What is 2/25 plus 2/22? (Answer: 47/275)

Exact Answer

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Problem: What is 2/25 plus 2/22?
Formula / Expression: 2/25 + 2/22
Final Answer: 47/275
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 22 = 550.
Working: LCD(25, 22) = 550

Step 2: Convert to Equivalent Fractions with Common Denominator 550
Multiply the numerator and denominator of 2/25 by 22, and multiply the numerator and denominator of 2/22 by 25 so both fractions share the common base 550.
Working: 2 × 22/25 × 22 = 44/550 and 2 × 25/22 × 25 = 50/550

Step 3: Add the Numerators
Now add the numerators (44 + 50 = 94) and keep the common denominator 550 unchanged.
Working: 44 + 50/550 = 94/550

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 550, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/550 ÷ 2 = 47/275

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 275 produces a repeating decimal (approximately 0.170909, or 17.0909%).
Working: 47 ÷ 275 = 0.170909 (17.0909%)

Key Values:
- Simplified Fraction: 47/275
- Mixed Number Form: 47/275
- Decimal Value: 0.170909
- Percentage: 17.0909%

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Solved with FractionsCalc:
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2/25 + 2/22 = 47/275

Simplified Fraction

47/275

Mixed Number

Proper (47/275)

Decimal Value

0.170909

Percentage

17.0909%

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Step-by-Step Solution: 2/25 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 22 = 550.

LCD(25, 22) = 550

Step 2

Convert to Equivalent Fractions with Common Denominator 550

Multiply the numerator and denominator of 2/25 by 22, and multiply the numerator and denominator of 2/22 by 25 so both fractions share the common base 550.

2 × 22/25 × 22 = 44/550 and 2 × 25/22 × 25 = 50/550

Step 3

Add the Numerators

Now add the numerators (44 + 50 = 94) and keep the common denominator 550 unchanged.

44 + 50/550 = 94/550

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 550, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/550 ÷ 2 = 47/275

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 275 produces a repeating decimal (approximately 0.170909, or 17.0909%).

47 ÷ 275 = 0.170909 (17.0909%)

Visual Representation

The diagram below illustrates 2/25 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/275`
Mixed Number Form	`47/275`
Decimal Form	`0.170909`
Percentage	`17.0909%`

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Frequently Asked Questions

What is 2/25 plus 2/22 as a fraction?

2/25 + 2/22 in simplest fraction form is 47/275.

What is 2/25 plus 2/22 as a decimal?

2/25 + 2/22 converted to a decimal is 0.170909.

What is 2/25 plus 2/22 as a percentage?

2/25 + 2/22 expressed as a percentage is 17.0909%.

Does 2/25 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.170909...) because the denominator contains prime factors other than 2 and 5.