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Some variations of these symbols include
The last five of the above symbols are inequality symbols. We can negate (change to the opposite) any of the above statements by drawing a line through the relation symbol (as in ), as shown below:
is not greater than can be expressed as either
is not less than can be expressed as either
and both indicate that is less than .
Grouping symbols are used to indicate that a particular collection of numbers and meaningful operations are to be grouped together and considered as one number. The grouping symbols commonly used in algebra are
In a computation in which more than one operation is involved, grouping symbols help tell us which operations to perform first. If possible, we perform operations inside grouping symbols first.
.
The fraction bar separates the two groups of numbers
and
. Perform the operations in the numerator and denominator separately.
Use the grouping symbols to help perform the following operations.
The following examples show how to use algebraic notation to write each expression.
9 minus becomes
46 times becomes
7 times becomes
4 divided by 3, times becomes
times divided by (2 times ) becomes
Introduce a variable ( any letter will do but here we’ll let represent the number) and use appropriate algebraic symbols to write the statement: A number plus 4 is strictly greater than 6. The answer is .
Suppose we wish to find the value of . We could
We now have two values for one number. To determine the correct value we must use the standard order of operations .
As we proceed in our study of algebra, we will come upon another operation, exponentiation, that will need to be inserted before multiplication and division. (See Section [link] .)
USe the order of operations to find the value of each number.
Use the order of operations to find each value.
For the following problems, use the order of operations to find each value.
For the following problems, state whether the given statements are the same or different.
Represent the product of 3 and five different ways.
For the following problems, rewrite each phrase using algebraic notation.
Ten minus three
51 divided by
3 times times
divided by
For the following problems, introduce a variable (any letter will do) and use appropriate algebraic symbols towrite the given statement.
Five times a number, minus one, equals zero.
A number divided by six is greater than or equal to forty-four.
Sixteen minus twice a number equals five.
Determine whether the statements for the following problems are true or false.
The number of different ways 5 people can be arranged in a row is . How many ways is this?
120
A box contains 10 computer chips. Three chips are to be chosen at random. The number of ways this can be done is
How many ways is this?
The probability of obtaining four of a kind in a five-card poker hand is
What is this probability?
Three people are on an elevator in a five story building. If each person randomly selects a floor on which to get off, the probability that at least two people get off on the same floor is
What is this probability?
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