Given:
The expression is [tex]\dfrac{7}{\frac{5}{8}}[/tex].
To find:
The shows the correct way to use the rule ""multiply by the reciprocal"" for the given expression.
Solution:
According to the rule "multiply by the reciprocal", if a,b,c,d are four number, then
[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times \dfrac{d}{c}[/tex]
We have,
[tex]\dfrac{7}{\frac{5}{8}}[/tex]
It can be written as
[tex]\dfrac{7}{\frac{5}{8}}=\dfrac{\dfrac{7}{1}}{\dfrac{5}{8}}[/tex]
Using the rule "multiply by the reciprocal", we get
[tex]\dfrac{\dfrac{7}{1}}{\dfrac{5}{8}}=\dfrac{7}{1}\times \dfrac{8}{5}[/tex]
[tex]\dfrac{\dfrac{7}{1}}{\dfrac{5}{8}}=\dfrac{7\times 8}{1\times 5}[/tex]
[tex]\dfrac{\dfrac{7}{1}}{\dfrac{5}{8}}=\dfrac{56}{5}[/tex]
Therefore, the correct option is D.
