What is 5/22 plus 2/4? (Answer: 8/11)

Exact Answer

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Problem: What is 5/22 plus 2/4?
Formula / Expression: 5/22 + 2/4
Final Answer: 8/11
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).
Working: LCD(22, 4) = 44

Step 2: Convert to Equivalent Fractions with Common Denominator 44
Multiply the numerator and denominator of 5/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.
Working: 5 × 2/22 × 2 = 10/44 and 2 × 11/4 × 11 = 22/44

Step 3: Add the Numerators
Now add the numerators (10 + 22 = 32) and keep the common denominator 44 unchanged.
Working: 10 + 22/44 = 32/44

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 44, which is 4. Divide both the numerator and denominator by 4.
Working: 32 ÷ 4/44 ÷ 4 = 8/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 11 produces a repeating decimal (approximately 0.727273, or 72.7273%).
Working: 8 ÷ 11 = 0.727273 (72.7273%)

Key Values:
- Simplified Fraction: 8/11
- Mixed Number Form: 8/11
- Decimal Value: 0.727273
- Percentage: 72.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-2-4/
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5/22 + 2/4 = 8/11

Simplified Fraction

8/11

Mixed Number

Proper (8/11)

Decimal Value

0.727273

Percentage

72.7273%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 44 (which is smaller than their product 22 × 4 = 88, keeping the calculation simpler).

LCD(22, 4) = 44

Step 2

Convert to Equivalent Fractions with Common Denominator 44

Multiply the numerator and denominator of 5/22 by 2, and multiply the numerator and denominator of 2/4 by 11 so both fractions share the common base 44.

5 × 2/22 × 2 = 10/44 and 2 × 11/4 × 11 = 22/44

Step 3

Add the Numerators

Now add the numerators (10 + 22 = 32) and keep the common denominator 44 unchanged.

10 + 22/44 = 32/44

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 44, which is 4. Divide both the numerator and denominator by 4.

32 ÷ 4/44 ÷ 4 = 8/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 11 produces a repeating decimal (approximately 0.727273, or 72.7273%).

8 ÷ 11 = 0.727273 (72.7273%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/11`
Mixed Number Form	`8/11`
Decimal Form	`0.727273`
Percentage	`72.7273%`

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Frequently Asked Questions

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

5/22 + 2/4 in simplest fraction form is 8/11.

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

5/22 + 2/4 converted to a decimal is 0.727273.

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

5/22 + 2/4 expressed as a percentage is 72.7273%.

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

It results in a repeating decimal (approximately 0.727273...) because the denominator contains prime factors other than 2 and 5.