What is 4/9 plus 9/20? (Answer: 161/180)

Exact Answer

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Problem: What is 4/9 plus 9/20?
Formula / Expression: 4/9 + 9/20
Final Answer: 161/180
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 4/9 by 20, and multiply the numerator and denominator of 9/20 by 9 so both fractions share the common base 180.
Working: 4 × 20/9 × 20 = 80/180 and 9 × 9/20 × 9 = 81/180

Step 3: Add the Numerators
Now add the numerators (80 + 81 = 161) and keep the common denominator 180 unchanged.
Working: 80 + 81/180 = 161/180

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 161 and 180 is 1, confirming that 161/180 cannot be reduced further—it is already in its simplest irreducible form.
Working: 161/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 161 by denominator 180 produces a repeating decimal (approximately 0.894444, or 89.4444%).
Working: 161 ÷ 180 = 0.894444 (89.4444%)

Key Values:
- Simplified Fraction: 161/180
- Mixed Number Form: 161/180
- Decimal Value: 0.894444
- Percentage: 89.4444%

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4/9 + 9/20 = 161/180

Simplified Fraction

161/180

Mixed Number

Proper (161/180)

Decimal Value

0.894444

Percentage

89.4444%

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Step-by-Step Solution: 4/9 + 9/20

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 20) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 4/9 by 20, and multiply the numerator and denominator of 9/20 by 9 so both fractions share the common base 180.

4 × 20/9 × 20 = 80/180 and 9 × 9/20 × 9 = 81/180

Step 3

Add the Numerators

Now add the numerators (80 + 81 = 161) and keep the common denominator 180 unchanged.

80 + 81/180 = 161/180

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 161 and 180 is 1, confirming that 161/180 cannot be reduced further—it is already in its simplest irreducible form.

161/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 161 by denominator 180 produces a repeating decimal (approximately 0.894444, or 89.4444%).

161 ÷ 180 = 0.894444 (89.4444%)

Visual Representation

The diagram below illustrates 4/9 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`161/180`
Mixed Number Form	`161/180`
Decimal Form	`0.894444`
Percentage	`89.4444%`

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Frequently Asked Questions

What is 4/9 plus 9/20 as a fraction?

4/9 + 9/20 in simplest fraction form is 161/180.

What is 4/9 plus 9/20 as a decimal?

4/9 + 9/20 converted to a decimal is 0.894444.

What is 4/9 plus 9/20 as a percentage?

4/9 + 9/20 expressed as a percentage is 89.4444%.

Does 4/9 plus 9/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.894444...) because the denominator contains prime factors other than 2 and 5.