What is 3/47 plus 2/9? (Answer: 121/423)

Exact Answer

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Problem: What is 3/47 plus 2/9?
Formula / Expression: 3/47 + 2/9
Final Answer: 121/423
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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 3/47 by 9, and multiply the numerator and denominator of 2/9 by 47 so both fractions share the common base 423.
Working: 3 × 9/47 × 9 = 27/423 and 2 × 47/9 × 47 = 94/423

Step 3: Add the Numerators
Now add the numerators (27 + 94 = 121) and keep the common denominator 423 unchanged.
Working: 27 + 94/423 = 121/423

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 121 and 423 is 1, confirming that 121/423 cannot be reduced further—it is already in its simplest irreducible form.
Working: 121/423

Step 5: Decimal & Percentage Representation
Dividing the numerator 121 by denominator 423 produces a repeating decimal (approximately 0.286052, or 28.6052%).
Working: 121 ÷ 423 = 0.286052 (28.6052%)

Key Values:
- Simplified Fraction: 121/423
- Mixed Number Form: 121/423
- Decimal Value: 0.286052
- Percentage: 28.6052%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-47-plus-2-9/
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3/47 + 2/9 = 121/423

Simplified Fraction

121/423

Mixed Number

Proper (121/423)

Decimal Value

0.286052

Percentage

28.6052%

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Step-by-Step Solution: 3/47 + 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 3/47 by 9, and multiply the numerator and denominator of 2/9 by 47 so both fractions share the common base 423.

3 × 9/47 × 9 = 27/423 and 2 × 47/9 × 47 = 94/423

Step 3

Add the Numerators

Now add the numerators (27 + 94 = 121) and keep the common denominator 423 unchanged.

27 + 94/423 = 121/423

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 121 and 423 is 1, confirming that 121/423 cannot be reduced further—it is already in its simplest irreducible form.

121/423

Step 5

Decimal & Percentage Representation

Dividing the numerator 121 by denominator 423 produces a repeating decimal (approximately 0.286052, or 28.6052%).

121 ÷ 423 = 0.286052 (28.6052%)

Visual Representation

The diagram below illustrates 3/47 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`121/423`
Mixed Number Form	`121/423`
Decimal Form	`0.286052`
Percentage	`28.6052%`

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Frequently Asked Questions

What is 3/47 plus 2/9 as a fraction?

3/47 + 2/9 in simplest fraction form is 121/423.

What is 3/47 plus 2/9 as a decimal?

3/47 + 2/9 converted to a decimal is 0.286052.

What is 3/47 plus 2/9 as a percentage?

3/47 + 2/9 expressed as a percentage is 28.6052%.

Does 3/47 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.286052...) because the denominator contains prime factors other than 2 and 5.