What is 5/27 plus 9/39? (Answer: 146/351)

Exact Answer

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Problem: What is 5/27 plus 9/39?
Formula / Expression: 5/27 + 9/39
Final Answer: 146/351
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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 5/27 by 13, and multiply the numerator and denominator of 9/39 by 9 so both fractions share the common base 351.
Working: 5 × 13/27 × 13 = 65/351 and 9 × 9/39 × 9 = 81/351

Step 3: Add the Numerators
Now add the numerators (65 + 81 = 146) and keep the common denominator 351 unchanged.
Working: 65 + 81/351 = 146/351

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 146 and 351 is 1, confirming that 146/351 cannot be reduced further—it is already in its simplest irreducible form.
Working: 146/351

Step 5: Decimal & Percentage Representation
Dividing the numerator 146 by denominator 351 produces a repeating decimal (approximately 0.415954, or 41.5954%).
Working: 146 ÷ 351 = 0.415954 (41.5954%)

Key Values:
- Simplified Fraction: 146/351
- Mixed Number Form: 146/351
- Decimal Value: 0.415954
- Percentage: 41.5954%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-27-plus-9-39/
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5/27 + 9/39 = 146/351

Simplified Fraction

146/351

Mixed Number

Proper (146/351)

Decimal Value

0.415954

Percentage

41.5954%

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Step-by-Step Solution: 5/27 + 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 5/27 by 13, and multiply the numerator and denominator of 9/39 by 9 so both fractions share the common base 351.

5 × 13/27 × 13 = 65/351 and 9 × 9/39 × 9 = 81/351

Step 3

Add the Numerators

Now add the numerators (65 + 81 = 146) and keep the common denominator 351 unchanged.

65 + 81/351 = 146/351

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 146 and 351 is 1, confirming that 146/351 cannot be reduced further—it is already in its simplest irreducible form.

146/351

Step 5

Decimal & Percentage Representation

Dividing the numerator 146 by denominator 351 produces a repeating decimal (approximately 0.415954, or 41.5954%).

146 ÷ 351 = 0.415954 (41.5954%)

Visual Representation

The diagram below illustrates 5/27 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`146/351`
Mixed Number Form	`146/351`
Decimal Form	`0.415954`
Percentage	`41.5954%`

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Frequently Asked Questions

What is 5/27 plus 9/39 as a fraction?

5/27 + 9/39 in simplest fraction form is 146/351.

What is 5/27 plus 9/39 as a decimal?

5/27 + 9/39 converted to a decimal is 0.415954.

What is 5/27 plus 9/39 as a percentage?

5/27 + 9/39 expressed as a percentage is 41.5954%.

Does 5/27 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.415954...) because the denominator contains prime factors other than 2 and 5.