What is 2/16 plus 9/22? (Answer: 47/88)

Exact Answer

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Problem: What is 2/16 plus 9/22?
Formula / Expression: 2/16 + 9/22
Final Answer: 47/88
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 176 (which is smaller than their product 16 × 22 = 352, keeping the calculation simpler).
Working: LCD(16, 22) = 176

Step 2: Convert to Equivalent Fractions with Common Denominator 176
Multiply the numerator and denominator of 2/16 by 11, and multiply the numerator and denominator of 9/22 by 8 so both fractions share the common base 176.
Working: 2 × 11/16 × 11 = 22/176 and 9 × 8/22 × 8 = 72/176

Step 3: Add the Numerators
Now add the numerators (22 + 72 = 94) and keep the common denominator 176 unchanged.
Working: 22 + 72/176 = 94/176

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 176, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/176 ÷ 2 = 47/88

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 88 produces a repeating decimal (approximately 0.534091, or 53.4091%).
Working: 47 ÷ 88 = 0.534091 (53.4091%)

Key Values:
- Simplified Fraction: 47/88
- Mixed Number Form: 47/88
- Decimal Value: 0.534091
- Percentage: 53.4091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-16-plus-9-22/
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2/16 + 9/22 = 47/88

Simplified Fraction

47/88

Mixed Number

Proper (47/88)

Decimal Value

0.534091

Percentage

53.4091%

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Step-by-Step Solution: 2/16 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 176 (which is smaller than their product 16 × 22 = 352, keeping the calculation simpler).

LCD(16, 22) = 176

Step 2

Convert to Equivalent Fractions with Common Denominator 176

Multiply the numerator and denominator of 2/16 by 11, and multiply the numerator and denominator of 9/22 by 8 so both fractions share the common base 176.

2 × 11/16 × 11 = 22/176 and 9 × 8/22 × 8 = 72/176

Step 3

Add the Numerators

Now add the numerators (22 + 72 = 94) and keep the common denominator 176 unchanged.

22 + 72/176 = 94/176

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 176, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/176 ÷ 2 = 47/88

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 88 produces a repeating decimal (approximately 0.534091, or 53.4091%).

47 ÷ 88 = 0.534091 (53.4091%)

Visual Representation

The diagram below illustrates 2/16 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/88`
Mixed Number Form	`47/88`
Decimal Form	`0.534091`
Percentage	`53.4091%`

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Frequently Asked Questions

What is 2/16 plus 9/22 as a fraction?

2/16 + 9/22 in simplest fraction form is 47/88.

What is 2/16 plus 9/22 as a decimal?

2/16 + 9/22 converted to a decimal is 0.534091.

What is 2/16 plus 9/22 as a percentage?

2/16 + 9/22 expressed as a percentage is 53.4091%.

Does 2/16 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.534091...) because the denominator contains prime factors other than 2 and 5.