What is 2/22 plus 4/5? (Answer: 49/55)

Exact Answer

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Problem: What is 2/22 plus 4/5?
Formula / Expression: 2/22 + 4/5
Final Answer: 49/55
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 5 = 110.
Working: LCD(22, 5) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/22 by 5, and multiply the numerator and denominator of 4/5 by 22 so both fractions share the common base 110.
Working: 2 × 5/22 × 5 = 10/110 and 4 × 22/5 × 22 = 88/110

Step 3: Add the Numerators
Now add the numerators (10 + 88 = 98) and keep the common denominator 110 unchanged.
Working: 10 + 88/110 = 98/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 98 ÷ 2/110 ÷ 2 = 49/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 55 produces a repeating decimal (approximately 0.890909, or 89.0909%).
Working: 49 ÷ 55 = 0.890909 (89.0909%)

Key Values:
- Simplified Fraction: 49/55
- Mixed Number Form: 49/55
- Decimal Value: 0.890909
- Percentage: 89.0909%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-4-5/
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2/22 + 4/5 = 49/55

Simplified Fraction

49/55

Mixed Number

Proper (49/55)

Decimal Value

0.890909

Percentage

89.0909%

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Step-by-Step Solution: 2/22 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 5 = 110.

LCD(22, 5) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/22 by 5, and multiply the numerator and denominator of 4/5 by 22 so both fractions share the common base 110.

2 × 5/22 × 5 = 10/110 and 4 × 22/5 × 22 = 88/110

Step 3

Add the Numerators

Now add the numerators (10 + 88 = 98) and keep the common denominator 110 unchanged.

10 + 88/110 = 98/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 98 and 110, which is 2. Divide both the numerator and denominator by 2.

98 ÷ 2/110 ÷ 2 = 49/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 55 produces a repeating decimal (approximately 0.890909, or 89.0909%).

49 ÷ 55 = 0.890909 (89.0909%)

Visual Representation

The diagram below illustrates 2/22 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/55`
Mixed Number Form	`49/55`
Decimal Form	`0.890909`
Percentage	`89.0909%`

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Frequently Asked Questions

What is 2/22 plus 4/5 as a fraction?

2/22 + 4/5 in simplest fraction form is 49/55.

What is 2/22 plus 4/5 as a decimal?

2/22 + 4/5 converted to a decimal is 0.890909.

What is 2/22 plus 4/5 as a percentage?

2/22 + 4/5 expressed as a percentage is 89.0909%.

Does 2/22 plus 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.890909...) because the denominator contains prime factors other than 2 and 5.