What is 3/9 plus 9/20? (Answer: 47/60)

Exact Answer

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Problem: What is 3/9 plus 9/20?
Formula / Expression: 3/9 + 9/20
Final Answer: 47/60
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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 9/20 by 9 so both fractions share the common base 180.
Working: 3 × 20/9 × 20 = 60/180 and 9 × 9/20 × 9 = 81/180

Step 3: Add the Numerators
Now add the numerators (60 + 81 = 141) and keep the common denominator 180 unchanged.
Working: 60 + 81/180 = 141/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 141 and 180, which is 3. Divide both the numerator and denominator by 3.
Working: 141 ÷ 3/180 ÷ 3 = 47/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 60 produces a repeating decimal (approximately 0.783333, or 78.3333%).
Working: 47 ÷ 60 = 0.783333 (78.3333%)

Key Values:
- Simplified Fraction: 47/60
- Mixed Number Form: 47/60
- Decimal Value: 0.783333
- Percentage: 78.3333%

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Solved with FractionsCalc:
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3/9 + 9/20 = 47/60

Simplified Fraction

47/60

Mixed Number

Proper (47/60)

Decimal Value

0.783333

Percentage

78.3333%

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Step-by-Step Solution: 3/9 + 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 3/9 by 20, and multiply the numerator and denominator of 9/20 by 9 so both fractions share the common base 180.

3 × 20/9 × 20 = 60/180 and 9 × 9/20 × 9 = 81/180

Step 3

Add the Numerators

Now add the numerators (60 + 81 = 141) and keep the common denominator 180 unchanged.

60 + 81/180 = 141/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 141 and 180, which is 3. Divide both the numerator and denominator by 3.

141 ÷ 3/180 ÷ 3 = 47/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 60 produces a repeating decimal (approximately 0.783333, or 78.3333%).

47 ÷ 60 = 0.783333 (78.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/60`
Mixed Number Form	`47/60`
Decimal Form	`0.783333`
Percentage	`78.3333%`

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Frequently Asked Questions

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

3/9 + 9/20 in simplest fraction form is 47/60.

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

3/9 + 9/20 converted to a decimal is 0.783333.

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

3/9 + 9/20 expressed as a percentage is 78.3333%.

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

It results in a repeating decimal (approximately 0.783333...) because the denominator contains prime factors other than 2 and 5.