What is 9/20 plus 5/9? (Answer: 181/180)

Exact Answer

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Problem: What is 9/20 plus 5/9?
Formula / Expression: 9/20 + 5/9
Final Answer: 1 1/180 (181/180)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 9 = 180.
Working: LCD(20, 9) = 180

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 9/20 by 9, and multiply the numerator and denominator of 5/9 by 20 so both fractions share the common base 180.
Working: 9 × 9/20 × 9 = 81/180 and 5 × 20/9 × 20 = 100/180

Step 3: Add the Numerators
Now add the numerators (81 + 100 = 181) and keep the common denominator 180 unchanged.
Working: 81 + 100/180 = 181/180

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 180 is 1, confirming that 181/180 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/180

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (181) is greater than the denominator (180), divide 181 by 180: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/180.
Working: 181/180 = 1 1/180

Step 6: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 180 produces a repeating decimal (approximately 1.005556, or 100.5556%).
Working: 181 ÷ 180 = 1.005556 (100.5556%)

Key Values:
- Simplified Fraction: 181/180
- Mixed Number Form: 1 1/180
- Decimal Value: 1.005556
- Percentage: 100.5556%

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Solved with FractionsCalc:
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9/20 + 5/9 = 181/180

Simplified Fraction

181/180

Mixed Number

1 1/180

Decimal Value

1.005556

Percentage

100.5556%

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Step-by-Step Solution: 9/20 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 9 = 180.

LCD(20, 9) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 9/20 by 9, and multiply the numerator and denominator of 5/9 by 20 so both fractions share the common base 180.

9 × 9/20 × 9 = 81/180 and 5 × 20/9 × 20 = 100/180

Step 3

Add the Numerators

Now add the numerators (81 + 100 = 181) and keep the common denominator 180 unchanged.

81 + 100/180 = 181/180

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 180 is 1, confirming that 181/180 cannot be reduced further—it is already in its simplest irreducible form.

181/180

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (181) is greater than the denominator (180), divide 181 by 180: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/180.

181/180 = 11/180

Step 6

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 180 produces a repeating decimal (approximately 1.005556, or 100.5556%).

181 ÷ 180 = 1.005556 (100.5556%)

Visual Representation

The diagram below illustrates 9/20 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/180`
Mixed Number Form	`1 1/180`
Decimal Form	`1.005556`
Percentage	`100.5556%`

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Frequently Asked Questions

What is 9/20 plus 5/9 as a fraction?

9/20 + 5/9 in simplest fraction form is 181/180 (or 1 1/180 as a mixed number).

What is 9/20 plus 5/9 as a decimal?

9/20 + 5/9 converted to a decimal is 1.005556.

What is 9/20 plus 5/9 as a percentage?

9/20 + 5/9 expressed as a percentage is 100.5556%.

How do you write 9/20 plus 5/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 181/180 can be written as the mixed number 1 1/180.

Does 9/20 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.005556...) because the denominator contains prime factors other than 2 and 5.