Question

I NEED HELP WITH THIS PROBLEM ASAP PLEASE!! THANK YOU VERY MUCH!! <3

Answer 1

Answer:

OPTION C

OPTION E

Step-by-step explanation:

Distributive property of Addition:

                            a(b + c) = ab + bc

In other words, 'a' is distributed over 'b' and 'c'.

Also, note that a mixed fraction, of the form $\textbf{c} \frac{\textbf{x}}{\textbf{y}} = \textbf{c} + \frac{\textbf{x}}{\textbf{y}}$

If a mixed fraction is of the type $\textbf{-p}\frac{\textbf{q}}{\textbf{r}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-(p + } \frac{\textbf{q}}{\textbf{r}}) \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-p} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{q}}{\textbf{r}}$

OPTION A:

$\textbf{3} \bigg ( \textbf{-4} \frac{\textbf{1}}{\textbf{2}} \bigg )$

This can be written as: $3 \bigg ( - 4 - \frac{1}{2} \bigg )$

Now, we distribute 3 over -4 and $-\frac{1}{2}$.

$= 3(-4) + 3\bigg (-\frac{1}{2} \bigg )$

Therefore, OPTION A is incorrect.

OPTION B: $\textbf{2} \frac{\textbf{1}}{\textbf{4}} \bigg ( \textbf{1} \frac{\textbf{3}}{\textbf{4}} \bigg )$

Now, this is written as: $2 + \frac{1}{2} \bigg ( 1 + \frac{3}{4} \bigg )$

We have distribute 2 and $\frac{1}{2}$ separately over 1 and $\frac{3}{4}$.

So, we should have $2 (1) + 2 \bigg ( \frac{3}{4} \bigg ) + \frac{1}{2} (1) + \frac{1}{2}. \frac{3}{4}$

So, OPTION B is incorrect.

OPTION C: $\textbf{-4} \bigg( - 5 \frac{\textbf{1}}{\textbf{3}} \bigg )$

$= - 4 \bigg ( -5 - \frac{1}{3} \bigg)$

$= -4(-5) + (-4) \bigg (- \frac{1}{3} \bigg )$

Hence, OPTION C is correct.

Similar method will help us know that OPTION D has used the Distributive property incorrectly and OPTION E has.

So, the answers are:

OPTION A

OPTION C

OPTION E