What is 5/22 plus 2/8? (Answer: 21/44)

Exact Answer

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Problem: What is 5/22 plus 2/8?
Formula / Expression: 5/22 + 2/8
Final Answer: 21/44
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 88 (which is smaller than their product 22 × 8 = 176, keeping the calculation simpler).
Working: LCD(22, 8) = 88

Step 2: Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 5/22 by 4, and multiply the numerator and denominator of 2/8 by 11 so both fractions share the common base 88.
Working: 5 × 4/22 × 4 = 20/88 and 2 × 11/8 × 11 = 22/88

Step 3: Add the Numerators
Now add the numerators (20 + 22 = 42) and keep the common denominator 88 unchanged.
Working: 20 + 22/88 = 42/88

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 88, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/88 ÷ 2 = 21/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 44 produces a repeating decimal (approximately 0.477273, or 47.7273%).
Working: 21 ÷ 44 = 0.477273 (47.7273%)

Key Values:
- Simplified Fraction: 21/44
- Mixed Number Form: 21/44
- Decimal Value: 0.477273
- Percentage: 47.7273%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-22-plus-2-8/
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5/22 + 2/8 = 21/44

Simplified Fraction

21/44

Mixed Number

Proper (21/44)

Decimal Value

0.477273

Percentage

47.7273%

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Step-by-Step Solution: 5/22 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 88 (which is smaller than their product 22 × 8 = 176, keeping the calculation simpler).

LCD(22, 8) = 88

Step 2

Convert to Equivalent Fractions with Common Denominator 88

Multiply the numerator and denominator of 5/22 by 4, and multiply the numerator and denominator of 2/8 by 11 so both fractions share the common base 88.

5 × 4/22 × 4 = 20/88 and 2 × 11/8 × 11 = 22/88

Step 3

Add the Numerators

Now add the numerators (20 + 22 = 42) and keep the common denominator 88 unchanged.

20 + 22/88 = 42/88

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 88, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/88 ÷ 2 = 21/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 44 produces a repeating decimal (approximately 0.477273, or 47.7273%).

21 ÷ 44 = 0.477273 (47.7273%)

Visual Representation

The diagram below illustrates 5/22 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/44`
Mixed Number Form	`21/44`
Decimal Form	`0.477273`
Percentage	`47.7273%`

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Frequently Asked Questions

What is 5/22 plus 2/8 as a fraction?

5/22 + 2/8 in simplest fraction form is 21/44.

What is 5/22 plus 2/8 as a decimal?

5/22 + 2/8 converted to a decimal is 0.477273.

What is 5/22 plus 2/8 as a percentage?

5/22 + 2/8 expressed as a percentage is 47.7273%.

Does 5/22 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.477273...) because the denominator contains prime factors other than 2 and 5.