What is 9/26 plus 2/5? (Answer: 97/130)

Exact Answer

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Problem: What is 9/26 plus 2/5?
Formula / Expression: 9/26 + 2/5
Final Answer: 97/130
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 5 = 130.
Working: LCD(26, 5) = 130

Step 2: Convert to Equivalent Fractions with Common Denominator 130
Multiply the numerator and denominator of 9/26 by 5, and multiply the numerator and denominator of 2/5 by 26 so both fractions share the common base 130.
Working: 9 × 5/26 × 5 = 45/130 and 2 × 26/5 × 26 = 52/130

Step 3: Add the Numerators
Now add the numerators (45 + 52 = 97) and keep the common denominator 130 unchanged.
Working: 45 + 52/130 = 97/130

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 130 is 1, confirming that 97/130 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/130

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 130 produces a repeating decimal (approximately 0.746154, or 74.6154%).
Working: 97 ÷ 130 = 0.746154 (74.6154%)

Key Values:
- Simplified Fraction: 97/130
- Mixed Number Form: 97/130
- Decimal Value: 0.746154
- Percentage: 74.6154%

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Solved with FractionsCalc:
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9/26 + 2/5 = 97/130

Simplified Fraction

97/130

Mixed Number

Proper (97/130)

Decimal Value

0.746154

Percentage

74.6154%

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Step-by-Step Solution: 9/26 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 5 = 130.

LCD(26, 5) = 130

Step 2

Convert to Equivalent Fractions with Common Denominator 130

Multiply the numerator and denominator of 9/26 by 5, and multiply the numerator and denominator of 2/5 by 26 so both fractions share the common base 130.

9 × 5/26 × 5 = 45/130 and 2 × 26/5 × 26 = 52/130

Step 3

Add the Numerators

Now add the numerators (45 + 52 = 97) and keep the common denominator 130 unchanged.

45 + 52/130 = 97/130

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 130 is 1, confirming that 97/130 cannot be reduced further—it is already in its simplest irreducible form.

97/130

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 130 produces a repeating decimal (approximately 0.746154, or 74.6154%).

97 ÷ 130 = 0.746154 (74.6154%)

Visual Representation

The diagram below illustrates 9/26 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/130`
Mixed Number Form	`97/130`
Decimal Form	`0.746154`
Percentage	`74.6154%`

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Frequently Asked Questions

What is 9/26 plus 2/5 as a fraction?

9/26 + 2/5 in simplest fraction form is 97/130.

What is 9/26 plus 2/5 as a decimal?

9/26 + 2/5 converted to a decimal is 0.746154.

What is 9/26 plus 2/5 as a percentage?

9/26 + 2/5 expressed as a percentage is 74.6154%.

Does 9/26 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.746154...) because the denominator contains prime factors other than 2 and 5.