What is 7/26 plus 9/13? (Answer: 25/26)

Exact Answer

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Problem: What is 7/26 plus 9/13?
Formula / Expression: 7/26 + 9/13
Final Answer: 25/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.
Working: LCD(26, 13) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 7/26 by 1, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.
Working: 7 × 1/26 × 1 = 7/26 and 9 × 2/13 × 2 = 18/26

Step 3: Add the Numerators
Now add the numerators (7 + 18 = 25) and keep the common denominator 26 unchanged.
Working: 7 + 18/26 = 25/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 26 is 1, confirming that 25/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 26 produces a repeating decimal (approximately 0.961538, or 96.1538%).
Working: 25 ÷ 26 = 0.961538 (96.1538%)

Key Values:
- Simplified Fraction: 25/26
- Mixed Number Form: 25/26
- Decimal Value: 0.961538
- Percentage: 96.1538%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-26-plus-9-13/
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7/26 + 9/13 = 25/26

Simplified Fraction

25/26

Mixed Number

Proper (25/26)

Decimal Value

0.961538

Percentage

96.1538%

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Step-by-Step Solution: 7/26 + 9/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 26 is an exact multiple of 13 (13 × 2 = 26). The Least Common Denominator (LCD) is simply 26, meaning we only need to scale one fraction.

LCD(26, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 7/26 by 1, and multiply the numerator and denominator of 9/13 by 2 so both fractions share the common base 26.

7 × 1/26 × 1 = 7/26 and 9 × 2/13 × 2 = 18/26

Step 3

Add the Numerators

Now add the numerators (7 + 18 = 25) and keep the common denominator 26 unchanged.

7 + 18/26 = 25/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 26 is 1, confirming that 25/26 cannot be reduced further—it is already in its simplest irreducible form.

25/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 26 produces a repeating decimal (approximately 0.961538, or 96.1538%).

25 ÷ 26 = 0.961538 (96.1538%)

Visual Representation

The diagram below illustrates 7/26 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/26`
Mixed Number Form	`25/26`
Decimal Form	`0.961538`
Percentage	`96.1538%`

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Frequently Asked Questions

What is 7/26 plus 9/13 as a fraction?

7/26 + 9/13 in simplest fraction form is 25/26.

What is 7/26 plus 9/13 as a decimal?

7/26 + 9/13 converted to a decimal is 0.961538.

What is 7/26 plus 9/13 as a percentage?

7/26 + 9/13 expressed as a percentage is 96.1538%.

Does 7/26 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.961538...) because the denominator contains prime factors other than 2 and 5.