What is 2/46 plus 2/9? (Answer: 55/207)

Exact Answer

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Problem: What is 2/46 plus 2/9?
Formula / Expression: 2/46 + 2/9
Final Answer: 55/207
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 9 = 414.
Working: LCD(46, 9) = 414

Step 2: Convert to Equivalent Fractions with Common Denominator 414
Multiply the numerator and denominator of 2/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.
Working: 2 × 9/46 × 9 = 18/414 and 2 × 46/9 × 46 = 92/414

Step 3: Add the Numerators
Now add the numerators (18 + 92 = 110) and keep the common denominator 414 unchanged.
Working: 18 + 92/414 = 110/414

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 110 and 414, which is 2. Divide both the numerator and denominator by 2.
Working: 110 ÷ 2/414 ÷ 2 = 55/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 207 produces a repeating decimal (approximately 0.2657, or 26.57%).
Working: 55 ÷ 207 = 0.2657 (26.57%)

Key Values:
- Simplified Fraction: 55/207
- Mixed Number Form: 55/207
- Decimal Value: 0.2657
- Percentage: 26.57%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-46-plus-2-9/
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2/46 + 2/9 = 55/207

Simplified Fraction

55/207

Mixed Number

Proper (55/207)

Decimal Value

0.2657

Percentage

26.57%

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Step-by-Step Solution: 2/46 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 9 = 414.

LCD(46, 9) = 414

Step 2

Convert to Equivalent Fractions with Common Denominator 414

Multiply the numerator and denominator of 2/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.

2 × 9/46 × 9 = 18/414 and 2 × 46/9 × 46 = 92/414

Step 3

Add the Numerators

Now add the numerators (18 + 92 = 110) and keep the common denominator 414 unchanged.

18 + 92/414 = 110/414

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 110 and 414, which is 2. Divide both the numerator and denominator by 2.

110 ÷ 2/414 ÷ 2 = 55/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 207 produces a repeating decimal (approximately 0.2657, or 26.57%).

55 ÷ 207 = 0.2657 (26.57%)

Visual Representation

The diagram below illustrates 2/46 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/207`
Mixed Number Form	`55/207`
Decimal Form	`0.2657`
Percentage	`26.57%`

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Frequently Asked Questions

What is 2/46 plus 2/9 as a fraction?

2/46 + 2/9 in simplest fraction form is 55/207.

What is 2/46 plus 2/9 as a decimal?

2/46 + 2/9 converted to a decimal is 0.2657.

What is 2/46 plus 2/9 as a percentage?

2/46 + 2/9 expressed as a percentage is 26.57%.

Does 2/46 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.2657...) because the denominator contains prime factors other than 2 and 5.