What is 2/9 plus 6/20? (Answer: 47/90)

Exact Answer

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Problem: What is 2/9 plus 6/20?
Formula / Expression: 2/9 + 6/20
Final Answer: 47/90
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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 2/9 by 20, and multiply the numerator and denominator of 6/20 by 9 so both fractions share the common base 180.
Working: 2 × 20/9 × 20 = 40/180 and 6 × 9/20 × 9 = 54/180

Step 3: Add the Numerators
Now add the numerators (40 + 54 = 94) and keep the common denominator 180 unchanged.
Working: 40 + 54/180 = 94/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/180 ÷ 2 = 47/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 90 produces a repeating decimal (approximately 0.522222, or 52.2222%).
Working: 47 ÷ 90 = 0.522222 (52.2222%)

Key Values:
- Simplified Fraction: 47/90
- Mixed Number Form: 47/90
- Decimal Value: 0.522222
- Percentage: 52.2222%

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Solved with FractionsCalc:
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2/9 + 6/20 = 47/90

Simplified Fraction

47/90

Mixed Number

Proper (47/90)

Decimal Value

0.522222

Percentage

52.2222%

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Step-by-Step Solution: 2/9 + 6/20

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 2/9 by 20, and multiply the numerator and denominator of 6/20 by 9 so both fractions share the common base 180.

2 × 20/9 × 20 = 40/180 and 6 × 9/20 × 9 = 54/180

Step 3

Add the Numerators

Now add the numerators (40 + 54 = 94) and keep the common denominator 180 unchanged.

40 + 54/180 = 94/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 180, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/180 ÷ 2 = 47/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 90 produces a repeating decimal (approximately 0.522222, or 52.2222%).

47 ÷ 90 = 0.522222 (52.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 6/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/90`
Mixed Number Form	`47/90`
Decimal Form	`0.522222`
Percentage	`52.2222%`

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Frequently Asked Questions

What is 2/9 plus 6/20 as a fraction?

2/9 + 6/20 in simplest fraction form is 47/90.

What is 2/9 plus 6/20 as a decimal?

2/9 + 6/20 converted to a decimal is 0.522222.

What is 2/9 plus 6/20 as a percentage?

2/9 + 6/20 expressed as a percentage is 52.2222%.

Does 2/9 plus 6/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.522222...) because the denominator contains prime factors other than 2 and 5.