What is 8/39 plus 2/9? (Answer: 50/117)

Exact Answer

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Problem: What is 8/39 plus 2/9?
Formula / Expression: 8/39 + 2/9
Final Answer: 50/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 117 (which is smaller than their product 39 × 9 = 351, keeping the calculation simpler).
Working: LCD(39, 9) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 8/39 by 3, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.
Working: 8 × 3/39 × 3 = 24/117 and 2 × 13/9 × 13 = 26/117

Step 3: Add the Numerators
Now add the numerators (24 + 26 = 50) and keep the common denominator 117 unchanged.
Working: 24 + 26/117 = 50/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 50 and 117 is 1, confirming that 50/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 50/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 50 by denominator 117 produces a repeating decimal (approximately 0.42735, or 42.735%).
Working: 50 ÷ 117 = 0.42735 (42.735%)

Key Values:
- Simplified Fraction: 50/117
- Mixed Number Form: 50/117
- Decimal Value: 0.42735
- Percentage: 42.735%

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Solved with FractionsCalc:
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8/39 + 2/9 = 50/117

Simplified Fraction

50/117

Mixed Number

Proper (50/117)

Decimal Value

0.42735

Percentage

42.735%

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Step-by-Step Solution: 8/39 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 117 (which is smaller than their product 39 × 9 = 351, keeping the calculation simpler).

LCD(39, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 8/39 by 3, and multiply the numerator and denominator of 2/9 by 13 so both fractions share the common base 117.

8 × 3/39 × 3 = 24/117 and 2 × 13/9 × 13 = 26/117

Step 3

Add the Numerators

Now add the numerators (24 + 26 = 50) and keep the common denominator 117 unchanged.

24 + 26/117 = 50/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 50 and 117 is 1, confirming that 50/117 cannot be reduced further—it is already in its simplest irreducible form.

50/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 50 by denominator 117 produces a repeating decimal (approximately 0.42735, or 42.735%).

50 ÷ 117 = 0.42735 (42.735%)

Visual Representation

The diagram below illustrates 8/39 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`50/117`
Mixed Number Form	`50/117`
Decimal Form	`0.42735`
Percentage	`42.735%`

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Frequently Asked Questions

What is 8/39 plus 2/9 as a fraction?

8/39 + 2/9 in simplest fraction form is 50/117.

What is 8/39 plus 2/9 as a decimal?

8/39 + 2/9 converted to a decimal is 0.42735.

What is 8/39 plus 2/9 as a percentage?

8/39 + 2/9 expressed as a percentage is 42.735%.

Does 8/39 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.42735...) because the denominator contains prime factors other than 2 and 5.