What is 4/22 plus 2/3? (Answer: 28/33)

Exact Answer

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Problem: What is 4/22 plus 2/3?
Formula / Expression: 4/22 + 2/3
Final Answer: 28/33
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.
Working: LCD(22, 3) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 4/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.
Working: 4 × 3/22 × 3 = 12/66 and 2 × 22/3 × 22 = 44/66

Step 3: Add the Numerators
Now add the numerators (12 + 44 = 56) and keep the common denominator 66 unchanged.
Working: 12 + 44/66 = 56/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 56 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 56 ÷ 2/66 ÷ 2 = 28/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 33 produces a repeating decimal (approximately 0.848485, or 84.8485%).
Working: 28 ÷ 33 = 0.848485 (84.8485%)

Key Values:
- Simplified Fraction: 28/33
- Mixed Number Form: 28/33
- Decimal Value: 0.848485
- Percentage: 84.8485%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-22-plus-2-3/
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4/22 + 2/3 = 28/33

Simplified Fraction

28/33

Mixed Number

Proper (28/33)

Decimal Value

0.848485

Percentage

84.8485%

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Step-by-Step Solution: 4/22 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.

LCD(22, 3) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 4/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.

4 × 3/22 × 3 = 12/66 and 2 × 22/3 × 22 = 44/66

Step 3

Add the Numerators

Now add the numerators (12 + 44 = 56) and keep the common denominator 66 unchanged.

12 + 44/66 = 56/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 56 and 66, which is 2. Divide both the numerator and denominator by 2.

56 ÷ 2/66 ÷ 2 = 28/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 33 produces a repeating decimal (approximately 0.848485, or 84.8485%).

28 ÷ 33 = 0.848485 (84.8485%)

Visual Representation

The diagram below illustrates 4/22 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/33`
Mixed Number Form	`28/33`
Decimal Form	`0.848485`
Percentage	`84.8485%`

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Frequently Asked Questions

What is 4/22 plus 2/3 as a fraction?

4/22 + 2/3 in simplest fraction form is 28/33.

What is 4/22 plus 2/3 as a decimal?

4/22 + 2/3 converted to a decimal is 0.848485.

What is 4/22 plus 2/3 as a percentage?

4/22 + 2/3 expressed as a percentage is 84.8485%.

Does 4/22 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.848485...) because the denominator contains prime factors other than 2 and 5.