What is 3/9 plus 8/20? (Answer: 11/15)

Exact Answer

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Problem: What is 3/9 plus 8/20?
Formula / Expression: 3/9 + 8/20
Final Answer: 11/15
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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 3/9 by 20, and multiply the numerator and denominator of 8/20 by 9 so both fractions share the common base 180.
Working: 3 × 20/9 × 20 = 60/180 and 8 × 9/20 × 9 = 72/180

Step 3: Add the Numerators
Now add the numerators (60 + 72 = 132) and keep the common denominator 180 unchanged.
Working: 60 + 72/180 = 132/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 132 and 180, which is 12. Divide both the numerator and denominator by 12.
Working: 132 ÷ 12/180 ÷ 12 = 11/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).
Working: 11 ÷ 15 = 0.733333 (73.3333%)

Key Values:
- Simplified Fraction: 11/15
- Mixed Number Form: 11/15
- Decimal Value: 0.733333
- Percentage: 73.3333%

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Solved with FractionsCalc:
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3/9 + 8/20 = 11/15

Simplified Fraction

11/15

Mixed Number

Proper (11/15)

Decimal Value

0.733333

Percentage

73.3333%

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Step-by-Step Solution: 3/9 + 8/20

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 3/9 by 20, and multiply the numerator and denominator of 8/20 by 9 so both fractions share the common base 180.

3 × 20/9 × 20 = 60/180 and 8 × 9/20 × 9 = 72/180

Step 3

Add the Numerators

Now add the numerators (60 + 72 = 132) and keep the common denominator 180 unchanged.

60 + 72/180 = 132/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 132 and 180, which is 12. Divide both the numerator and denominator by 12.

132 ÷ 12/180 ÷ 12 = 11/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 15 produces a repeating decimal (approximately 0.733333, or 73.3333%).

11 ÷ 15 = 0.733333 (73.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 8/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/15`
Mixed Number Form	`11/15`
Decimal Form	`0.733333`
Percentage	`73.3333%`

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Frequently Asked Questions

What is 3/9 plus 8/20 as a fraction?

3/9 + 8/20 in simplest fraction form is 11/15.

What is 3/9 plus 8/20 as a decimal?

3/9 + 8/20 converted to a decimal is 0.733333.

What is 3/9 plus 8/20 as a percentage?

3/9 + 8/20 expressed as a percentage is 73.3333%.

Does 3/9 plus 8/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.733333...) because the denominator contains prime factors other than 2 and 5.