What is 2/50 plus 2/9? (Answer: 59/225)

Exact Answer

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Problem: What is 2/50 plus 2/9?
Formula / Expression: 2/50 + 2/9
Final Answer: 59/225
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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 2/50 by 9, and multiply the numerator and denominator of 2/9 by 50 so both fractions share the common base 450.
Working: 2 × 9/50 × 9 = 18/450 and 2 × 50/9 × 50 = 100/450

Step 3: Add the Numerators
Now add the numerators (18 + 100 = 118) and keep the common denominator 450 unchanged.
Working: 18 + 100/450 = 118/450

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 450, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/450 ÷ 2 = 59/225

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 225 produces a repeating decimal (approximately 0.262222, or 26.2222%).
Working: 59 ÷ 225 = 0.262222 (26.2222%)

Key Values:
- Simplified Fraction: 59/225
- Mixed Number Form: 59/225
- Decimal Value: 0.262222
- Percentage: 26.2222%

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Solved with FractionsCalc:
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2/50 + 2/9 = 59/225

Simplified Fraction

59/225

Mixed Number

Proper (59/225)

Decimal Value

0.262222

Percentage

26.2222%

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Step-by-Step Solution: 2/50 + 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 2/50 by 9, and multiply the numerator and denominator of 2/9 by 50 so both fractions share the common base 450.

2 × 9/50 × 9 = 18/450 and 2 × 50/9 × 50 = 100/450

Step 3

Add the Numerators

Now add the numerators (18 + 100 = 118) and keep the common denominator 450 unchanged.

18 + 100/450 = 118/450

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 450, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/450 ÷ 2 = 59/225

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 225 produces a repeating decimal (approximately 0.262222, or 26.2222%).

59 ÷ 225 = 0.262222 (26.2222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/225`
Mixed Number Form	`59/225`
Decimal Form	`0.262222`
Percentage	`26.2222%`

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Frequently Asked Questions

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

2/50 + 2/9 in simplest fraction form is 59/225.

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

2/50 + 2/9 converted to a decimal is 0.262222.

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

2/50 + 2/9 expressed as a percentage is 26.2222%.

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

It results in a repeating decimal (approximately 0.262222...) because the denominator contains prime factors other than 2 and 5.