How do you multiply mixed rational numbers like a decimal and a fraction?

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How do you multiply mixed rational numbers like a decimal and a fraction?

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Answer 1 · 2018-04-01T16:46:48

See explanation below.

Explanation:

To multiply two rational numbers without a calculator, it is easiest to express them both as fractions, then multiply their numerators and denominators.

For example, if you have

$1.6 \times \frac{5}{9} = ?$ $1.6xx5/9=?$

You can express $1.6$ $1.6$ as $\frac{8}{5}$ $8/5$ , so it becomes

$8/cancel5xxcancel5/9=8/9=0.88888...$

How did I know that $1.6=8/5$ ?

Try to see that 1.6 can be expressed as:

$color(red)1.6$

$=1+6/10$

$=10/10+6/10$

$=16/10$

$=(cancel2xx8)/(cancel2xx5)$

$=color(red)(8/5)$

Similarly, if we had a really weird number like 1.234, we can do the same thing:

$color(red)1.234$

$=1+2/10+3/100+4/1000$

$=1000/1000+200/1000+30/1000+4/1000$

$=1234/1000$

$=(cancel2xx617)/(cancel2xx500)$

$=color(red)(617/500)$

Using this method, ANY rational number, by definition, can be expressed as a fraction.

Hope this helps!

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How do you multiply mixed rational numbers like a decimal and a fraction?

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