Which is greater than 1 or 1
Comparison operators: less than, equal to and greater than
Comparisons are made all the time in real life: does someone have more money than someone else? Who got more votes in a political election? Do I have less clothes in the closet than I need? Of course, these things must also be taken into account by mathematics in tasks. For this reason, we deal with the comparison operators here. The most important are: smaller, equal and larger.
Even if most of them are still not quite clear about this, we have already got to know the "same": 2 + 3 = 5. This means: on the left side of the "=" the value is just as large as on the right side. Calculation tip: First calculate the values on both sides of the "=" and then see whether the numbers are the same. We would like to illustrate this with a few examples:
- Exercise: 5 + 2 = 7 (is correct, because 5 + 2 = 7 and 7 = 7 are equal)
- Exercise: 2 + 1 = 3 (is correct, because 2 + 1 = 3 and 3 = 3 are equal)
- Exercise: 6 + 3 = 7 + 2 (is correct, because 6 + 3 = 9 and 7 + 2 = 9. This means that 9 = 9 is on the sheet and that is the same)
- Exercise: 2 + 3 = 12 (is wrong, because 2 + 3 = 5. And 5 = 12 is wrong, the numbers are not equal )
The thing is actually simple: Calculate the value to the left of the "=" and to the right of it and see if the numbers are the same. If so, the equals sign "=" is correct.
Smaller and bigger
As shown in the last example, it can happen that the values on both sides unequal are. In this case, there are two more characters to consider in math. This is the character "<", which stands for smaller. And the sign ">" which stands for larger. A few examples should clarify this.
- 5> 3 (because the number 5 is greater than the number 3)
- 3 <5 (because the number 3 is smaller than the number 5)
- 8 <9 (because the number 8 is smaller than the number 9)
- 4> 3 (because the number 4 is greater than the number 3)
So you "compare" both numbers and then insert the appropriate symbol. If the first number is greater than the second number, a ">" is set. If the first number is smaller than the second number, a "<" is set. If the two numbers are the same, an "=" is set. If there are several numbers on both sides, the respective side is first calculated and then compared. It will look like that:
- 3 + 4> 1 + 2, because 7> 3
- 5 + 2 <8 + 3, because 7 <11
- -2 3 <1 + 2, because -6 <3
Note: Always first simplify the task on both sides of the "=" and then compare. Tip: A negative number is always less than a positive number or zero.Show:
Less than or equal to or greater than or equal to
In addition to less than, equal to and greater than, there are also the terms less than or equal to "≤" and greater than or equal to "≥". For less than or equal to, this means that the number is either less than or equal. For greater than or equal to, the number is either greater than or equal to. This type of comparison is not used that often in pure mathematics. There the numbers are either the same size, smaller than or larger than another number. Anyone who is even more interested in this should take a look at IT. Because in the case of software problems, less-or-equal and greater-or-equal are often used.
Exercises / written exams
In order to be more confident when working on tasks with less than, equal to and greater than, we have put together a few more exercises and old exam tasks. Initially solves this independently and only then looks at our solutions.
Topics math class 1:
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