The best estimate is 40.92
Explanation:
First of all let's define some concepts:
- An improper fraction is a fraction where the numerator is a number larger than the denominator.
- A mixed fraction is a whole number followed by a proper fraction which is a fraction where the numerator is a number less than the denominator
To get the best estimate of the given expression we have to convert mixed fractions into improper fractions following these steps:
Step 1. Let's multiply the whole number part by the denominator of the proper fraction.
Step 2. Let's add that result to the numerator of the same fraction
Step 3. This result must be written above the denominator
So:
[tex]-14 \frac{1}{9}=-\frac{14\times 9+1}{9}=-\frac{126+1}{9}=-\frac{127}{9} \\ \\ \\ -2\frac{9}{10}=-\frac{2\times 10+9}{10}=-\frac{29}{10}[/tex]
So, our expression becomes:
[tex]-14\frac{1}{9}\left(-2\frac{9}{10}\right)=(-1)(-1)\left(\frac{127}{9}\right)\left(\frac{29}{10}\right)=\frac{127\times 29}{9\times 10} \\ \\ \\ Finally: \\ \\ =\frac{3683}{90} \approx \boxed{40.92}[/tex]
Learn more:
Distributive property: https://brainly.com/question/569172
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