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

Question

Gabriel Agustin · Accepted Answer

#7#

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.

#color(blue)(1)color(red)(-[30div[7+3(-4)]]) " "larr# There are 2 terms

Start with the innermost bracket, then work outwards:

=#color(blue)(1)color(red)(-[30div[7color(black)(-12]])#

=#color(blue)(1)color(red)(-[30div[color(black)(-5]])" "larr# now divide

=#color(blue)(1)color(black)(-[-6])#

=#color(blue)(1)color(red)(+6)" "larr# final answer for each term

=#7#

Skylar Adams · Answer

#7#

When evaluating expressions with #color(blue)"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(-4)=3xx(-4)=-12larrcolor(red)"innermost bracket"#

Now we have.

#[7+(-12)]=[7-12]=-5larrcolor(red)" next inner bracket"#

and finally.

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

The expression is now.

#1-(-6)=1+6=7larrcolor(red)"the value of the expression"#

Roman Alvarez · Answer

undefined To find the value of $1 - \left[30 \div \left(7 + 3(-4)\right)\right]$, follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

1. Evaluate the expression inside the innermost parentheses: $7 + 3(-4) = 7 - 12 = -5$.
2. Replace the innermost parentheses with the result: $30 \div (-5) = -6$.
3. Replace the division with the result: $1 - (-6) = 1 + 6 = 7$.

Therefore, the value of the expression is $7$.