What is 3/50 plus 2/9? (Answer: 127/450)

Exact Answer

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Problem: What is 3/50 plus 2/9?
Formula / Expression: 3/50 + 2/9
Final Answer: 127/450
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 50 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 9 = 450.
Working: LCD(50, 9) = 450

Step 2: Convert to Equivalent Fractions with Common Denominator 450
Multiply the numerator and denominator of 3/50 by 9, and multiply the numerator and denominator of 2/9 by 50 so both fractions share the common base 450.
Working: 3 × 9/50 × 9 = 27/450 and 2 × 50/9 × 50 = 100/450

Step 3: Add the Numerators
Now add the numerators (27 + 100 = 127) and keep the common denominator 450 unchanged.
Working: 27 + 100/450 = 127/450

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 127 and 450 is 1, confirming that 127/450 cannot be reduced further—it is already in its simplest irreducible form.
Working: 127/450

Step 5: Decimal & Percentage Representation
Dividing the numerator 127 by denominator 450 produces a repeating decimal (approximately 0.282222, or 28.2222%).
Working: 127 ÷ 450 = 0.282222 (28.2222%)

Key Values:
- Simplified Fraction: 127/450
- Mixed Number Form: 127/450
- Decimal Value: 0.282222
- Percentage: 28.2222%

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Solved with FractionsCalc:
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3/50 + 2/9 = 127/450

Simplified Fraction

127/450

Mixed Number

Proper (127/450)

Decimal Value

0.282222

Percentage

28.2222%

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Step-by-Step Solution: 3/50 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 50 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 9 = 450.

LCD(50, 9) = 450

Step 2

Convert to Equivalent Fractions with Common Denominator 450

Multiply the numerator and denominator of 3/50 by 9, and multiply the numerator and denominator of 2/9 by 50 so both fractions share the common base 450.

3 × 9/50 × 9 = 27/450 and 2 × 50/9 × 50 = 100/450

Step 3

Add the Numerators

Now add the numerators (27 + 100 = 127) and keep the common denominator 450 unchanged.

27 + 100/450 = 127/450

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 127 and 450 is 1, confirming that 127/450 cannot be reduced further—it is already in its simplest irreducible form.

127/450

Step 5

Decimal & Percentage Representation

Dividing the numerator 127 by denominator 450 produces a repeating decimal (approximately 0.282222, or 28.2222%).

127 ÷ 450 = 0.282222 (28.2222%)

Visual Representation

The diagram below illustrates 3/50 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`127/450`
Mixed Number Form	`127/450`
Decimal Form	`0.282222`
Percentage	`28.2222%`

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Frequently Asked Questions

What is 3/50 plus 2/9 as a fraction?

3/50 + 2/9 in simplest fraction form is 127/450.

What is 3/50 plus 2/9 as a decimal?

3/50 + 2/9 converted to a decimal is 0.282222.

What is 3/50 plus 2/9 as a percentage?

3/50 + 2/9 expressed as a percentage is 28.2222%.

Does 3/50 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.282222...) because the denominator contains prime factors other than 2 and 5.