Understanding Order of Operations: Multiplication, Division, and Parentheses

6 Questions

What is the result of the expression $6 \div 2 \times 3$?

What is the value of the expression $(5 + 3) \times 2 - 4$?

Evaluate the expression $3 \times (4 \div 2) + 2$.

What is the value of the expression $4 \times (3 + 2) \div 2$?

Evaluate the expression $6 \div 3 \times (2 + 1)$.

What is the value of the expression $(4 \times 2) \div (2 + 2)$?

Study Notes

Understanding the Order of Operations: Multiplication, Division, and Parentheses

The order of operations is a crucial concept in mathematics, helping to ensure consistency and accuracy in solving complex equations. By understanding the order in which different types of arithmetic operations should be performed, you can arrive at the correct solution every time. In this article, we'll focus on three key aspects of the order of operations: multiplication, division, and parentheses.

Multiplication and Division

According to the order of operations, multiplication and division should be performed together, starting from the left side and proceeding in the same direction. This means that if an equation contains both multiplication and division signs, you should address them in order from left to right. For example:

2 * 3 / 4 = 6 / 4 = 1.5

Here's how the process works:

Multiply 2 and 3 (resulting in 6).
Divide the result (6) by 4 (which gives you 1.5).

So, the equation 2 * 3 / 4 follows the order of operations and equals 1.5.

Parentheses

Parentheses are used to group expressions together, indicating that the arithmetic operation within them should be performed before any other operations outside of those parentheses. For instance:

(2 + 3) / 4 = 5 / 4 = 1.25

In this case, we first add 2 to 3 (resulting in 5), then divide by 4 (giving us 1.25). This follows the order of operations because the addition inside the parentheses is done before the division on the right side.

The Order of Operations Acronym - PEMDAS

The mnemonic acronym PEMDAS (Please Excuse My Dear Aunt Sally) is a helpful tool for remembering the correct order of operations. Each letter in the acronym corresponds to a specific type of operation:

P: Parentheses or brackets
E: Exponents (powers or square roots)
M: Multiplication and division (from left to right)
D: Addition and subtraction (from left to right)

By following the order outlined by PEMDAS, you can ensure that your calculations are accurate and consistent with the conventions of algebra and mathematics.