What is 2/20 plus 5/9? (Answer: 59/90)

Exact Answer

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Problem: What is 2/20 plus 5/9?
Formula / Expression: 2/20 + 5/9
Final Answer: 59/90
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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 2/20 by 9, and multiply the numerator and denominator of 5/9 by 20 so both fractions share the common base 180.
Working: 2 × 9/20 × 9 = 18/180 and 5 × 20/9 × 20 = 100/180

Step 3: Add the Numerators
Now add the numerators (18 + 100 = 118) and keep the common denominator 180 unchanged.
Working: 18 + 100/180 = 118/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/180 ÷ 2 = 59/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 90 produces a repeating decimal (approximately 0.655556, or 65.5556%).
Working: 59 ÷ 90 = 0.655556 (65.5556%)

Key Values:
- Simplified Fraction: 59/90
- Mixed Number Form: 59/90
- Decimal Value: 0.655556
- Percentage: 65.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-20-plus-5-9/
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2/20 + 5/9 = 59/90

Simplified Fraction

59/90

Mixed Number

Proper (59/90)

Decimal Value

0.655556

Percentage

65.5556%

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Step-by-Step Solution: 2/20 + 5/9

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 2/20 by 9, and multiply the numerator and denominator of 5/9 by 20 so both fractions share the common base 180.

2 × 9/20 × 9 = 18/180 and 5 × 20/9 × 20 = 100/180

Step 3

Add the Numerators

Now add the numerators (18 + 100 = 118) and keep the common denominator 180 unchanged.

18 + 100/180 = 118/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 180, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/180 ÷ 2 = 59/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 90 produces a repeating decimal (approximately 0.655556, or 65.5556%).

59 ÷ 90 = 0.655556 (65.5556%)

Visual Representation

The diagram below illustrates 2/20 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/90`
Mixed Number Form	`59/90`
Decimal Form	`0.655556`
Percentage	`65.5556%`

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Frequently Asked Questions

What is 2/20 plus 5/9 as a fraction?

2/20 + 5/9 in simplest fraction form is 59/90.

What is 2/20 plus 5/9 as a decimal?

2/20 + 5/9 converted to a decimal is 0.655556.

What is 2/20 plus 5/9 as a percentage?

2/20 + 5/9 expressed as a percentage is 65.5556%.

Does 2/20 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.655556...) because the denominator contains prime factors other than 2 and 5.