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Mathematics 20 Online
OpenStudy (thadds2003):

HELLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPZZZZZZZ!!!!!

OpenStudy (thadds2003):

OpenStudy (michele_laino):

hint: Please, compute this quantities, first: \[\begin{gathered} 4\frac{2}{7} = 4 + \frac{2}{7} = \frac{{\left( {4 \times 7} \right) + 2}}{7} = ...? \hfill \\ \hfill \\ 2\frac{1}{5} = 2 \times \frac{1}{5} = \frac{{\left( {2 \times 5} \right) + 1}}{5} = ...? \hfill \\ \end{gathered} \]

OpenStudy (thadds2003):

ok........

OpenStudy (thadds2003):

first one is 4.28?

OpenStudy (michele_laino):

please write the results as ratios

OpenStudy (thadds2003):

4/28.

OpenStudy (michele_laino):

hint: we can write this: \[4\frac{2}{7} = 4 + \frac{2}{7} = \frac{{\left( {4 \times 7} \right) + 2}}{7} = \frac{{28 + 2}}{7} = ...?\] please complete

OpenStudy (thadds2003):

30/7?

OpenStudy (michele_laino):

yes! Next we have: \[2\frac{1}{5} = 2 \times \frac{1}{5} = \frac{{\left( {2 \times 5} \right) + 1}}{5} = \frac{{10 + 1}}{5} = ...?\]

OpenStudy (thadds2003):

11/5

OpenStudy (michele_laino):

yes! so we can write: \[4\frac{2}{7} \cdot 2\frac{1}{5} = \frac{{30}}{7} \times \frac{{11}}{5} = ...?\]

OpenStudy (thadds2003):

= 9/42?

OpenStudy (michele_laino):

hint: \[4\frac{2}{7} \cdot 2\frac{1}{5} = \frac{{30}}{7} \times \frac{{11}}{5} = \frac{{30 \times 11}}{{7 \times 5}} = ...?\]

OpenStudy (thadds2003):

330/35

OpenStudy (michele_laino):

correct! now we have to reduce such ratio. In order to do taht we can divide numerator and denominator by 5. SO what is: \(330/5=...?\) and \(35/5=...?\)

OpenStudy (thadds2003):

66 and 7

OpenStudy (michele_laino):

that's right, so the final result is: \[\Large 4\frac{2}{7} \cdot 2\frac{1}{5} = \frac{{30}}{7} \times \frac{{11}}{5} = \frac{{30 \times 11}}{{7 \times 5}} = \frac{{{\mathbf{66}}}}{{\mathbf{7}}}\]

OpenStudy (thadds2003):

but you have to convert to a improper.

OpenStudy (michele_laino):

yes! Then please what is \(66:7=...?\) please wrie the answer without the decimal part

OpenStudy (michele_laino):

write*

OpenStudy (thadds2003):

wait, what do the two dots mean?

OpenStudy (michele_laino):

I asked the result of this division: \(66/7=...?\) I have used this symbol \(:\) instead of \(/\)

OpenStudy (thadds2003):

shoot.

OpenStudy (michele_laino):

quotient is...? remainder is...?

OpenStudy (thadds2003):

ok, i had to calculate it, and i keep on getting 9.42.

OpenStudy (michele_laino):

therefore quotient is 9, so we get \(9 \times 7=63\) and remainder is \(66-63=3\) am I right?

OpenStudy (thadds2003):

yes.

OpenStudy (michele_laino):

so, the requested answer is: \[\large 4\frac{2}{7} \cdot 2\frac{1}{5} = \frac{{30}}{7} \times \frac{{11}}{5} = \frac{{30 \times 11}}{{7 \times 5}} = \frac{{66}}{7} = {\mathbf{9}}\frac{{\mathbf{3}}}{{\mathbf{7}}}\]

OpenStudy (thadds2003):

thx.

OpenStudy (michele_laino):

:)

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