5.10: Number comparisons using < ,>, and =
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- Victoria Dominguez, Cristian Martinez, & Sanaa Saykali
- Citrus College via ASCCC Open Educational Resources Initiative
The number line is to compare numbers. Here are the symbols used when comparing two or more numbers:
| Symbols used | Read as |
| \(<\) | less than |
| \(\leq\) | less than or equal to |
| \(>\) | greater than |
| \(\geq\) | greater then or equal to |
| \(=\) | equals |
Caution: \(\leq\) and \(\geq\) are used if the numbers that are being compared satisfy at least one of the two conditions.
Note: Moving further to the left of the origin, the numbers are decreasing in value. Moving further to the right of the origin, the numbers are increasing in value.
Examples 1.2.1
| Statement | Reason |
| \(−3 < −2\) | Since -3 is further to the left of -2 |
| \(5 > 1\) | Since 5 is further to the right of 1 |
| \(2 > −6\) | Since 2 is further to the right of -6 |
| \(3 \geq 3\) | 3 is not greater than 3, but they are equal! |
Hint: The symbol \(>\) is pointing to the right direction. The numbers in the right direction are increasing so use this symbol when the first number is greater than the second number. Think similarly for less than.( \(<\) pointing left so less than )
Exercise 1.2.1
For the following exercises compare the following numbers and fill in the blank by using the appropriate symbol \(<\), \(>\), \(\geq\), \(\leq\) or \(=\)
- \(−1\underline{\qquad} 4\)
- \(−4\underline{\qquad} 9\)
- \(0\underline{\qquad} −2\)
- \(3\underline{\qquad} 3\)
- \(−12\underline{\qquad} 12\)
- \(4\underline{\qquad} 6\)
- \(−1\underline{\qquad} -1\)
- \(5\underline{\qquad} −2\)
- \(35\underline{\qquad} 53\)
- \(−29\underline{\qquad} −37\)