Question

How is writing expressions with variables and numbers similar to writing expressions using words?

Answer 1

Answer:

Sometimes in math we describe an expression with a phrase. For example, the phrase

   "2222 more than 5555"

can be written as the expression

   2+52 + 52+52, plus, 5.

Similarly, when we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).

For example,

   "3333 more than xxxx"

can be written as the algebraic expression

   x+3x+ 3x+3x, plus, 3.

But why? Why use math if we can describe things in words? One of the many reasons is that math is more precise and easier to work with than words are. This is a question you should keep thinking about as we dig deeper into algebra.

Different words for addition, subtraction, multiplication, and division

Here is a table that summarizes common words for each operation:

Operation Words Example algebraic expression

Addition plus, sum, more than, increased by x+3x + 3x+3x, plus, 3

Subtraction subtracted, minus, difference, less than, decreased by p−6p - 6p−6p, minus, 6

Multiplication times, product 8k8k8k8, k

Division divided, quotient a÷9a \div 9a÷9a, divided by, 9

For example, the word "product" tells us to use multiplication. So, the phrase

   "the product of 8888 and kkkk

Let's take a look at a trickier example

Write an expression for "mmmm decreased by 7777".

Notice that the phrase "decreased by" tells us to use subtraction.

So the expression is m−7m - 7m−7m, minus, 7.

Answer 2

The expressions in which the numbers, or variables, or both, are connected by operational signs (+, - etc.) are called algebraic expressions. For example 5, 4x, a+b, x−y.