/117
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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 7/39 by 6 so both fractions share the common base 234.
Working: 2 × 13/18 × 13 = 26/234 and 7 × 6/39 × 6 = 42/234

Step 3: Add the Numerators
Now add the numerators (26 + 42 = 68) and keep the common denominator 234 unchanged.
Working: 26 + 42/234 = 68/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 68 ÷ 2/234 ÷ 2 = 34/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 117 produces a repeating decimal (approximately 0.290598, or 29.0598%).
Working: 34 ÷ 117 = 0.290598 (29.0598%)

Key Values:
- Simplified Fraction: 34/117
- Mixed Number Form: 34/117
- Decimal Value: 0.290598
- Percentage: 29.0598%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-18-plus-7-39/
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2/18 + 7/39 = 34/117

Simplified Fraction

34/117

Mixed Number

Proper (34/117)

Decimal Value

0.290598

Percentage

29.0598%

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Step-by-Step Solution: 2/18 + 7/39

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 7/39 by 6 so both fractions share the common base 234.

2 × 13/18 × 13 = 26/234 and 7 × 6/39 × 6 = 42/234

Step 3

Add the Numerators

Now add the numerators (26 + 42 = 68) and keep the common denominator 234 unchanged.

26 + 42/234 = 68/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 234, which is 2. Divide both the numerator and denominator by 2.

68 ÷ 2/234 ÷ 2 = 34/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 117 produces a repeating decimal (approximately 0.290598, or 29.0598%).

34 ÷ 117 = 0.290598 (29.0598%)

Visual Representation

The diagram below illustrates 2/18 plus 7/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/117`
Mixed Number Form	`34/117`
Decimal Form	`0.290598`
Percentage	`29.0598%`

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Frequently Asked Questions

What is 2/18 plus 7/39 as a fraction?

2/18 + 7/39 in simplest fraction form is 34/117.

What is 2/18 plus 7/39 as a decimal?

2/18 + 7/39 converted to a decimal is 0.290598.

What is 2/18 plus 7/39 as a percentage?

2/18 + 7/39 expressed as a percentage is 29.0598%.

Does 2/18 plus 7/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.290598...) because the denominator contains prime factors other than 2 and 5.