Answer:
Option (d) is correct.
[tex]\left(3\frac{1}{2}-9\frac{3}{4}\right)\div \left(-2.5\right)=2.5[/tex]
Step-by-step explanation:
Given: Expression [tex]\left(3\frac{1}{2}-9\frac{3}{4}\right)\div \left(-2.5\right)[/tex]
We have to find the value of the given expression [tex]\left(3\frac{1}{2}-9\frac{3}{4}\right)\div \left(-2.5\right)[/tex]
Consider the given expression [tex]\left(3\frac{1}{2}-9\frac{3}{4}\right)\div \left(-2.5\right)[/tex]
Convert mixed fraction into fraction as [tex]a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
We get,
[tex]=\left(\frac{7}{2}-\frac{39}{4}\right)\div \left(-2.5\right)[/tex]
[tex]\frac{7}{2}-\frac{39}{4}=-\left(\frac{39}{4}-\frac{7}{2}\right)[/tex]
[tex]=\frac{\frac{39}{4}-\frac{7}{2}}{2.5}[/tex]
Consider [tex]\frac{39}{4}-\frac{7}{2}[/tex]
Make denominator equal.
we get,
[tex]=\frac{39}{4}-\frac{14}{4}=\frac{25}{4}[/tex]
Thus, [tex]\left(\frac{7}{2}-\frac{39}{4}\right)\div \left(-2.5\right)[/tex] becomes [tex]=\frac{\frac{25}{4}}{2.5}[/tex]
Apply fraction rule, [tex]\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
we have,
[tex]=\frac{25}{4\cdot \:2.5}[/tex]
Simplify, we have
= 2.5
Thus, [tex]\left(3\frac{1}{2}-9\frac{3}{4}\right)\div \left(-2.5\right)=2.5[/tex]
