What is 1/9 plus 2/8? (Answer: 13/36)

Exact Answer

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Problem: What is 1/9 plus 2/8?
Formula / Expression: 1/9 + 2/8
Final Answer: 13/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.
Working: LCD(9, 8) = 72

Step 2: Convert to Equivalent Fractions with Common Denominator 72
Multiply the numerator and denominator of 1/9 by 8, and multiply the numerator and denominator of 2/8 by 9 so both fractions share the common base 72.
Working: 1 × 8/9 × 8 = 8/72 and 2 × 9/8 × 9 = 18/72

Step 3: Add the Numerators
Now add the numerators (8 + 18 = 26) and keep the common denominator 72 unchanged.
Working: 8 + 18/72 = 26/72

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 72, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/72 ÷ 2 = 13/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).
Working: 13 ÷ 36 = 0.361111 (36.1111%)

Key Values:
- Simplified Fraction: 13/36
- Mixed Number Form: 13/36
- Decimal Value: 0.361111
- Percentage: 36.1111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-2-8/
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1/9 + 2/8 = 13/36

Simplified Fraction

13/36

Mixed Number

Proper (13/36)

Decimal Value

0.361111

Percentage

36.1111%

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Step-by-Step Solution: 1/9 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 8 = 72.

LCD(9, 8) = 72

Step 2

Convert to Equivalent Fractions with Common Denominator 72

Multiply the numerator and denominator of 1/9 by 8, and multiply the numerator and denominator of 2/8 by 9 so both fractions share the common base 72.

1 × 8/9 × 8 = 8/72 and 2 × 9/8 × 9 = 18/72

Step 3

Add the Numerators

Now add the numerators (8 + 18 = 26) and keep the common denominator 72 unchanged.

8 + 18/72 = 26/72

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 72, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/72 ÷ 2 = 13/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).

13 ÷ 36 = 0.361111 (36.1111%)

Visual Representation

The diagram below illustrates 1/9 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/36`
Mixed Number Form	`13/36`
Decimal Form	`0.361111`
Percentage	`36.1111%`

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Frequently Asked Questions

What is 1/9 plus 2/8 as a fraction?

1/9 + 2/8 in simplest fraction form is 13/36.

What is 1/9 plus 2/8 as a decimal?

1/9 + 2/8 converted to a decimal is 0.361111.

What is 1/9 plus 2/8 as a percentage?

1/9 + 2/8 expressed as a percentage is 36.1111%.

Does 1/9 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.361111...) because the denominator contains prime factors other than 2 and 5.