What is 1/3 plus 8/9? (Answer: 11/9)

Exact Answer

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Problem: What is 1/3 plus 8/9?
Formula / Expression: 1/3 + 8/9
Final Answer: 1 2/9 (11/9)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
Working: LCD(3, 9) = 9

Step 2: Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 1/3 by 3, and multiply the numerator and denominator of 8/9 by 1 so both fractions share the common base 9.
Working: 1 × 3/3 × 3 = 3/9 and 8 × 1/9 × 1 = 8/9

Step 3: Add the Numerators
Now add the numerators (3 + 8 = 11) and keep the common denominator 9 unchanged.
Working: 3 + 8/9 = 11/9

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 9 is 1, confirming that 11/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/9

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.
Working: 11/9 = 1 2/9

Step 6: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).
Working: 11 ÷ 9 = 1.222222 (122.2222%)

Key Values:
- Simplified Fraction: 11/9
- Mixed Number Form: 1 2/9
- Decimal Value: 1.222222
- Percentage: 122.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-8-9/
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1/3 + 8/9 = 11/9

Simplified Fraction

11/9

Mixed Number

1 2/9

Decimal Value

1.222222

Percentage

122.2222%

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Step-by-Step Solution: 1/3 + 8/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.

LCD(3, 9) = 9

Step 2

Convert to Equivalent Fractions with Common Denominator 9

Multiply the numerator and denominator of 1/3 by 3, and multiply the numerator and denominator of 8/9 by 1 so both fractions share the common base 9.

1 × 3/3 × 3 = 3/9 and 8 × 1/9 × 1 = 8/9

Step 3

Add the Numerators

Now add the numerators (3 + 8 = 11) and keep the common denominator 9 unchanged.

3 + 8/9 = 11/9

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 9 is 1, confirming that 11/9 cannot be reduced further—it is already in its simplest irreducible form.

11/9

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.

11/9 = 12/9

Step 6

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).

11 ÷ 9 = 1.222222 (122.2222%)

Visual Representation

The diagram below illustrates 1/3 plus 8/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/9`
Mixed Number Form	`1 2/9`
Decimal Form	`1.222222`
Percentage	`122.2222%`

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Frequently Asked Questions

What is 1/3 plus 8/9 as a fraction?

1/3 + 8/9 in simplest fraction form is 11/9 (or 1 2/9 as a mixed number).

What is 1/3 plus 8/9 as a decimal?

1/3 + 8/9 converted to a decimal is 1.222222.

What is 1/3 plus 8/9 as a percentage?

1/3 + 8/9 expressed as a percentage is 122.2222%.

How do you write 1/3 plus 8/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 11/9 can be written as the mixed number 1 2/9.

Does 1/3 plus 8/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.222222...) because the denominator contains prime factors other than 2 and 5.