What is 4/47 plus 2/9? (Answer: 130/423)

Exact Answer

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Problem: What is 4/47 plus 2/9?
Formula / Expression: 4/47 + 2/9
Final Answer: 130/423
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 47 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 9 = 423.
Working: LCD(47, 9) = 423

Step 2: Convert to Equivalent Fractions with Common Denominator 423
Multiply the numerator and denominator of 4/47 by 9, and multiply the numerator and denominator of 2/9 by 47 so both fractions share the common base 423.
Working: 4 × 9/47 × 9 = 36/423 and 2 × 47/9 × 47 = 94/423

Step 3: Add the Numerators
Now add the numerators (36 + 94 = 130) and keep the common denominator 423 unchanged.
Working: 36 + 94/423 = 130/423

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 130 and 423 is 1, confirming that 130/423 cannot be reduced further—it is already in its simplest irreducible form.
Working: 130/423

Step 5: Decimal & Percentage Representation
Dividing the numerator 130 by denominator 423 produces a repeating decimal (approximately 0.307329, or 30.7329%).
Working: 130 ÷ 423 = 0.307329 (30.7329%)

Key Values:
- Simplified Fraction: 130/423
- Mixed Number Form: 130/423
- Decimal Value: 0.307329
- Percentage: 30.7329%

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Solved with FractionsCalc:
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4/47 + 2/9 = 130/423

Simplified Fraction

130/423

Mixed Number

Proper (130/423)

Decimal Value

0.307329

Percentage

30.7329%

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Step-by-Step Solution: 4/47 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 47 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 47 × 9 = 423.

LCD(47, 9) = 423

Step 2

Convert to Equivalent Fractions with Common Denominator 423

Multiply the numerator and denominator of 4/47 by 9, and multiply the numerator and denominator of 2/9 by 47 so both fractions share the common base 423.

4 × 9/47 × 9 = 36/423 and 2 × 47/9 × 47 = 94/423

Step 3

Add the Numerators

Now add the numerators (36 + 94 = 130) and keep the common denominator 423 unchanged.

36 + 94/423 = 130/423

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 130 and 423 is 1, confirming that 130/423 cannot be reduced further—it is already in its simplest irreducible form.

130/423

Step 5

Decimal & Percentage Representation

Dividing the numerator 130 by denominator 423 produces a repeating decimal (approximately 0.307329, or 30.7329%).

130 ÷ 423 = 0.307329 (30.7329%)

Visual Representation

The diagram below illustrates 4/47 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`130/423`
Mixed Number Form	`130/423`
Decimal Form	`0.307329`
Percentage	`30.7329%`

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Frequently Asked Questions

What is 4/47 plus 2/9 as a fraction?

4/47 + 2/9 in simplest fraction form is 130/423.

What is 4/47 plus 2/9 as a decimal?

4/47 + 2/9 converted to a decimal is 0.307329.

What is 4/47 plus 2/9 as a percentage?

4/47 + 2/9 expressed as a percentage is 30.7329%.

Does 4/47 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.307329...) because the denominator contains prime factors other than 2 and 5.