What is 5/46 plus 2/9? (Answer: 137/414)

Exact Answer

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Problem: What is 5/46 plus 2/9?
Formula / Expression: 5/46 + 2/9
Final Answer: 137/414
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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 5/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.
Working: 5 × 9/46 × 9 = 45/414 and 2 × 46/9 × 46 = 92/414

Step 3: Add the Numerators
Now add the numerators (45 + 92 = 137) and keep the common denominator 414 unchanged.
Working: 45 + 92/414 = 137/414

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 137 and 414 is 1, confirming that 137/414 cannot be reduced further—it is already in its simplest irreducible form.
Working: 137/414

Step 5: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 414 produces a repeating decimal (approximately 0.330918, or 33.0918%).
Working: 137 ÷ 414 = 0.330918 (33.0918%)

Key Values:
- Simplified Fraction: 137/414
- Mixed Number Form: 137/414
- Decimal Value: 0.330918
- Percentage: 33.0918%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-46-plus-2-9/
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5/46 + 2/9 = 137/414

Simplified Fraction

137/414

Mixed Number

Proper (137/414)

Decimal Value

0.330918

Percentage

33.0918%

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Step-by-Step Solution: 5/46 + 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 5/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.

5 × 9/46 × 9 = 45/414 and 2 × 46/9 × 46 = 92/414

Step 3

Add the Numerators

Now add the numerators (45 + 92 = 137) and keep the common denominator 414 unchanged.

45 + 92/414 = 137/414

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 137 and 414 is 1, confirming that 137/414 cannot be reduced further—it is already in its simplest irreducible form.

137/414

Step 5

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 414 produces a repeating decimal (approximately 0.330918, or 33.0918%).

137 ÷ 414 = 0.330918 (33.0918%)

Visual Representation

The diagram below illustrates 5/46 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/414`
Mixed Number Form	`137/414`
Decimal Form	`0.330918`
Percentage	`33.0918%`

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Frequently Asked Questions

What is 5/46 plus 2/9 as a fraction?

5/46 + 2/9 in simplest fraction form is 137/414.

What is 5/46 plus 2/9 as a decimal?

5/46 + 2/9 converted to a decimal is 0.330918.

What is 5/46 plus 2/9 as a percentage?

5/46 + 2/9 expressed as a percentage is 33.0918%.

Does 5/46 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.330918...) because the denominator contains prime factors other than 2 and 5.