What is 1/9 plus 9/19? (Answer: 100/171)

Exact Answer

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Problem: What is 1/9 plus 9/19?
Formula / Expression: 1/9 + 9/19
Final Answer: 100/171
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.
Working: LCD(9, 19) = 171

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 1/9 by 19, and multiply the numerator and denominator of 9/19 by 9 so both fractions share the common base 171.
Working: 1 × 19/9 × 19 = 19/171 and 9 × 9/19 × 9 = 81/171

Step 3: Add the Numerators
Now add the numerators (19 + 81 = 100) and keep the common denominator 171 unchanged.
Working: 19 + 81/171 = 100/171

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 100 and 171 is 1, confirming that 100/171 cannot be reduced further—it is already in its simplest irreducible form.
Working: 100/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 100 by denominator 171 produces a repeating decimal (approximately 0.584795, or 58.4795%).
Working: 100 ÷ 171 = 0.584795 (58.4795%)

Key Values:
- Simplified Fraction: 100/171
- Mixed Number Form: 100/171
- Decimal Value: 0.584795
- Percentage: 58.4795%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-9-19/
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1/9 + 9/19 = 100/171

Simplified Fraction

100/171

Mixed Number

Proper (100/171)

Decimal Value

0.584795

Percentage

58.4795%

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Step-by-Step Solution: 1/9 + 9/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 19 = 171.

LCD(9, 19) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 1/9 by 19, and multiply the numerator and denominator of 9/19 by 9 so both fractions share the common base 171.

1 × 19/9 × 19 = 19/171 and 9 × 9/19 × 9 = 81/171

Step 3

Add the Numerators

Now add the numerators (19 + 81 = 100) and keep the common denominator 171 unchanged.

19 + 81/171 = 100/171

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 100 and 171 is 1, confirming that 100/171 cannot be reduced further—it is already in its simplest irreducible form.

100/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 100 by denominator 171 produces a repeating decimal (approximately 0.584795, or 58.4795%).

100 ÷ 171 = 0.584795 (58.4795%)

Visual Representation

The diagram below illustrates 1/9 plus 9/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`100/171`
Mixed Number Form	`100/171`
Decimal Form	`0.584795`
Percentage	`58.4795%`

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Frequently Asked Questions

What is 1/9 plus 9/19 as a fraction?

1/9 + 9/19 in simplest fraction form is 100/171.

What is 1/9 plus 9/19 as a decimal?

1/9 + 9/19 converted to a decimal is 0.584795.

What is 1/9 plus 9/19 as a percentage?

1/9 + 9/19 expressed as a percentage is 58.4795%.

Does 1/9 plus 9/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.584795...) because the denominator contains prime factors other than 2 and 5.