1.05 Writing mathematical statements with whole numbers
Introduction
Whenever you want to describe something, the hardest part can be finding the right words, or, in the case of mathematics, the right symbols. The language of mathematics is used all around the world. However, instead of writing sentences with words, we write mathematical sentences using numbers and symbols. In order to translate between our language and the language of mathematics, we will need to get familiar with some common expressions.
Basic operations
Let's start with the four basic operations. These symbols tell us what to do with our numbers and are usually referred to as: plus, minus, times and divide.
| Word desription | Mathematical operation | Mathematical symbol |
|---|---|---|
| \text{Sum of} | \text{Addition (plus)} | + |
| \text{Difference between} | \text{Subtraction (minus)} | - |
| \text{Product of} | \text{Multiplication (times)} | \times |
| \text{Quotient of} | \text{Division (divide)} | \div |
However, there are other ways we can refer to them.
Here are a few ways that we can refer to the same operation using different words:
- 4+9 can be described by: "the sum of 4 and 9" or "4 plus 9" or "9 more than 4".
- 8-3 can be described by: "the difference between 8 and 3" or "8 minus 3" or "3 less than 8".
- 5\times6 can be described by: "the product of 5 and 6" or "5 times 6" or "6 groups of 5".
- 9\div3 can be described by: "the quotient of 9 and 3" or "9 divided by 3" or 9 shared between 3".
Notice that when writing "8-3" as "3 less than 8" the order of the numbers switches around. This is important to remember because "8-3" and "3-8" have different solutions.
Understanding how to translate problems from words into mathematics can make them easier to solve.
Examples
Example 1
Which of the following is described by 'five groups of six'?
A summary of terms that can be used in mathematical statements to describe the basic operations:
Equality and inequality symbols
In addition to the four basic operations, we also have some symbols to describe the relationship between numbers:
| Word description | Symbol | Example |
|---|---|---|
| \text{Greater than} | \gt | \text{"}5\text{ is greater than }2" \text{ can be written as "}5\gt2" |
| \text{Less than} | \lt | " 3\text{ is less than }7" \text{ can be written as } "3\lt7" |
| \text{Greater than or equal to} | \geq | "5 \text{ is greater than or equal to } 4" \text{ can be written as } "5 \geq 4" |
| \text{Less than or equal to} | \leq | "6 \text{ is less than or equal to } 7" \text{ can be written as } "6 \leq 7" |
| \text{Equal to} | = | "4 \text{ is equal to } 4" \text{ can be written as } "4=4" |
| \text{Not equal to} | \neq | "4 \text{ is not equal to } 5" \text{ can be written as } "4 \neq 5" |
Examples
Example 2
Write the following word statement using mathematical symbols: "nineteen is greater than eleven plus six".
We have some symbols to describe the relationship between numbers:
| Word description | Symbol |
|---|---|
| \text{Greater than} | \gt |
| \text{Less than} | \lt |
| \text{Greater than or equal to} | \geq |
| \text{Less than or equal to} | \leq |
| \text{Equal to} | = |
| \text{Not equal to} | \neq |