What is 5/6 plus 8/9?
5/6 plus 8/9 equals 31/18 (or 1 13/18 as a mixed number) (or 1.722222 in decimal form). Learn the step-by-step solution to add 5/6 and 8/9 using Least Common Denominator and simplification.
Exact Answer
5/6 + 8/9 = 31/18
Simplified Fraction
31/18
Mixed Number
1 13/18
Decimal Value
1.722222
Percentage
172.2222%
Step-by-Step Solution: 5/6 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 6 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 18 (which is smaller than their product 6 × 9 = 54, keeping the calculation simpler).
LCD(6, 9) = 18
Step 2
Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 5/6 by 3, and multiply the numerator and denominator of 8/9 by 2 so both fractions share the common base 18.
5 × 3/6 × 3 = 15/18 and 8 × 2/9 × 2 = 16/18
Step 3
Add the Numerators
Now add the numerators (15 + 16 = 31) and keep the common denominator 18 unchanged.
15 + 16/18 = 31/18
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 18 is 1, confirming that 31/18 cannot be reduced further—it is already in its simplest irreducible form.
31/18
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (18), divide 31 by 18: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/18.
31/18 = 113/18
Step 6
Decimal & Percentage Representation
Dividing the numerator 31 by denominator 18 produces a repeating decimal (approximately 1.722222, or 172.2222%).
31 ÷ 18 = 1.722222 (172.2222%)
Visual Representation
The diagram below illustrates 5/6 plus 8/9 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 31/18 |
| Mixed Number Form | 1 13/18 |
| Decimal Form | 1.722222 |
| Percentage | 172.2222% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 5/6 plus 8/9 as a fraction?
5/6 + 8/9 in simplest fraction form is 31/18 (or 1 13/18 as a mixed number).
What is 5/6 plus 8/9 as a decimal?
5/6 + 8/9 converted to a decimal is 1.722222.
What is 5/6 plus 8/9 as a percentage?
5/6 + 8/9 expressed as a percentage is 172.2222%.
How do you write 5/6 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 31/18 can be written as the mixed number 1 13/18.
Does 5/6 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.722222...) because the denominator contains prime factors other than 2 and 5.