What is 1/5 plus 2/9? (Answer: 19/45)

Exact Answer

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Problem: What is 1/5 plus 2/9?
Formula / Expression: 1/5 + 2/9
Final Answer: 19/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.
Working: LCD(5, 9) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 1/5 by 9, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.
Working: 1 × 9/5 × 9 = 9/45 and 2 × 5/9 × 5 = 10/45

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 45 unchanged.
Working: 9 + 10/45 = 19/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 45 is 1, confirming that 19/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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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1/5 + 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: 1/5 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.

LCD(5, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 1/5 by 9, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.

1 × 9/5 × 9 = 9/45 and 2 × 5/9 × 5 = 10/45

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 45 unchanged.

9 + 10/45 = 19/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 45 is 1, confirming that 19/45 cannot be reduced further—it is already in its simplest irreducible form.

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 1/5 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 1/5 plus 2/9 as a fraction?

1/5 + 2/9 in simplest fraction form is 19/45.

What is 1/5 plus 2/9 as a decimal?

1/5 + 2/9 converted to a decimal is 0.422222.

What is 1/5 plus 2/9 as a percentage?

1/5 + 2/9 expressed as a percentage is 42.2222%.

Does 1/5 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.