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Basic Operations

When it comes to math, you always want to make sure you have a good grasp of foundational concepts before moving on to more complex aspects of the subject. A great place to start is with the basic operations.

What are the basic operations?

There are four basic arithmetic operations: addition, subtraction, multiplication, and division. Here is an overview of these operations:

 Operation Operator Example Word Phrase Addition + $8+4=12$ The sum of 8 and 4 is 12. Subtraction - $8-4=4$ The difference of 8 and 4 is 4. Multiplication ×∗ $8×4=32$ The product of 8 and 4 is 32. Division / ÷ $8÷4=12$ The quotient of 8 and 4 is 2.

Exponents and parentheses

The exponentiation operation is another arithmetic operation. It involves using exponents to evaluate powers. The exponent tells you the number of times you should use the base (x) as a factor. The expression ${x}^{3}$ means x to the third power, while ${5}^{3}$ means 5 to the third power or $5×5×5$

Parentheses, like exponents, are often used for multiplication. For example, an equation like $5{\left(3+4\right)}^{3}$ can be translated as $5×{\left(3+4\right)}^{3}$ . You can also use parentheses to group numbers.

Understanding the order of operations

As you delve into more complex math problems, you'll discover some that use more than one operator. In this case, it will be important to understand the order of operations and PEMDAS.

PEMDAS stands for Parentheses, Exponents, Multiplication-Division, and Addition-Subtraction. It represents the order in which you should work through math expressions that involve more than one operation. Let's say that you encounter a problem like the following:

$4×2+{\left(7-5\right)}^{2}$

You'll want to first calculate within the parentheses: $4×2+{\left(2\right)}^{2}$ . Then, simplify exponential expressions: $4×2+4$ . Next, work through multiplications and divisions (from left to right): $8+4$ . And finally, work through additions and subtractions (from left to right): $8+4=12$ .

Practice questions on the basic operations

a. Write the word phrase for $3+2=5$ .

The sum of 3 and 2 is 5.

b. Write the word phrase for $10÷2=5$ .

The quotient of 10 and 2 is 5.

c. How can $2{\left(6+1\right)}^{3}$ be rewritten?

Answer: $2{\left(7\right)}^{3}$

d. For the problem $5×1+{\left(3-2\right)}^{2}$ , what should be calculated first?

Calculate within the parentheses first $\left(3-2\right)=1$

e. What is another way to write ${7}^{3}$ ?

7 to the third power or $\left(7×7×7\right)$

f. Solve this expression using PEMDAS: $7×3+2{\left(4-1\right)}^{2}$

$7×3+2{\left(3\right)}^{2}$

$7×3+2\left(9\right)$

$21+18$

$39$

Get help learning about basic operations

Understanding arithmetic operations is essential to successfully solve just about any math problem. It's important to get comfortable with the four basic operations and also gain a quality understanding of exponents, parentheses, and how to work through math expressions using the correct order of operations (PEMDAS). If your student wants to better understand these operations or needs assistance with an assignment or test preparation, working with a tutor can make a significant difference. Reach out to the Educational Directors at Varsity Tutors today to learn more about the benefits of tutoring.

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