What is 2/23 plus 2/22? (Answer: 45/253)

Exact Answer

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Problem: What is 2/23 plus 2/22?
Formula / Expression: 2/23 + 2/22
Final Answer: 45/253
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 22 = 506.
Working: LCD(23, 22) = 506

Step 2: Convert to Equivalent Fractions with Common Denominator 506
Multiply the numerator and denominator of 2/23 by 22, and multiply the numerator and denominator of 2/22 by 23 so both fractions share the common base 506.
Working: 2 × 22/23 × 22 = 44/506 and 2 × 23/22 × 23 = 46/506

Step 3: Add the Numerators
Now add the numerators (44 + 46 = 90) and keep the common denominator 506 unchanged.
Working: 44 + 46/506 = 90/506

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 506, which is 2. Divide both the numerator and denominator by 2.
Working: 90 ÷ 2/506 ÷ 2 = 45/253

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 253 produces a repeating decimal (approximately 0.177866, or 17.7866%).
Working: 45 ÷ 253 = 0.177866 (17.7866%)

Key Values:
- Simplified Fraction: 45/253
- Mixed Number Form: 45/253
- Decimal Value: 0.177866
- Percentage: 17.7866%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-23-plus-2-22/
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2/23 + 2/22 = 45/253

Simplified Fraction

45/253

Mixed Number

Proper (45/253)

Decimal Value

0.177866

Percentage

17.7866%

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Step-by-Step Solution: 2/23 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 22 = 506.

LCD(23, 22) = 506

Step 2

Convert to Equivalent Fractions with Common Denominator 506

Multiply the numerator and denominator of 2/23 by 22, and multiply the numerator and denominator of 2/22 by 23 so both fractions share the common base 506.

2 × 22/23 × 22 = 44/506 and 2 × 23/22 × 23 = 46/506

Step 3

Add the Numerators

Now add the numerators (44 + 46 = 90) and keep the common denominator 506 unchanged.

44 + 46/506 = 90/506

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 506, which is 2. Divide both the numerator and denominator by 2.

90 ÷ 2/506 ÷ 2 = 45/253

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 253 produces a repeating decimal (approximately 0.177866, or 17.7866%).

45 ÷ 253 = 0.177866 (17.7866%)

Visual Representation

The diagram below illustrates 2/23 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/253`
Mixed Number Form	`45/253`
Decimal Form	`0.177866`
Percentage	`17.7866%`

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Frequently Asked Questions

What is 2/23 plus 2/22 as a fraction?

2/23 + 2/22 in simplest fraction form is 45/253.

What is 2/23 plus 2/22 as a decimal?

2/23 + 2/22 converted to a decimal is 0.177866.

What is 2/23 plus 2/22 as a percentage?

2/23 + 2/22 expressed as a percentage is 17.7866%.

Does 2/23 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.177866...) because the denominator contains prime factors other than 2 and 5.