More Practice with the Form $\,a\cdot\frac bc\,$
Need some basic practice with the form $\,a\cdot\frac{b}{c}\,$ first?
Practice with the form $\,a\cdot\frac{b}{c}$
Examples
Simplify:
$\displaystyle\,4\cdot\frac{3}{2}$
Solution:
$$
\cssId{s8}{4\cdot\frac{3}{2}}
\cssId{s9}{ \ =\ \frac{4}{2}\cdot 3}
\cssId{s10}{\ =\ 2\cdot 3}\
\cssId{s11}{\ =\ 6}
$$
You should be able to go from the original expression to the final answer without writing anything down. The solution above shows the thought process.
Always be on the lookout for factors in the denominator that go into factors in the numerator evenly!
Simplify:
$\displaystyle \,\frac{-3}{-5}\cdot -10$
Solution:
$$
\cssId{s18}{\frac{-3}{-5}\cdot -10}
\cssId{s19}{\ =\ - \frac{10}{5}\cdot 3}
\cssId{s20}{\ =\ -2\cdot 3}
\cssId{s21}{\ =\ -6}
$$
Here, use a two-step process:
- Figure out the sign first (negative); type in the minus sign.
- Then, do the mental arithmetic with positive numbers.