Question

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Answer 1

Question 3

Given expression:

`\sf \left((-8)/(9) * (1)/(-5)\right)+\left((-8)/(9) * (-7)/(11)\right)`

Both parentheses share a common term.

To factor out a common term: ab + ac = a(b + c)

`\textsf{Factor out the common term }(-8)/(9)`

`\sf \implies(-8)/(9) * \left((1)/(-5)+(-7)/(11)\right)`

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Question 4

To calculate the amount of money Rajni had to begin with, sum the three amounts she spent:

`\sf \implies total=10\frac14+25\frac34+16\frac12`

As
`\sf a(b)/(c)=a+(b)/(c)`, then:

`\sf \implies 10+\frac14+25+\frac34+16+\frac12`

Collect and sum the whole numbers:

`\sf \implies (10+25+16)+\frac14+\frac34+\frac12`

`\sf \implies 51+\frac14+\frac34+\frac12`

As
`\sf \frac14+\frac34=\frac44=1`, then

`\sf \implies 51+1+\frac12`

`\sf \implies 52+\frac12`

`\sf \implies 52\frac12`