Question

Evaluate each expression. $$ 100-10 \cdot 2 $$

Short answer

80

Step-by-step solution

Apply the order of operations

First, identify the operations involved in the given expression: subtraction and multiplication. According to the order of operations (PEMDAS/BODMAS), we must perform the multiplication before the subtraction.

Perform the multiplication

Calculate the product of 10 and 2: \[ 10 \times 2 = 20\]

Perform the subtraction

Subtract the result of the multiplication from 100: \[ 100 - 20 = 80\]

Key concepts

PEMDAS

To solve mathematical expressions like ours, you need to follow the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule tells us which operations to perform first.
In our example, the expression is: \[ 100 - 10 \cdot 2 \]
According to PEMDAS, multiplication comes before subtraction. This means we'll handle the multiplication \[10 \cdot 2 \] first, before doing the subtraction.

Multiplication

Now let’s focus on the multiplication part of our expression: \[ 10 \cdot 2 \]
Multiplication means you are adding a number (in this case, 10) repeatedly. Here, we are adding 10 two times.
\[ 10 \times 2 = 10 + 10 = 20 \].
So, \[ 10 \cdot 2 = 20 \].
After performing the multiplication, our expression now looks like this: \[ 100 - 20 \]

Subtraction

The next step is handling the subtraction: \[ 100 - 20 \]
Subtraction means taking away one number from another. Here we need to subtract 20 from 100.
If you subtract 20 from 100, you get: \[ 100 - 20 = 80 \]
So, the final answer to the expression \[ 100 - 10 \cdot 2 \] is 80.
Remember, following the order of operations correctly will always lead you to the right answer!