What is 2/19 plus 8/9? (Answer: 170/171)

Exact Answer

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Problem: What is 2/19 plus 8/9?
Formula / Expression: 2/19 + 8/9
Final Answer: 170/171
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 171
Multiply the numerator and denominator of 2/19 by 9, and multiply the numerator and denominator of 8/9 by 19 so both fractions share the common base 171.
Working: 2 × 9/19 × 9 = 18/171 and 8 × 19/9 × 19 = 152/171

Step 3: Add the Numerators
Now add the numerators (18 + 152 = 170) and keep the common denominator 171 unchanged.
Working: 18 + 152/171 = 170/171

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 170 and 171 is 1, confirming that 170/171 cannot be reduced further—it is already in its simplest irreducible form.
Working: 170/171

Step 5: Decimal & Percentage Representation
Dividing the numerator 170 by denominator 171 produces a repeating decimal (approximately 0.994152, or 99.4152%).
Working: 170 ÷ 171 = 0.994152 (99.4152%)

Key Values:
- Simplified Fraction: 170/171
- Mixed Number Form: 170/171
- Decimal Value: 0.994152
- Percentage: 99.4152%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-19-plus-8-9/
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2/19 + 8/9 = 170/171

Simplified Fraction

170/171

Mixed Number

Proper (170/171)

Decimal Value

0.994152

Percentage

99.4152%

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Step-by-Step Solution: 2/19 + 8/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(19, 9) = 171

Step 2

Convert to Equivalent Fractions with Common Denominator 171

Multiply the numerator and denominator of 2/19 by 9, and multiply the numerator and denominator of 8/9 by 19 so both fractions share the common base 171.

2 × 9/19 × 9 = 18/171 and 8 × 19/9 × 19 = 152/171

Step 3

Add the Numerators

Now add the numerators (18 + 152 = 170) and keep the common denominator 171 unchanged.

18 + 152/171 = 170/171

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 170 and 171 is 1, confirming that 170/171 cannot be reduced further—it is already in its simplest irreducible form.

170/171

Step 5

Decimal & Percentage Representation

Dividing the numerator 170 by denominator 171 produces a repeating decimal (approximately 0.994152, or 99.4152%).

170 ÷ 171 = 0.994152 (99.4152%)

Visual Representation

The diagram below illustrates 2/19 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`170/171`
Mixed Number Form	`170/171`
Decimal Form	`0.994152`
Percentage	`99.4152%`

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Frequently Asked Questions

What is 2/19 plus 8/9 as a fraction?

2/19 + 8/9 in simplest fraction form is 170/171.

What is 2/19 plus 8/9 as a decimal?

2/19 + 8/9 converted to a decimal is 0.994152.

What is 2/19 plus 8/9 as a percentage?

2/19 + 8/9 expressed as a percentage is 99.4152%.

Does 2/19 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.994152...) because the denominator contains prime factors other than 2 and 5.