What is 3/20 plus 3/9? (Answer: 29/60)

Exact Answer

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Problem: What is 3/20 plus 3/9?
Formula / Expression: 3/20 + 3/9
Final Answer: 29/60
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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 3/9 by 20 so both fractions share the common base 180.
Working: 3 × 9/20 × 9 = 27/180 and 3 × 20/9 × 20 = 60/180

Step 3: Add the Numerators
Now add the numerators (27 + 60 = 87) and keep the common denominator 180 unchanged.
Working: 27 + 60/180 = 87/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 87 and 180, which is 3. Divide both the numerator and denominator by 3.
Working: 87 ÷ 3/180 ÷ 3 = 29/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 60 produces a repeating decimal (approximately 0.483333, or 48.3333%).
Working: 29 ÷ 60 = 0.483333 (48.3333%)

Key Values:
- Simplified Fraction: 29/60
- Mixed Number Form: 29/60
- Decimal Value: 0.483333
- Percentage: 48.3333%

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Solved with FractionsCalc:
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3/20 + 3/9 = 29/60

Simplified Fraction

29/60

Mixed Number

Proper (29/60)

Decimal Value

0.483333

Percentage

48.3333%

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

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 3/9 by 20 so both fractions share the common base 180.

3 × 9/20 × 9 = 27/180 and 3 × 20/9 × 20 = 60/180

Step 3

Add the Numerators

Now add the numerators (27 + 60 = 87) and keep the common denominator 180 unchanged.

27 + 60/180 = 87/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 87 and 180, which is 3. Divide both the numerator and denominator by 3.

87 ÷ 3/180 ÷ 3 = 29/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 60 produces a repeating decimal (approximately 0.483333, or 48.3333%).

29 ÷ 60 = 0.483333 (48.3333%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/60`
Mixed Number Form	`29/60`
Decimal Form	`0.483333`
Percentage	`48.3333%`

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Frequently Asked Questions

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

3/20 + 3/9 in simplest fraction form is 29/60.

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

3/20 + 3/9 converted to a decimal is 0.483333.

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

3/20 + 3/9 expressed as a percentage is 48.3333%.

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

It results in a repeating decimal (approximately 0.483333...) because the denominator contains prime factors other than 2 and 5.