What is 2/16 plus 3/9? (Answer: 11/24)

Exact Answer

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Problem: What is 2/16 plus 3/9?
Formula / Expression: 2/16 + 3/9
Final Answer: 11/24
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 9 = 144.
Working: LCD(16, 9) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 2/16 by 9, and multiply the numerator and denominator of 3/9 by 16 so both fractions share the common base 144.
Working: 2 × 9/16 × 9 = 18/144 and 3 × 16/9 × 16 = 48/144

Step 3: Add the Numerators
Now add the numerators (18 + 48 = 66) and keep the common denominator 144 unchanged.
Working: 18 + 48/144 = 66/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 66 and 144, which is 6. Divide both the numerator and denominator by 6.
Working: 66 ÷ 6/144 ÷ 6 = 11/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).
Working: 11 ÷ 24 = 0.458333 (45.8333%)

Key Values:
- Simplified Fraction: 11/24
- Mixed Number Form: 11/24
- Decimal Value: 0.458333
- Percentage: 45.8333%

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Solved with FractionsCalc:
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2/16 + 3/9 = 11/24

Simplified Fraction

11/24

Mixed Number

Proper (11/24)

Decimal Value

0.458333

Percentage

45.8333%

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Step-by-Step Solution: 2/16 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 9 = 144.

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 2/16 by 9, and multiply the numerator and denominator of 3/9 by 16 so both fractions share the common base 144.

2 × 9/16 × 9 = 18/144 and 3 × 16/9 × 16 = 48/144

Step 3

Add the Numerators

Now add the numerators (18 + 48 = 66) and keep the common denominator 144 unchanged.

18 + 48/144 = 66/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 66 and 144, which is 6. Divide both the numerator and denominator by 6.

66 ÷ 6/144 ÷ 6 = 11/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).

11 ÷ 24 = 0.458333 (45.8333%)

Visual Representation

The diagram below illustrates 2/16 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/24`
Mixed Number Form	`11/24`
Decimal Form	`0.458333`
Percentage	`45.8333%`

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Frequently Asked Questions

What is 2/16 plus 3/9 as a fraction?

2/16 + 3/9 in simplest fraction form is 11/24.

What is 2/16 plus 3/9 as a decimal?

2/16 + 3/9 converted to a decimal is 0.458333.

What is 2/16 plus 3/9 as a percentage?

2/16 + 3/9 expressed as a percentage is 45.8333%.

Does 2/16 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.458333...) because the denominator contains prime factors other than 2 and 5.