What is 2/8 plus 9/22? (Answer: 29/44)

Exact Answer

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Problem: What is 2/8 plus 9/22?
Formula / Expression: 2/8 + 9/22
Final Answer: 29/44
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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 9/22 by 4 so both fractions share the common base 88.
Working: 2 × 11/8 × 11 = 22/88 and 9 × 4/22 × 4 = 36/88

Step 3: Add the Numerators
Now add the numerators (22 + 36 = 58) and keep the common denominator 88 unchanged.
Working: 22 + 36/88 = 58/88

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 88, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/88 ÷ 2 = 29/44

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 44 produces a repeating decimal (approximately 0.659091, or 65.9091%).
Working: 29 ÷ 44 = 0.659091 (65.9091%)

Key Values:
- Simplified Fraction: 29/44
- Mixed Number Form: 29/44
- Decimal Value: 0.659091
- Percentage: 65.9091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-8-plus-9-22/
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2/8 + 9/22 = 29/44

Simplified Fraction

29/44

Mixed Number

Proper (29/44)

Decimal Value

0.659091

Percentage

65.9091%

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Step-by-Step Solution: 2/8 + 9/22

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 9/22 by 4 so both fractions share the common base 88.

2 × 11/8 × 11 = 22/88 and 9 × 4/22 × 4 = 36/88

Step 3

Add the Numerators

Now add the numerators (22 + 36 = 58) and keep the common denominator 88 unchanged.

22 + 36/88 = 58/88

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 88, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/88 ÷ 2 = 29/44

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 44 produces a repeating decimal (approximately 0.659091, or 65.9091%).

29 ÷ 44 = 0.659091 (65.9091%)

Visual Representation

The diagram below illustrates 2/8 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/44`
Mixed Number Form	`29/44`
Decimal Form	`0.659091`
Percentage	`65.9091%`

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Frequently Asked Questions

What is 2/8 plus 9/22 as a fraction?

2/8 + 9/22 in simplest fraction form is 29/44.

What is 2/8 plus 9/22 as a decimal?

2/8 + 9/22 converted to a decimal is 0.659091.

What is 2/8 plus 9/22 as a percentage?

2/8 + 9/22 expressed as a percentage is 65.9091%.

Does 2/8 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.659091...) because the denominator contains prime factors other than 2 and 5.