What is 3/10 plus 8/9?
3/10 plus 8/9 equals 107/90 (or 1 17/90 as a mixed number) (or 1.188889 in decimal form). Learn the step-by-step solution to add 3/10 and 8/9 using Least Common Denominator and simplification.
Exact Answer
3/10 + 8/9 = 107/90
Simplified Fraction
107/90
Mixed Number
1 17/90
Decimal Value
1.188889
Percentage
118.8889%
Step-by-Step Solution: 3/10 + 8/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
LCD(10, 9) = 90
Step 2
Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 3/10 by 9, and multiply the numerator and denominator of 8/9 by 10 so both fractions share the common base 90.
3 × 9/10 × 9 = 27/90 and 8 × 10/9 × 10 = 80/90
Step 3
Add the Numerators
Now add the numerators (27 + 80 = 107) and keep the common denominator 90 unchanged.
27 + 80/90 = 107/90
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 107 and 90 is 1, confirming that 107/90 cannot be reduced further—it is already in its simplest irreducible form.
107/90
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (107) is greater than the denominator (90), divide 107 by 90: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/90.
107/90 = 117/90
Step 6
Decimal & Percentage Representation
Dividing the numerator 107 by denominator 90 produces a repeating decimal (approximately 1.188889, or 118.8889%).
107 ÷ 90 = 1.188889 (118.8889%)
Visual Representation
The diagram below illustrates 3/10 plus 8/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 107/90 |
| Mixed Number Form | 1 17/90 |
| Decimal Form | 1.188889 |
| Percentage | 118.8889% |
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Frequently Asked Questions
What is 3/10 plus 8/9 as a fraction?
3/10 + 8/9 in simplest fraction form is 107/90 (or 1 17/90 as a mixed number).
What is 3/10 plus 8/9 as a decimal?
3/10 + 8/9 converted to a decimal is 1.188889.
What is 3/10 plus 8/9 as a percentage?
3/10 + 8/9 expressed as a percentage is 118.8889%.
How do you write 3/10 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 107/90 can be written as the mixed number 1 17/90.
Does 3/10 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.188889...) because the denominator contains prime factors other than 2 and 5.