What is 5/22 plus 2/3? (Answer: 59/66)

Exact Answer

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Problem: What is 5/22 plus 2/3?
Formula / Expression: 5/22 + 2/3
Final Answer: 59/66
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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 5/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.
Working: 5 × 3/22 × 3 = 15/66 and 2 × 22/3 × 22 = 44/66

Step 3: Add the Numerators
Now add the numerators (15 + 44 = 59) and keep the common denominator 66 unchanged.
Working: 15 + 44/66 = 59/66

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 66 is 1, confirming that 59/66 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/66

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 66 produces a repeating decimal (approximately 0.893939, or 89.3939%).
Working: 59 ÷ 66 = 0.893939 (89.3939%)

Key Values:
- Simplified Fraction: 59/66
- Mixed Number Form: 59/66
- Decimal Value: 0.893939
- Percentage: 89.3939%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-2-3/
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5/22 + 2/3 = 59/66

Simplified Fraction

59/66

Mixed Number

Proper (59/66)

Decimal Value

0.893939

Percentage

89.3939%

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Step-by-Step Solution: 5/22 + 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 5/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.

5 × 3/22 × 3 = 15/66 and 2 × 22/3 × 22 = 44/66

Step 3

Add the Numerators

Now add the numerators (15 + 44 = 59) and keep the common denominator 66 unchanged.

15 + 44/66 = 59/66

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 66 is 1, confirming that 59/66 cannot be reduced further—it is already in its simplest irreducible form.

59/66

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 66 produces a repeating decimal (approximately 0.893939, or 89.3939%).

59 ÷ 66 = 0.893939 (89.3939%)

Visual Representation

The diagram below illustrates 5/22 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/66`
Mixed Number Form	`59/66`
Decimal Form	`0.893939`
Percentage	`89.3939%`

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Frequently Asked Questions

What is 5/22 plus 2/3 as a fraction?

5/22 + 2/3 in simplest fraction form is 59/66.

What is 5/22 plus 2/3 as a decimal?

5/22 + 2/3 converted to a decimal is 0.893939.

What is 5/22 plus 2/3 as a percentage?

5/22 + 2/3 expressed as a percentage is 89.3939%.

Does 5/22 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.893939...) because the denominator contains prime factors other than 2 and 5.