What is 4/26 plus 9/39? (Answer: 5/13)

Exact Answer

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Problem: What is 4/26 plus 9/39?
Formula / Expression: 4/26 + 9/39
Final Answer: 5/13
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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 4/26 by 3, and multiply the numerator and denominator of 9/39 by 2 so both fractions share the common base 78.
Working: 4 × 3/26 × 3 = 12/78 and 9 × 2/39 × 2 = 18/78

Step 3: Add the Numerators
Now add the numerators (12 + 18 = 30) and keep the common denominator 78 unchanged.
Working: 12 + 18/78 = 30/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 30 and 78, which is 6. Divide both the numerator and denominator by 6.
Working: 30 ÷ 6/78 ÷ 6 = 5/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).
Working: 5 ÷ 13 = 0.384615 (38.4615%)

Key Values:
- Simplified Fraction: 5/13
- Mixed Number Form: 5/13
- Decimal Value: 0.384615
- Percentage: 38.4615%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-26-plus-9-39/
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4/26 + 9/39 = 5/13

Simplified Fraction

5/13

Mixed Number

Proper (5/13)

Decimal Value

0.384615

Percentage

38.4615%

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Step-by-Step Solution: 4/26 + 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 4/26 by 3, and multiply the numerator and denominator of 9/39 by 2 so both fractions share the common base 78.

4 × 3/26 × 3 = 12/78 and 9 × 2/39 × 2 = 18/78

Step 3

Add the Numerators

Now add the numerators (12 + 18 = 30) and keep the common denominator 78 unchanged.

12 + 18/78 = 30/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 30 and 78, which is 6. Divide both the numerator and denominator by 6.

30 ÷ 6/78 ÷ 6 = 5/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).

5 ÷ 13 = 0.384615 (38.4615%)

Visual Representation

The diagram below illustrates 4/26 plus 9/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/13`
Mixed Number Form	`5/13`
Decimal Form	`0.384615`
Percentage	`38.4615%`

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Frequently Asked Questions

What is 4/26 plus 9/39 as a fraction?

4/26 + 9/39 in simplest fraction form is 5/13.

What is 4/26 plus 9/39 as a decimal?

4/26 + 9/39 converted to a decimal is 0.384615.

What is 4/26 plus 9/39 as a percentage?

4/26 + 9/39 expressed as a percentage is 38.4615%.

Does 4/26 plus 9/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.384615...) because the denominator contains prime factors other than 2 and 5.