What is 8/22 plus 2/5? (Answer: 42/55)

Exact Answer

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Problem: What is 8/22 plus 2/5?
Formula / Expression: 8/22 + 2/5
Final Answer: 42/55
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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 8/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.
Working: 8 × 5/22 × 5 = 40/110 and 2 × 22/5 × 22 = 44/110

Step 3: Add the Numerators
Now add the numerators (40 + 44 = 84) and keep the common denominator 110 unchanged.
Working: 40 + 44/110 = 84/110

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 110, which is 2. Divide both the numerator and denominator by 2.
Working: 84 ÷ 2/110 ÷ 2 = 42/55

Step 5: Decimal & Percentage Representation
Dividing the numerator 42 by denominator 55 produces a repeating decimal (approximately 0.763636, or 76.3636%).
Working: 42 ÷ 55 = 0.763636 (76.3636%)

Key Values:
- Simplified Fraction: 42/55
- Mixed Number Form: 42/55
- Decimal Value: 0.763636
- Percentage: 76.3636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-22-plus-2-5/
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8/22 + 2/5 = 42/55

Simplified Fraction

42/55

Mixed Number

Proper (42/55)

Decimal Value

0.763636

Percentage

76.3636%

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

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 8/22 by 5, and multiply the numerator and denominator of 2/5 by 22 so both fractions share the common base 110.

8 × 5/22 × 5 = 40/110 and 2 × 22/5 × 22 = 44/110

Step 3

Add the Numerators

Now add the numerators (40 + 44 = 84) and keep the common denominator 110 unchanged.

40 + 44/110 = 84/110

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 110, which is 2. Divide both the numerator and denominator by 2.

84 ÷ 2/110 ÷ 2 = 42/55

Step 5

Decimal & Percentage Representation

Dividing the numerator 42 by denominator 55 produces a repeating decimal (approximately 0.763636, or 76.3636%).

42 ÷ 55 = 0.763636 (76.3636%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`42/55`
Mixed Number Form	`42/55`
Decimal Form	`0.763636`
Percentage	`76.3636%`

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Frequently Asked Questions

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

8/22 + 2/5 in simplest fraction form is 42/55.

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

8/22 + 2/5 converted to a decimal is 0.763636.

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

8/22 + 2/5 expressed as a percentage is 76.3636%.

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

It results in a repeating decimal (approximately 0.763636...) because the denominator contains prime factors other than 2 and 5.