What is 3/9 plus 7/20? (Answer: 41/60)

Exact Answer

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Problem: What is 3/9 plus 7/20?
Formula / Expression: 3/9 + 7/20
Final Answer: 41/60
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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 7/20 by 9 so both fractions share the common base 180.
Working: 3 × 20/9 × 20 = 60/180 and 7 × 9/20 × 9 = 63/180

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 180 unchanged.
Working: 60 + 63/180 = 123/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 180, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/180 ÷ 3 = 41/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 60 produces a repeating decimal (approximately 0.683333, or 68.3333%).
Working: 41 ÷ 60 = 0.683333 (68.3333%)

Key Values:
- Simplified Fraction: 41/60
- Mixed Number Form: 41/60
- Decimal Value: 0.683333
- Percentage: 68.3333%

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Solved with FractionsCalc:
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3/9 + 7/20 = 41/60

Simplified Fraction

41/60

Mixed Number

Proper (41/60)

Decimal Value

0.683333

Percentage

68.3333%

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Step-by-Step Solution: 3/9 + 7/20

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 7/20 by 9 so both fractions share the common base 180.

3 × 20/9 × 20 = 60/180 and 7 × 9/20 × 9 = 63/180

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 180 unchanged.

60 + 63/180 = 123/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 180, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/180 ÷ 3 = 41/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 60 produces a repeating decimal (approximately 0.683333, or 68.3333%).

41 ÷ 60 = 0.683333 (68.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 7/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/60`
Mixed Number Form	`41/60`
Decimal Form	`0.683333`
Percentage	`68.3333%`

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Frequently Asked Questions

What is 3/9 plus 7/20 as a fraction?

3/9 + 7/20 in simplest fraction form is 41/60.

What is 3/9 plus 7/20 as a decimal?

3/9 + 7/20 converted to a decimal is 0.683333.

What is 3/9 plus 7/20 as a percentage?

3/9 + 7/20 expressed as a percentage is 68.3333%.

Does 3/9 plus 7/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.683333...) because the denominator contains prime factors other than 2 and 5.