What is 2/9 plus 8/10?
2/9 plus 8/10 equals 46/45 (or 1 1/45 as a mixed number) (or 1.022222 in decimal form). Learn the step-by-step solution to add 2/9 and 8/10 using Least Common Denominator and simplification.
Exact Answer
2/9 + 8/10 = 46/45
Simplified Fraction
46/45
Mixed Number
1 1/45
Decimal Value
1.022222
Percentage
102.2222%
Step-by-Step Solution: 2/9 + 8/10
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.
LCD(9, 10) = 90
Step 2
Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.
2 × 10/9 × 10 = 20/90 and 8 × 9/10 × 9 = 72/90
Step 3
Add the Numerators
Now add the numerators (20 + 72 = 92) and keep the common denominator 90 unchanged.
20 + 72/90 = 92/90
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 92 and 90, which is 2. Divide both the numerator and denominator by 2.
92 ÷ 2/90 ÷ 2 = 46/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (46) is greater than the denominator (45), divide 46 by 45: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/45.
46/45 = 11/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 46 by denominator 45 produces a repeating decimal (approximately 1.022222, or 102.2222%).
46 ÷ 45 = 1.022222 (102.2222%)
Visual Representation
The diagram below illustrates 2/9 plus 8/10 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 46/45 |
| Mixed Number Form | 1 1/45 |
| Decimal Form | 1.022222 |
| Percentage | 102.2222% |
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Frequently Asked Questions
What is 2/9 plus 8/10 as a fraction?
2/9 + 8/10 in simplest fraction form is 46/45 (or 1 1/45 as a mixed number).
What is 2/9 plus 8/10 as a decimal?
2/9 + 8/10 converted to a decimal is 1.022222.
What is 2/9 plus 8/10 as a percentage?
2/9 + 8/10 expressed as a percentage is 102.2222%.
How do you write 2/9 plus 8/10 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 46/45 can be written as the mixed number 1 1/45.
Does 2/9 plus 8/10 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.022222...) because the denominator contains prime factors other than 2 and 5.