What is 4/26 plus 4/9? (Answer: 70/117)

Exact Answer

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Problem: What is 4/26 plus 4/9?
Formula / Expression: 4/26 + 4/9
Final Answer: 70/117
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 4/26 by 9, and multiply the numerator and denominator of 4/9 by 26 so both fractions share the common base 234.
Working: 4 × 9/26 × 9 = 36/234 and 4 × 26/9 × 26 = 104/234

Step 3: Add the Numerators
Now add the numerators (36 + 104 = 140) and keep the common denominator 234 unchanged.
Working: 36 + 104/234 = 140/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 140 ÷ 2/234 ÷ 2 = 70/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 70 by denominator 117 produces a repeating decimal (approximately 0.598291, or 59.8291%).
Working: 70 ÷ 117 = 0.598291 (59.8291%)

Key Values:
- Simplified Fraction: 70/117
- Mixed Number Form: 70/117
- Decimal Value: 0.598291
- Percentage: 59.8291%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-26-plus-4-9/
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4/26 + 4/9 = 70/117

Simplified Fraction

70/117

Mixed Number

Proper (70/117)

Decimal Value

0.598291

Percentage

59.8291%

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Step-by-Step Solution: 4/26 + 4/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(26, 9) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 4/26 by 9, and multiply the numerator and denominator of 4/9 by 26 so both fractions share the common base 234.

4 × 9/26 × 9 = 36/234 and 4 × 26/9 × 26 = 104/234

Step 3

Add the Numerators

Now add the numerators (36 + 104 = 140) and keep the common denominator 234 unchanged.

36 + 104/234 = 140/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 234, which is 2. Divide both the numerator and denominator by 2.

140 ÷ 2/234 ÷ 2 = 70/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 70 by denominator 117 produces a repeating decimal (approximately 0.598291, or 59.8291%).

70 ÷ 117 = 0.598291 (59.8291%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`70/117`
Mixed Number Form	`70/117`
Decimal Form	`0.598291`
Percentage	`59.8291%`

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Frequently Asked Questions

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

4/26 + 4/9 in simplest fraction form is 70/117.

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

4/26 + 4/9 converted to a decimal is 0.598291.

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

4/26 + 4/9 expressed as a percentage is 59.8291%.

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

It results in a repeating decimal (approximately 0.598291...) because the denominator contains prime factors other than 2 and 5.