What is 4/9 plus 8/10?
4/9 plus 8/10 equals 56/45 (or 1 11/45 as a mixed number) (or 1.244444 in decimal form). Learn the step-by-step solution to add 4/9 and 8/10 using Least Common Denominator and simplification.
Exact Answer
4/9 + 8/10 = 56/45
Simplified Fraction
56/45
Mixed Number
1 11/45
Decimal Value
1.244444
Percentage
124.4444%
Step-by-Step Solution: 4/9 + 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 4/9 by 10, and multiply the numerator and denominator of 8/10 by 9 so both fractions share the common base 90.
4 × 10/9 × 10 = 40/90 and 8 × 9/10 × 9 = 72/90
Step 3
Add the Numerators
Now add the numerators (40 + 72 = 112) and keep the common denominator 90 unchanged.
40 + 72/90 = 112/90
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 112 and 90, which is 2. Divide both the numerator and denominator by 2.
112 ÷ 2/90 ÷ 2 = 56/45
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (56) is greater than the denominator (45), divide 56 by 45: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/45.
56/45 = 111/45
Step 6
Decimal & Percentage Representation
Dividing the numerator 56 by denominator 45 produces a repeating decimal (approximately 1.244444, or 124.4444%).
56 ÷ 45 = 1.244444 (124.4444%)
Visual Representation
The diagram below illustrates 4/9 plus 8/10 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 56/45 |
| Mixed Number Form | 1 11/45 |
| Decimal Form | 1.244444 |
| Percentage | 124.4444% |
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Frequently Asked Questions
What is 4/9 plus 8/10 as a fraction?
4/9 + 8/10 in simplest fraction form is 56/45 (or 1 11/45 as a mixed number).
What is 4/9 plus 8/10 as a decimal?
4/9 + 8/10 converted to a decimal is 1.244444.
What is 4/9 plus 8/10 as a percentage?
4/9 + 8/10 expressed as a percentage is 124.4444%.
How do you write 4/9 plus 8/10 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 56/45 can be written as the mixed number 1 11/45.
Does 4/9 plus 8/10 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.244444...) because the denominator contains prime factors other than 2 and 5.