What is 3/20 plus 4/9? (Answer: 107/180)

Exact Answer

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Problem: What is 3/20 plus 4/9?
Formula / Expression: 3/20 + 4/9
Final Answer: 107/180
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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 3/20 by 9, and multiply the numerator and denominator of 4/9 by 20 so both fractions share the common base 180.
Working: 3 × 9/20 × 9 = 27/180 and 4 × 20/9 × 20 = 80/180

Step 3: Add the Numerators
Now add the numerators (27 + 80 = 107) and keep the common denominator 180 unchanged.
Working: 27 + 80/180 = 107/180

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 180 is 1, confirming that 107/180 cannot be reduced further—it is already in its simplest irreducible form.
Working: 107/180

Step 5: Decimal & Percentage Representation
Dividing the numerator 107 by denominator 180 produces a repeating decimal (approximately 0.594444, or 59.4444%).
Working: 107 ÷ 180 = 0.594444 (59.4444%)

Key Values:
- Simplified Fraction: 107/180
- Mixed Number Form: 107/180
- Decimal Value: 0.594444
- Percentage: 59.4444%

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3/20 + 4/9 = 107/180

Simplified Fraction

107/180

Mixed Number

Proper (107/180)

Decimal Value

0.594444

Percentage

59.4444%

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Step-by-Step Solution: 3/20 + 4/9

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 3/20 by 9, and multiply the numerator and denominator of 4/9 by 20 so both fractions share the common base 180.

3 × 9/20 × 9 = 27/180 and 4 × 20/9 × 20 = 80/180

Step 3

Add the Numerators

Now add the numerators (27 + 80 = 107) and keep the common denominator 180 unchanged.

27 + 80/180 = 107/180

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 107 and 180 is 1, confirming that 107/180 cannot be reduced further—it is already in its simplest irreducible form.

107/180

Step 5

Decimal & Percentage Representation

Dividing the numerator 107 by denominator 180 produces a repeating decimal (approximately 0.594444, or 59.4444%).

107 ÷ 180 = 0.594444 (59.4444%)

Visual Representation

The diagram below illustrates 3/20 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`107/180`
Mixed Number Form	`107/180`
Decimal Form	`0.594444`
Percentage	`59.4444%`

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Frequently Asked Questions

What is 3/20 plus 4/9 as a fraction?

3/20 + 4/9 in simplest fraction form is 107/180.

What is 3/20 plus 4/9 as a decimal?

3/20 + 4/9 converted to a decimal is 0.594444.

What is 3/20 plus 4/9 as a percentage?

3/20 + 4/9 expressed as a percentage is 59.4444%.

Does 3/20 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.594444...) because the denominator contains prime factors other than 2 and 5.