Order of Operations - Pre-Algebra

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Question

$3-7\ast8+4\div2=?$

Answer

Remember the order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally" stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction".

$3-7\ast8+4\div2=?$

$3-\left (7\ast8 \right )\left +(4\div2 \right )=$

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Question

Simplify:

$6-(2+5^{2})$

Answer

Follow the order of operations.

First take care of any exponents:

$6-(2+5^{2})$

= 6 - (2 + 25)

Then perform the operations in parentheses:

= 6 - 27

= -21

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Question

Simplify the expression below.

Answer

First, distribute the negative sign into the parentheses.

Next, combine like terms.

Note that all operations in this problem are addition and subtraction; there is no need to FOIL or multiply.

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Question

Simplify the expression.

Answer

The order of operations is parenthesis, exponents, multiplication, division, addition, subtraction (PEMDAS).

First, we will evaluate the parentheses. Within the parentheses, we need to solve the exponent, then multiply,

Now that the parenthesis is evaluated, we need to multiply.

Finally, we add and subtract. We can arrange the terms in any order.

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Question

Suppose you know the value of , and you want to evaluate the expression:

$3 (N + 7)^{2} - 9$

In which order would you carry out the four operations in the expression?

Answer

By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a subtraction. This is the correct order in the absence of grouping symbols.

In summary: Add, square, multiply, subtract

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Question

Suppose you know the value of , and you want to evaluate the expression:

$8 \cdot \left (N + 1 \right ) \div N^{2}$

In which order would you carry out the four operations in the expression?

Answer

By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a division. Since there are no more grouping symbols, square next. The multiplication is done next, as multiplications and divisions are performed in left-to-right order.

In summary: Add, square, multiply, divide

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Question

Solve the following problem: $17+4\cdot 2-6/2=$

Answer

First, work from left to right completing multiplication and division, then work from left to right completing addition and subtraction.

$17+(2\cdot 4)-(6/2)$

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

$2\left { 3+2[1+(3-2)]\right }$

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

$2\left { 3+2[1+(3-2)]\right }$

$=2\left { 3+2[1+(1)]\right }$

$=2\left { 3+2[2]\right }$

$=2\left { 3+4\right }$

$=2\left { 7\right }$

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

$3^3[2-(-4)]+2^4-6+3^{(4-2)}$

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

$3^3[2-(-4)]+2^4-6+3^{(4-2)}$

$=3^3[6]+2^4-6+3^{(2)}$

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Question

Simplify:

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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Question

Simplify:

$2^3(2-3)+3^{[2(1+3-2-1)]}-3[2-(-2)]$

Answer

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

$2^3(2-3)+3^{[2(1+3-2-1)]}-3[2-(-2)]$

$=2^3(-1)+3^{[2(1)]}-3[4]$

$=8(-1)+3^{2}-12$

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Question

Simplify:

$3[2+1+(3^2-4+1)]-2\left { 3[1+(-2)-(-4)+2^2]\right }$

Answer

In order to solve this problem, one must follow the mathematical order of operations. The correct order of mathematical operations consists of the following pattern: parenthesis, exponents, multiplication and division, and finally, addition and subtraction. One should work beginning with the innermost nested parentheses and complete the correct operations from left to right.

$3[2+1+(3^2-4+1)]-2\left { 3[1+(-2)-(-4)+2^2]\right }$

$=3[2+1+(9-4+1)]-2\left { 3[1+(-2)-(-4)+4]\right }$

Remember, subtracting a negative is the same as adding a positive number, and adding a negative is like subtracting a positive.

$=3[2+1+(6)]-2\left { 3[1-2+4+4]\right }$

$=3[9]-2\left { 3[7]\right }$

$=27-2\left { 21\right }$

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