What is 1/5 plus 5/9? (Answer: 34/45)

Exact Answer

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Problem: What is 1/5 plus 5/9?
Formula / Expression: 1/5 + 5/9
Final Answer: 34/45
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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 5/9 by 5 so both fractions share the common base 45.
Working: 1 × 9/5 × 9 = 9/45 and 5 × 5/9 × 5 = 25/45

Step 3: Add the Numerators
Now add the numerators (9 + 25 = 34) and keep the common denominator 45 unchanged.
Working: 9 + 25/45 = 34/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 34 and 45 is 1, confirming that 34/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 34/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 45 produces a repeating decimal (approximately 0.755556, or 75.5556%).
Working: 34 ÷ 45 = 0.755556 (75.5556%)

Key Values:
- Simplified Fraction: 34/45
- Mixed Number Form: 34/45
- Decimal Value: 0.755556
- Percentage: 75.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-plus-5-9/
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1/5 + 5/9 = 34/45

Simplified Fraction

34/45

Mixed Number

Proper (34/45)

Decimal Value

0.755556

Percentage

75.5556%

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Step-by-Step Solution: 1/5 + 5/9

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 5/9 by 5 so both fractions share the common base 45.

1 × 9/5 × 9 = 9/45 and 5 × 5/9 × 5 = 25/45

Step 3

Add the Numerators

Now add the numerators (9 + 25 = 34) and keep the common denominator 45 unchanged.

9 + 25/45 = 34/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 34 and 45 is 1, confirming that 34/45 cannot be reduced further—it is already in its simplest irreducible form.

34/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 45 produces a repeating decimal (approximately 0.755556, or 75.5556%).

34 ÷ 45 = 0.755556 (75.5556%)

Visual Representation

The diagram below illustrates 1/5 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/45`
Mixed Number Form	`34/45`
Decimal Form	`0.755556`
Percentage	`75.5556%`

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Frequently Asked Questions

What is 1/5 plus 5/9 as a fraction?

1/5 + 5/9 in simplest fraction form is 34/45.

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

1/5 + 5/9 converted to a decimal is 0.755556.

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

1/5 + 5/9 expressed as a percentage is 75.5556%.

Does 1/5 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.755556...) because the denominator contains prime factors other than 2 and 5.