What is 3/46 plus 2/9? (Answer: 119/414)

Exact Answer

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Problem: What is 3/46 plus 2/9?
Formula / Expression: 3/46 + 2/9
Final Answer: 119/414
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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 3/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.
Working: 3 × 9/46 × 9 = 27/414 and 2 × 46/9 × 46 = 92/414

Step 3: Add the Numerators
Now add the numerators (27 + 92 = 119) and keep the common denominator 414 unchanged.
Working: 27 + 92/414 = 119/414

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 119 and 414 is 1, confirming that 119/414 cannot be reduced further—it is already in its simplest irreducible form.
Working: 119/414

Step 5: Decimal & Percentage Representation
Dividing the numerator 119 by denominator 414 produces a repeating decimal (approximately 0.28744, or 28.744%).
Working: 119 ÷ 414 = 0.28744 (28.744%)

Key Values:
- Simplified Fraction: 119/414
- Mixed Number Form: 119/414
- Decimal Value: 0.28744
- Percentage: 28.744%

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Solved with FractionsCalc:
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3/46 + 2/9 = 119/414

Simplified Fraction

119/414

Mixed Number

Proper (119/414)

Decimal Value

0.28744

Percentage

28.744%

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Step-by-Step Solution: 3/46 + 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 3/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.

3 × 9/46 × 9 = 27/414 and 2 × 46/9 × 46 = 92/414

Step 3

Add the Numerators

Now add the numerators (27 + 92 = 119) and keep the common denominator 414 unchanged.

27 + 92/414 = 119/414

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 119 and 414 is 1, confirming that 119/414 cannot be reduced further—it is already in its simplest irreducible form.

119/414

Step 5

Decimal & Percentage Representation

Dividing the numerator 119 by denominator 414 produces a repeating decimal (approximately 0.28744, or 28.744%).

119 ÷ 414 = 0.28744 (28.744%)

Visual Representation

The diagram below illustrates 3/46 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`119/414`
Mixed Number Form	`119/414`
Decimal Form	`0.28744`
Percentage	`28.744%`

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Frequently Asked Questions

What is 3/46 plus 2/9 as a fraction?

3/46 + 2/9 in simplest fraction form is 119/414.

What is 3/46 plus 2/9 as a decimal?

3/46 + 2/9 converted to a decimal is 0.28744.

What is 3/46 plus 2/9 as a percentage?

3/46 + 2/9 expressed as a percentage is 28.744%.

Does 3/46 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.28744...) because the denominator contains prime factors other than 2 and 5.