What is 3/9 plus 9/26? (Answer: 53/78)

Exact Answer

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Problem: What is 3/9 plus 9/26?
Formula / Expression: 3/9 + 9/26
Final Answer: 53/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 26 = 234.
Working: LCD(9, 26) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 3/9 by 26, and multiply the numerator and denominator of 9/26 by 9 so both fractions share the common base 234.
Working: 3 × 26/9 × 26 = 78/234 and 9 × 9/26 × 9 = 81/234

Step 3: Add the Numerators
Now add the numerators (78 + 81 = 159) and keep the common denominator 234 unchanged.
Working: 78 + 81/234 = 159/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 159 and 234, which is 3. Divide both the numerator and denominator by 3.
Working: 159 ÷ 3/234 ÷ 3 = 53/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 78 produces a repeating decimal (approximately 0.679487, or 67.9487%).
Working: 53 ÷ 78 = 0.679487 (67.9487%)

Key Values:
- Simplified Fraction: 53/78
- Mixed Number Form: 53/78
- Decimal Value: 0.679487
- Percentage: 67.9487%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-26/
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3/9 + 9/26 = 53/78

Simplified Fraction

53/78

Mixed Number

Proper (53/78)

Decimal Value

0.679487

Percentage

67.9487%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 26 = 234.

LCD(9, 26) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 3/9 by 26, and multiply the numerator and denominator of 9/26 by 9 so both fractions share the common base 234.

3 × 26/9 × 26 = 78/234 and 9 × 9/26 × 9 = 81/234

Step 3

Add the Numerators

Now add the numerators (78 + 81 = 159) and keep the common denominator 234 unchanged.

78 + 81/234 = 159/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 159 and 234, which is 3. Divide both the numerator and denominator by 3.

159 ÷ 3/234 ÷ 3 = 53/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 78 produces a repeating decimal (approximately 0.679487, or 67.9487%).

53 ÷ 78 = 0.679487 (67.9487%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/78`
Mixed Number Form	`53/78`
Decimal Form	`0.679487`
Percentage	`67.9487%`

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Frequently Asked Questions

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

3/9 + 9/26 in simplest fraction form is 53/78.

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

3/9 + 9/26 converted to a decimal is 0.679487.

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

3/9 + 9/26 expressed as a percentage is 67.9487%.

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

It results in a repeating decimal (approximately 0.679487...) because the denominator contains prime factors other than 2 and 5.