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There is no general answer because either method works. And some people are more comfortable following one way while others prefer the other way.

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Q: When would it be most useful to use a fraction to find the answer to a division problem instead of using long division?

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You use scientific notation when it comes to "too large" or "too small" numbers. The reasons why using scientific notation is useful are that it saves time to do the computation and also that it makes people's life easier to compute values instead of writing them out completely!

If you are asking 'in what order are arithmetic operations performed'; One useful mnemonic is BEDMAS. This order is Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. Sometimes called Order of Operations.

Any complex problem can always be made easier to understand, analyze, and thus solve when it is laid out in visual form. Sets help us visualize the issue/problem and put the various data at their proper places. Sets thus help isolate each facet of the problem and can facilitate solving the problem one intersection at a time.

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It is often useful to convert division into multiplication, by inverting the fraction; dividing by 2/3 is the same as multiplying by 3/2.

for division

A fraction represents a physical counting division into subsets (smaller parts). These parts must nominally be the same size, or multiples of a minimum size. If you had 5 unequal parts, you could not perform any useful calculations. For example: the fraction 4/7.5 is a valid division but not a valid fraction, while 8/15 or 40/75 would be valid equivalents.

Cell division is useful in adults for tissue renewal and replacement of certain cells.

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explain how bacteria could be useful instead of hazardous.

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Find the GCF when you want to simplify a fraction. Find an LCM when you want to add and subtract fractions.

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It is called long division because you write down all the numbers for each step to solve the problem and for large numbers there is a lot of writing down. There is a technique called short division which is similar but is more mental, not requiring all the long division steps. But it is usually done only when you are dividing by a small number less than 10, so it is not that useful.

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