What is 2/20 plus 2/9? (Answer: 29/90)

Exact Answer

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Problem: What is 2/20 plus 2/9?
Formula / Expression: 2/20 + 2/9
Final Answer: 29/90
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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 2/9 by 20 so both fractions share the common base 180.
Working: 2 × 9/20 × 9 = 18/180 and 2 × 20/9 × 20 = 40/180

Step 3: Add the Numerators
Now add the numerators (18 + 40 = 58) and keep the common denominator 180 unchanged.
Working: 18 + 40/180 = 58/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 180, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/180 ÷ 2 = 29/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 90 produces a repeating decimal (approximately 0.322222, or 32.2222%).
Working: 29 ÷ 90 = 0.322222 (32.2222%)

Key Values:
- Simplified Fraction: 29/90
- Mixed Number Form: 29/90
- Decimal Value: 0.322222
- Percentage: 32.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-20-plus-2-9/
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2/20 + 2/9 = 29/90

Simplified Fraction

29/90

Mixed Number

Proper (29/90)

Decimal Value

0.322222

Percentage

32.2222%

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

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 2/9 by 20 so both fractions share the common base 180.

2 × 9/20 × 9 = 18/180 and 2 × 20/9 × 20 = 40/180

Step 3

Add the Numerators

Now add the numerators (18 + 40 = 58) and keep the common denominator 180 unchanged.

18 + 40/180 = 58/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 180, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/180 ÷ 2 = 29/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 90 produces a repeating decimal (approximately 0.322222, or 32.2222%).

29 ÷ 90 = 0.322222 (32.2222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/90`
Mixed Number Form	`29/90`
Decimal Form	`0.322222`
Percentage	`32.2222%`

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Frequently Asked Questions

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

2/20 + 2/9 in simplest fraction form is 29/90.

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

2/20 + 2/9 converted to a decimal is 0.322222.

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

2/20 + 2/9 expressed as a percentage is 32.2222%.

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

It results in a repeating decimal (approximately 0.322222...) because the denominator contains prime factors other than 2 and 5.