What is 4/46 plus 2/9? (Answer: 64/207)

Exact Answer

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Problem: What is 4/46 plus 2/9?
Formula / Expression: 4/46 + 2/9
Final Answer: 64/207
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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 4/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.
Working: 4 × 9/46 × 9 = 36/414 and 2 × 46/9 × 46 = 92/414

Step 3: Add the Numerators
Now add the numerators (36 + 92 = 128) and keep the common denominator 414 unchanged.
Working: 36 + 92/414 = 128/414

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 128 and 414, which is 2. Divide both the numerator and denominator by 2.
Working: 128 ÷ 2/414 ÷ 2 = 64/207

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 207 produces a repeating decimal (approximately 0.309179, or 30.9179%).
Working: 64 ÷ 207 = 0.309179 (30.9179%)

Key Values:
- Simplified Fraction: 64/207
- Mixed Number Form: 64/207
- Decimal Value: 0.309179
- Percentage: 30.9179%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-46-plus-2-9/
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4/46 + 2/9 = 64/207

Simplified Fraction

64/207

Mixed Number

Proper (64/207)

Decimal Value

0.309179

Percentage

30.9179%

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Step-by-Step Solution: 4/46 + 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 4/46 by 9, and multiply the numerator and denominator of 2/9 by 46 so both fractions share the common base 414.

4 × 9/46 × 9 = 36/414 and 2 × 46/9 × 46 = 92/414

Step 3

Add the Numerators

Now add the numerators (36 + 92 = 128) and keep the common denominator 414 unchanged.

36 + 92/414 = 128/414

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 128 and 414, which is 2. Divide both the numerator and denominator by 2.

128 ÷ 2/414 ÷ 2 = 64/207

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 207 produces a repeating decimal (approximately 0.309179, or 30.9179%).

64 ÷ 207 = 0.309179 (30.9179%)

Visual Representation

The diagram below illustrates 4/46 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/207`
Mixed Number Form	`64/207`
Decimal Form	`0.309179`
Percentage	`30.9179%`

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Frequently Asked Questions

What is 4/46 plus 2/9 as a fraction?

4/46 + 2/9 in simplest fraction form is 64/207.

What is 4/46 plus 2/9 as a decimal?

4/46 + 2/9 converted to a decimal is 0.309179.

What is 4/46 plus 2/9 as a percentage?

4/46 + 2/9 expressed as a percentage is 30.9179%.

Does 4/46 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309179...) because the denominator contains prime factors other than 2 and 5.