What is 1/3 plus 5/9? (Answer: 8/9)

Exact Answer

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Problem: What is 1/3 plus 5/9?
Formula / Expression: 1/3 + 5/9
Final Answer: 8/9
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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 5/9 by 1 so both fractions share the common base 9.
Working: 1 × 3/3 × 3 = 3/9 and 5 × 1/9 × 1 = 5/9

Step 3: Add the Numerators
Now add the numerators (3 + 5 = 8) and keep the common denominator 9 unchanged.
Working: 3 + 5/9 = 8/9

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 8 and 9 is 1, confirming that 8/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 8/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).
Working: 8 ÷ 9 = 0.888889 (88.8889%)

Key Values:
- Simplified Fraction: 8/9
- Mixed Number Form: 8/9
- Decimal Value: 0.888889
- Percentage: 88.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-5-9/
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1/3 + 5/9 = 8/9

Simplified Fraction

8/9

Mixed Number

Proper (8/9)

Decimal Value

0.888889

Percentage

88.8889%

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Step-by-Step Solution: 1/3 + 5/9

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 5/9 by 1 so both fractions share the common base 9.

1 × 3/3 × 3 = 3/9 and 5 × 1/9 × 1 = 5/9

Step 3

Add the Numerators

Now add the numerators (3 + 5 = 8) and keep the common denominator 9 unchanged.

3 + 5/9 = 8/9

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 8 and 9 is 1, confirming that 8/9 cannot be reduced further—it is already in its simplest irreducible form.

8/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).

8 ÷ 9 = 0.888889 (88.8889%)

Visual Representation

The diagram below illustrates 1/3 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/9`
Mixed Number Form	`8/9`
Decimal Form	`0.888889`
Percentage	`88.8889%`

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Frequently Asked Questions

What is 1/3 plus 5/9 as a fraction?

1/3 + 5/9 in simplest fraction form is 8/9.

What is 1/3 plus 5/9 as a decimal?

1/3 + 5/9 converted to a decimal is 0.888889.

What is 1/3 plus 5/9 as a percentage?

1/3 + 5/9 expressed as a percentage is 88.8889%.

Does 1/3 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.888889...) because the denominator contains prime factors other than 2 and 5.