ACT Math - How to find order of operations

Evaluate:

–1 + 2 * –3

–3

–7

Explanation

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

Solve the following equation:

(9 + 1) * (42 + 2) * (72 + 1) / 2 = ?

4500

1014.5

9000

1500

Explanation

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".

(9 + 1) * (42 + 2) * (72 + 1) / 2 =

(10) * (16 + 2) * (49 + 1) / 2 =

(10) * (18) * (50) / 2 =

9000/2 = 4500

Find the value of the following expression:

Explanation

To correctly solve this expression, you must follow the correct order of operations: Parentheses- ,

Exponents-,

Multplication/ Division-,

and Addition/Subtraction-.

Find the value of the following expression:

$\frac{(4*(8+2))^2}{10}-20$

Explanation

To correctly solve this expression, you must follow the correct order of operations:

Parentheses (starting with parenthesis inside other parenthesis)-

$\frac{(4*(8+2))^2}{10}-20=\frac{(4*(10))^2}{10}-20=\frac{(40)^2}{10}-20$ ,

Exponents-

$\frac{(40)^2}{10}-20=\frac{1600}{10}-20$ ,

Multplication/ Division-

$\frac{1600}{10}-20= 160-20$ ,

and Addition/Subtraction-

$-2 + 8/2 + (6 - 3) + 2^{0}=?$

Explanation

This is an order of operations, PEMDAS problem. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction.

First we evaluate the parentheses. .

Then, we evaluate the exponent. , since everything raised to the zeroth power equals .

Then, we do the division. $\frac{8}{2}=4$

Lastly, we add the .

Putting it all together, we have .

The expression $\dpi{100} \small a (b+(c+a))$ is equivalent to:

$\dpi{100} \small a^{2}+ab+ac$

$\dpi{100} \small a^{2}-ab+ac$

$\dpi{100} \small 2a+ab+ac$

$\dpi{100} \small 2a-ab+ac$

$\dpi{100} \small ab+ac$

Explanation

In order to find the equivalent expression, distribute to get .

Four times the sum of a number and one is four greater than the square of the difference between the number and six. Which of the following equations could be used to find the number?

$n+4=4+6n^{2}$

$4(n+1)=4+n^{2}-6$

$4n+1=4+n^{2}-6$

$4n+1=4+(n-6)^{2}$

$4(n+1)=4+(n-6)^{2}$

Explanation

Because the "is" represents the equals sign, we must look at everything before "is" and set that equal to everything after.

The first part of the sentence requires us to represent four times the sum of a number and one. This means we must find the sum of the number and one, then multiply this entire quantity by four. The sum of a number and one can be represented as

If we were to then multiply by four, we would write this as , because the entire quantity must be multiplied.

The second part of the sentence asks us to find four greater than the square of the difference between the number and six. This means we must first find the difference between the number and six, and then we must square this quantity. After we do that, we must increase that quantity by four.

The difference between a number and six is represented by

If we were to find the square of this quantity, we could write this as $(n-6)^{2}$

Because we want to write an expression that is four greater than this, we could write $4+(n-6)^{2}$

Thus, the final equation would be:

$4(n+1)=4+(n-6)^{2}$

Simplify:

Explanation

To solve, simply use PEMDAS to do the correct order of operations.

PEMDAS stands for,

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Thus,

$6+7*2-5+3*2\rightarrow 6+14-5+6=20+1=21$

Simplify the following expression:

Explanation

Use order of operations (PEMDAS) in order to simplify the expression:

PEMDAS means to do calculations in the following order.

P: Parentheses

E: Exponents

M: Multiplication

D: Division

Substituting in the above values we get our new equation to be:

A: Addition

S: Subtraction

From here we add and subtract from left to right

$\27+ 11 - 6 + 15 \=38-6+15\=32+15 \=47$

The operation ¤ is defined as “cube the number that is to the right of the ¤ and subtract the result from the number that is to the left of ¤.” What is the value of 100 ¤ (5 ¤ 1)?

**–**25

Explanation

Starting inside the parentheses, cube the number to the right of the symbol, which is 1, and then subtract that from the number to the left of the symbol, 5, to get 4. Then we perform the same operation by cubing 4 to get 64, and then subtracting that from 100 to get 36.

How to find order of operations

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