What is 3/27 plus 9/39? (Answer: 40/117)

Exact Answer

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Problem: What is 3/27 plus 9/39?
Formula / Expression: 3/27 + 9/39
Final Answer: 40/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 351 (which is smaller than their product 27 × 39 = 1053, keeping the calculation simpler).
Working: LCD(27, 39) = 351

Step 2: Convert to Equivalent Fractions with Common Denominator 351
Multiply the numerator and denominator of 3/27 by 13, and multiply the numerator and denominator of 9/39 by 9 so both fractions share the common base 351.
Working: 3 × 13/27 × 13 = 39/351 and 9 × 9/39 × 9 = 81/351

Step 3: Add the Numerators
Now add the numerators (39 + 81 = 120) and keep the common denominator 351 unchanged.
Working: 39 + 81/351 = 120/351

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 351, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/351 ÷ 3 = 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:
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3/27 + 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: 3/27 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 351 (which is smaller than their product 27 × 39 = 1053, keeping the calculation simpler).

LCD(27, 39) = 351

Step 2

Convert to Equivalent Fractions with Common Denominator 351

Multiply the numerator and denominator of 3/27 by 13, and multiply the numerator and denominator of 9/39 by 9 so both fractions share the common base 351.

3 × 13/27 × 13 = 39/351 and 9 × 9/39 × 9 = 81/351

Step 3

Add the Numerators

Now add the numerators (39 + 81 = 120) and keep the common denominator 351 unchanged.

39 + 81/351 = 120/351

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 351, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/351 ÷ 3 = 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 3/27 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 3/27 plus 9/39 as a fraction?

3/27 + 9/39 in simplest fraction form is 40/117.

What is 3/27 plus 9/39 as a decimal?

3/27 + 9/39 converted to a decimal is 0.34188.

What is 3/27 plus 9/39 as a percentage?

3/27 + 9/39 expressed as a percentage is 34.188%.

Does 3/27 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.