What is 2/26 plus 7/39? (Answer: 10/39)

Exact Answer

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Problem: What is 2/26 plus 7/39?
Formula / Expression: 2/26 + 7/39
Final Answer: 10/39
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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 2/26 by 3, and multiply the numerator and denominator of 7/39 by 2 so both fractions share the common base 78.
Working: 2 × 3/26 × 3 = 6/78 and 7 × 2/39 × 2 = 14/78

Step 3: Add the Numerators
Now add the numerators (6 + 14 = 20) and keep the common denominator 78 unchanged.
Working: 6 + 14/78 = 20/78

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 78, which is 2. Divide both the numerator and denominator by 2.
Working: 20 ÷ 2/78 ÷ 2 = 10/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 39 produces a repeating decimal (approximately 0.25641, or 25.641%).
Working: 10 ÷ 39 = 0.25641 (25.641%)

Key Values:
- Simplified Fraction: 10/39
- Mixed Number Form: 10/39
- Decimal Value: 0.25641
- Percentage: 25.641%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-26-plus-7-39/
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2/26 + 7/39 = 10/39

Simplified Fraction

10/39

Mixed Number

Proper (10/39)

Decimal Value

0.25641

Percentage

25.641%

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Step-by-Step Solution: 2/26 + 7/39

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 2/26 by 3, and multiply the numerator and denominator of 7/39 by 2 so both fractions share the common base 78.

2 × 3/26 × 3 = 6/78 and 7 × 2/39 × 2 = 14/78

Step 3

Add the Numerators

Now add the numerators (6 + 14 = 20) and keep the common denominator 78 unchanged.

6 + 14/78 = 20/78

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 78, which is 2. Divide both the numerator and denominator by 2.

20 ÷ 2/78 ÷ 2 = 10/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 39 produces a repeating decimal (approximately 0.25641, or 25.641%).

10 ÷ 39 = 0.25641 (25.641%)

Visual Representation

The diagram below illustrates 2/26 plus 7/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/39`
Mixed Number Form	`10/39`
Decimal Form	`0.25641`
Percentage	`25.641%`

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Frequently Asked Questions

What is 2/26 plus 7/39 as a fraction?

2/26 + 7/39 in simplest fraction form is 10/39.

What is 2/26 plus 7/39 as a decimal?

2/26 + 7/39 converted to a decimal is 0.25641.

What is 2/26 plus 7/39 as a percentage?

2/26 + 7/39 expressed as a percentage is 25.641%.

Does 2/26 plus 7/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.25641...) because the denominator contains prime factors other than 2 and 5.