What is 3/26 plus 9/39? (Answer: 9/26)

Exact Answer

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Problem: What is 3/26 plus 9/39?
Formula / Expression: 3/26 + 9/39
Final Answer: 9/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 39 share a common factor (GCD = 13). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 26 × 39 = 1014, keeping the calculation simpler).
Working: LCD(26, 39) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 3/26 by 3, and multiply the numerator and denominator of 9/39 by 2 so both fractions share the common base 78.
Working: 3 × 3/26 × 3 = 9/78 and 9 × 2/39 × 2 = 18/78

Step 3: Add the Numerators
Now add the numerators (9 + 18 = 27) and keep the common denominator 78 unchanged.
Working: 9 + 18/78 = 27/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 78, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/78 ÷ 3 = 9/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 26 produces a repeating decimal (approximately 0.346154, or 34.6154%).
Working: 9 ÷ 26 = 0.346154 (34.6154%)

Key Values:
- Simplified Fraction: 9/26
- Mixed Number Form: 9/26
- Decimal Value: 0.346154
- Percentage: 34.6154%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-26-plus-9-39/
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3/26 + 9/39 = 9/26

Simplified Fraction

9/26

Mixed Number

Proper (9/26)

Decimal Value

0.346154

Percentage

34.6154%

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Step-by-Step Solution: 3/26 + 9/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 39 share a common factor (GCD = 13). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 26 × 39 = 1014, keeping the calculation simpler).

LCD(26, 39) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 3/26 by 3, and multiply the numerator and denominator of 9/39 by 2 so both fractions share the common base 78.

3 × 3/26 × 3 = 9/78 and 9 × 2/39 × 2 = 18/78

Step 3

Add the Numerators

Now add the numerators (9 + 18 = 27) and keep the common denominator 78 unchanged.

9 + 18/78 = 27/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 78, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/78 ÷ 3 = 9/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 26 produces a repeating decimal (approximately 0.346154, or 34.6154%).

9 ÷ 26 = 0.346154 (34.6154%)

Visual Representation

The diagram below illustrates 3/26 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/26`
Mixed Number Form	`9/26`
Decimal Form	`0.346154`
Percentage	`34.6154%`

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Frequently Asked Questions

What is 3/26 plus 9/39 as a fraction?

3/26 + 9/39 in simplest fraction form is 9/26.

What is 3/26 plus 9/39 as a decimal?

3/26 + 9/39 converted to a decimal is 0.346154.

What is 3/26 plus 9/39 as a percentage?

3/26 + 9/39 expressed as a percentage is 34.6154%.

Does 3/26 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.346154...) because the denominator contains prime factors other than 2 and 5.