What is 3/18 plus 9/39? (Answer: 31/78)

Exact Answer

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Problem: What is 3/18 plus 9/39?
Formula / Expression: 3/18 + 9/39
Final Answer: 31/78
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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 3/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.
Working: 3 × 13/18 × 13 = 39/234 and 9 × 6/39 × 6 = 54/234

Step 3: Add the Numerators
Now add the numerators (39 + 54 = 93) and keep the common denominator 234 unchanged.
Working: 39 + 54/234 = 93/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 234, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/234 ÷ 3 = 31/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 78 produces a repeating decimal (approximately 0.397436, or 39.7436%).
Working: 31 ÷ 78 = 0.397436 (39.7436%)

Key Values:
- Simplified Fraction: 31/78
- Mixed Number Form: 31/78
- Decimal Value: 0.397436
- Percentage: 39.7436%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-18-plus-9-39/
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3/18 + 9/39 = 31/78

Simplified Fraction

31/78

Mixed Number

Proper (31/78)

Decimal Value

0.397436

Percentage

39.7436%

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Step-by-Step Solution: 3/18 + 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 3/18 by 13, and multiply the numerator and denominator of 9/39 by 6 so both fractions share the common base 234.

3 × 13/18 × 13 = 39/234 and 9 × 6/39 × 6 = 54/234

Step 3

Add the Numerators

Now add the numerators (39 + 54 = 93) and keep the common denominator 234 unchanged.

39 + 54/234 = 93/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 234, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/234 ÷ 3 = 31/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 78 produces a repeating decimal (approximately 0.397436, or 39.7436%).

31 ÷ 78 = 0.397436 (39.7436%)

Visual Representation

The diagram below illustrates 3/18 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/78`
Mixed Number Form	`31/78`
Decimal Form	`0.397436`
Percentage	`39.7436%`

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Frequently Asked Questions

What is 3/18 plus 9/39 as a fraction?

3/18 + 9/39 in simplest fraction form is 31/78.

What is 3/18 plus 9/39 as a decimal?

3/18 + 9/39 converted to a decimal is 0.397436.

What is 3/18 plus 9/39 as a percentage?

3/18 + 9/39 expressed as a percentage is 39.7436%.

Does 3/18 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.397436...) because the denominator contains prime factors other than 2 and 5.