What is 2/11 plus 9/16? (Answer: 131/176)

Exact Answer

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Problem: What is 2/11 plus 9/16?
Formula / Expression: 2/11 + 9/16
Final Answer: 131/176
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 16 = 176.
Working: LCD(11, 16) = 176

Step 2: Convert to Equivalent Fractions with Common Denominator 176
Multiply the numerator and denominator of 2/11 by 16, and multiply the numerator and denominator of 9/16 by 11 so both fractions share the common base 176.
Working: 2 × 16/11 × 16 = 32/176 and 9 × 11/16 × 11 = 99/176

Step 3: Add the Numerators
Now add the numerators (32 + 99 = 131) and keep the common denominator 176 unchanged.
Working: 32 + 99/176 = 131/176

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 131 and 176 is 1, confirming that 131/176 cannot be reduced further—it is already in its simplest irreducible form.
Working: 131/176

Step 5: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 176 produces a repeating decimal (approximately 0.744318, or 74.4318%).
Working: 131 ÷ 176 = 0.744318 (74.4318%)

Key Values:
- Simplified Fraction: 131/176
- Mixed Number Form: 131/176
- Decimal Value: 0.744318
- Percentage: 74.4318%

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Solved with FractionsCalc:
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2/11 + 9/16 = 131/176

Simplified Fraction

131/176

Mixed Number

Proper (131/176)

Decimal Value

0.744318

Percentage

74.4318%

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Step-by-Step Solution: 2/11 + 9/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 16 = 176.

LCD(11, 16) = 176

Step 2

Convert to Equivalent Fractions with Common Denominator 176

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

2 × 16/11 × 16 = 32/176 and 9 × 11/16 × 11 = 99/176

Step 3

Add the Numerators

Now add the numerators (32 + 99 = 131) and keep the common denominator 176 unchanged.

32 + 99/176 = 131/176

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 131 and 176 is 1, confirming that 131/176 cannot be reduced further—it is already in its simplest irreducible form.

131/176

Step 5

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 176 produces a repeating decimal (approximately 0.744318, or 74.4318%).

131 ÷ 176 = 0.744318 (74.4318%)

Visual Representation

The diagram below illustrates 2/11 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/176`
Mixed Number Form	`131/176`
Decimal Form	`0.744318`
Percentage	`74.4318%`

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Frequently Asked Questions

What is 2/11 plus 9/16 as a fraction?

2/11 + 9/16 in simplest fraction form is 131/176.

What is 2/11 plus 9/16 as a decimal?

2/11 + 9/16 converted to a decimal is 0.744318.

What is 2/11 plus 9/16 as a percentage?

2/11 + 9/16 expressed as a percentage is 74.4318%.

Does 2/11 plus 9/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.744318...) because the denominator contains prime factors other than 2 and 5.