What is 2/8 plus 10/22? (Answer: 31/44)

Exact Answer

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Problem: What is 2/8 plus 10/22?
Formula / Expression: 2/8 + 10/22
Final Answer: 31/44
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 2/8 by 11, and multiply the numerator and denominator of 10/22 by 4 so both fractions share the common base 88.
Working: 2 × 11/8 × 11 = 22/88 and 10 × 4/22 × 4 = 40/88

Step 3: Add the Numerators
Now add the numerators (22 + 40 = 62) and keep the common denominator 88 unchanged.
Working: 22 + 40/88 = 62/88

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 88, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/88 ÷ 2 = 31/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 44 produces a repeating decimal (approximately 0.704545, or 70.4545%).
Working: 31 ÷ 44 = 0.704545 (70.4545%)

Key Values:
- Simplified Fraction: 31/44
- Mixed Number Form: 31/44
- Decimal Value: 0.704545
- Percentage: 70.4545%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-10-22/
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2/8 + 10/22 = 31/44

Simplified Fraction

31/44

Mixed Number

Proper (31/44)

Decimal Value

0.704545

Percentage

70.4545%

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Step-by-Step Solution: 2/8 + 10/22

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 22) = 88

Step 2

Convert to Equivalent Fractions with Common Denominator 88

Multiply the numerator and denominator of 2/8 by 11, and multiply the numerator and denominator of 10/22 by 4 so both fractions share the common base 88.

2 × 11/8 × 11 = 22/88 and 10 × 4/22 × 4 = 40/88

Step 3

Add the Numerators

Now add the numerators (22 + 40 = 62) and keep the common denominator 88 unchanged.

22 + 40/88 = 62/88

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 88, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/88 ÷ 2 = 31/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 44 produces a repeating decimal (approximately 0.704545, or 70.4545%).

31 ÷ 44 = 0.704545 (70.4545%)

Visual Representation

The diagram below illustrates 2/8 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/44`
Mixed Number Form	`31/44`
Decimal Form	`0.704545`
Percentage	`70.4545%`

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Frequently Asked Questions

What is 2/8 plus 10/22 as a fraction?

2/8 + 10/22 in simplest fraction form is 31/44.

What is 2/8 plus 10/22 as a decimal?

2/8 + 10/22 converted to a decimal is 0.704545.

What is 2/8 plus 10/22 as a percentage?

2/8 + 10/22 expressed as a percentage is 70.4545%.

Does 2/8 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.704545...) because the denominator contains prime factors other than 2 and 5.