Answer:
Question 3
Given expression:
[tex]\sf \left(\dfrac{-8}{9} \times \dfrac{1}{-5}\right)+\left(\dfrac{-8}{9} \times \dfrac{-7}{11}\right)[/tex]
Both parentheses share a common term.
To factor out a common term: ab + ac = a(b + c)
[tex]\textsf{Factor out the common term }\dfrac{-8}{9}[/tex]
[tex]\sf \implies\dfrac{-8}{9} \times \left(\dfrac{1}{-5}+\dfrac{-7}{11}\right)[/tex]
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Question 4
To calculate the amount of money Rajni had to begin with, sum the three amounts she spent:
[tex]\sf \implies total=10\frac14+25\frac34+16\frac12[/tex]
As [tex]\sf a\frac{b}{c}=a+\frac{b}{c}[/tex], then:
[tex]\sf \implies 10+\frac14+25+\frac34+16+\frac12[/tex]
Collect and sum the whole numbers:
[tex]\sf \implies (10+25+16)+\frac14+\frac34+\frac12[/tex]
[tex]\sf \implies 51+\frac14+\frac34+\frac12[/tex]
As [tex]\sf \frac14+\frac34=\frac44=1[/tex], then
[tex]\sf \implies 51+1+\frac12[/tex]
[tex]\sf \implies 52+\frac12[/tex]
[tex]\sf \implies 52\frac12[/tex]
