What is 2/10 plus 8/9?
2/10 plus 8/9 equals 49/45 (or 1 4/45 as a mixed number) (or 1.088889 in decimal form). Learn the step-by-step solution to add 2/10 and 8/9 using Least Common Denominator and simplification.
Exact Answer
2/10 + 8/9 = 49/45
Simplified Fraction
49/45
Mixed Number
1 4/45
Decimal Value
1.088889
Percentage
108.8889%
Step-by-Step Solution: 2/10 + 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 2/10 by 9, and multiply the numerator and denominator of 8/9 by 10 so both fractions share the common base 90.
2 × 9/10 × 9 = 18/90 and 8 × 10/9 × 10 = 80/90
Step 3
Add the Numerators
Now add the numerators (18 + 80 = 98) and keep the common denominator 90 unchanged.
18 + 80/90 = 98/90
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 98 and 90, which is 2. Divide both the numerator and denominator by 2.
98 ÷ 2/90 ÷ 2 = 49/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (49) is greater than the denominator (45), divide 49 by 45: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/45.
49/45 = 14/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 49 by denominator 45 produces a repeating decimal (approximately 1.088889, or 108.8889%).
49 ÷ 45 = 1.088889 (108.8889%)
Visual Representation
The diagram below illustrates 2/10 plus 8/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 49/45 |
| Mixed Number Form | 1 4/45 |
| Decimal Form | 1.088889 |
| Percentage | 108.8889% |
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Frequently Asked Questions
What is 2/10 plus 8/9 as a fraction?
2/10 + 8/9 in simplest fraction form is 49/45 (or 1 4/45 as a mixed number).
What is 2/10 plus 8/9 as a decimal?
2/10 + 8/9 converted to a decimal is 1.088889.
What is 2/10 plus 8/9 as a percentage?
2/10 + 8/9 expressed as a percentage is 108.8889%.
How do you write 2/10 plus 8/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 49/45 can be written as the mixed number 1 4/45.
Does 2/10 plus 8/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.088889...) because the denominator contains prime factors other than 2 and 5.