What is 2/16 plus 8/9? (Answer: 73/72)

Exact Answer

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Problem: What is 2/16 plus 8/9?
Formula / Expression: 2/16 + 8/9
Final Answer: 1 1/72 (73/72)
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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 8/9 by 16 so both fractions share the common base 144.
Working: 2 × 9/16 × 9 = 18/144 and 8 × 16/9 × 16 = 128/144

Step 3: Add the Numerators
Now add the numerators (18 + 128 = 146) and keep the common denominator 144 unchanged.
Working: 18 + 128/144 = 146/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 146 and 144, which is 2. Divide both the numerator and denominator by 2.
Working: 146 ÷ 2/144 ÷ 2 = 73/72

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (73) is greater than the denominator (72), divide 73 by 72: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/72.
Working: 73/72 = 1 1/72

Step 6: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 72 produces a repeating decimal (approximately 1.013889, or 101.3889%).
Working: 73 ÷ 72 = 1.013889 (101.3889%)

Key Values:
- Simplified Fraction: 73/72
- Mixed Number Form: 1 1/72
- Decimal Value: 1.013889
- Percentage: 101.3889%

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Solved with FractionsCalc:
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2/16 + 8/9 = 73/72

Simplified Fraction

73/72

Mixed Number

1 1/72

Decimal Value

1.013889

Percentage

101.3889%

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Step-by-Step Solution: 2/16 + 8/9

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 8/9 by 16 so both fractions share the common base 144.

2 × 9/16 × 9 = 18/144 and 8 × 16/9 × 16 = 128/144

Step 3

Add the Numerators

Now add the numerators (18 + 128 = 146) and keep the common denominator 144 unchanged.

18 + 128/144 = 146/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 146 and 144, which is 2. Divide both the numerator and denominator by 2.

146 ÷ 2/144 ÷ 2 = 73/72

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (73) is greater than the denominator (72), divide 73 by 72: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/72.

73/72 = 11/72

Step 6

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 72 produces a repeating decimal (approximately 1.013889, or 101.3889%).

73 ÷ 72 = 1.013889 (101.3889%)

Visual Representation

The diagram below illustrates 2/16 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/72`
Mixed Number Form	`1 1/72`
Decimal Form	`1.013889`
Percentage	`101.3889%`

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Frequently Asked Questions

What is 2/16 plus 8/9 as a fraction?

2/16 + 8/9 in simplest fraction form is 73/72 (or 1 1/72 as a mixed number).

What is 2/16 plus 8/9 as a decimal?

2/16 + 8/9 converted to a decimal is 1.013889.

What is 2/16 plus 8/9 as a percentage?

2/16 + 8/9 expressed as a percentage is 101.3889%.

How do you write 2/16 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 73/72 can be written as the mixed number 1 1/72.

Does 2/16 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.013889...) because the denominator contains prime factors other than 2 and 5.