# How do you find the value of 1-[30div[7+3(-4)]]?

Oct 23, 2016

$7$

#### Explanation:

When evaluating expressions with $\textcolor{b l u e}{\text{mixed operations}}$ we have to follow a certain order.

Follow the procedure as set out in the acronym PEMDAS.

Since there are ' brackets within brackets' start by evaluating the ' inner' brackets and work ' out'.

That is $3 \left(- 4\right) = 3 \times \left(- 4\right) = - 12 \leftarrow \textcolor{red}{\text{innermost bracket}}$

Now we have.

$\left[7 + \left(- 12\right)\right] = \left[7 - 12\right] = - 5 \leftarrow \textcolor{red}{\text{ next inner bracket}}$

and finally.

[30÷(-5)]=-6larrcolor(red)"final set of brackets"

The expression is now.

$1 - \left(- 6\right) = 1 + 6 = 7 \leftarrow \textcolor{red}{\text{the value of the expression}}$

Oct 23, 2016

$7$

#### Explanation:

In any calculation involving different operations, the MOST important thing is to count the number of TERMS first. Each term is kept separate until the last line, and then they are added or subtracted.

Within each term:
- brackets are done first,
-then powers and roots,
-then multiply and divide.

$\textcolor{b l u e}{1} \textcolor{red}{- \left[30 \div \left[7 + 3 \left(- 4\right)\right]\right]} \text{ } \leftarrow$ There are 2 terms

=color(blue)(1)color(red)(-[30div[7color(black)(-12]])
=color(blue)(1)color(red)(-[30div[color(black)(-5]])" "larr now divide
=$\textcolor{b l u e}{1} \textcolor{b l a c k}{- \left[- 6\right]}$
=$\textcolor{b l u e}{1} \textcolor{red}{+ 6} \text{ } \leftarrow$ final answer for each term
=$7$