What is 4/20 plus 2/9? (Answer: 19/45)

Exact Answer

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Problem: What is 4/20 plus 2/9?
Formula / Expression: 4/20 + 2/9
Final Answer: 19/45
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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 4/20 by 9, and multiply the numerator and denominator of 2/9 by 20 so both fractions share the common base 180.
Working: 4 × 9/20 × 9 = 36/180 and 2 × 20/9 × 20 = 40/180

Step 3: Add the Numerators
Now add the numerators (36 + 40 = 76) and keep the common denominator 180 unchanged.
Working: 36 + 40/180 = 76/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 180, which is 4. Divide both the numerator and denominator by 4.
Working: 76 ÷ 4/180 ÷ 4 = 19/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 45 produces a repeating decimal (approximately 0.422222, or 42.2222%).
Working: 19 ÷ 45 = 0.422222 (42.2222%)

Key Values:
- Simplified Fraction: 19/45
- Mixed Number Form: 19/45
- Decimal Value: 0.422222
- Percentage: 42.2222%

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Solved with FractionsCalc:
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4/20 + 2/9 = 19/45

Simplified Fraction

19/45

Mixed Number

Proper (19/45)

Decimal Value

0.422222

Percentage

42.2222%

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Step-by-Step Solution: 4/20 + 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 4/20 by 9, and multiply the numerator and denominator of 2/9 by 20 so both fractions share the common base 180.

4 × 9/20 × 9 = 36/180 and 2 × 20/9 × 20 = 40/180

Step 3

Add the Numerators

Now add the numerators (36 + 40 = 76) and keep the common denominator 180 unchanged.

36 + 40/180 = 76/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 180, which is 4. Divide both the numerator and denominator by 4.

76 ÷ 4/180 ÷ 4 = 19/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 45 produces a repeating decimal (approximately 0.422222, or 42.2222%).

19 ÷ 45 = 0.422222 (42.2222%)

Visual Representation

The diagram below illustrates 4/20 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/45`
Mixed Number Form	`19/45`
Decimal Form	`0.422222`
Percentage	`42.2222%`

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Frequently Asked Questions

What is 4/20 plus 2/9 as a fraction?

4/20 + 2/9 in simplest fraction form is 19/45.

What is 4/20 plus 2/9 as a decimal?

4/20 + 2/9 converted to a decimal is 0.422222.

What is 4/20 plus 2/9 as a percentage?

4/20 + 2/9 expressed as a percentage is 42.2222%.

Does 4/20 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.422222...) because the denominator contains prime factors other than 2 and 5.