All Pre-Algebra Resources
Example Questions
Example Question #3 : Number Lines
Find the inequality that corresponds to the following number line.
When looking at the number line, we can see that x is any integer between 2 and 7.
Anything to the right of an integer is considered "greater than" and anything left of an integer is considered "less than".
So, we know that x is greater than 2, but less than 7.
Now, since the circle above the 2 is shaded in, 2 is included in the solution. The circle above the 7 is not shaded in, so 7 is not included in the solution.
We now know that x is greater than or equal to 2, and it is still less than 7.
Using the statement above, we will create 2 inequalities.
Now, can also be written as . It has the same value, it just looks a little different.
So we have the two inequalities
and
We can combine them, and it'll look like this
Example Question #4 : Number Lines
Put in order from least to greatest.
Thus, in increasing order:
Example Question #3 : Number Lines
Find the inequality that corresponds with this number line.
When looking at the number line,
we see at -5 there is a filled in circle. We also see there is an arrow going to the right of -5. Every integer to the right of -5 is greater than -5 itself. Because the circle above -5 is filled in, we know -5 is included in the inequality. We get
Example Question #82 : Number Theory
Put the following numbers in order from least to greatest.
There is only one negative number in the numbers.
The next biggest is ,
Next is ,
Next is ,
Lastly is
Example Question #1 : Operations And Properties
Simplify the expression below.
First, distribute the negative sign into the parentheses.
Next, combine like terms.
Note that all operations in this problem are addition and subtraction; there is no need to FOIL or multiply.
Example Question #2 : Operations And Properties
Solve the following problem:
First, work from left to right completing multiplication and division, then work from left to right completing addition and subtraction.
Example Question #3 : Operations And Properties
Suppose you know the value of , and you want to evaluate the expression:
In which order would you carry out the four operations in the expression?
Add, square, multiply, divide
Multiply, divide, add, square
Add, multiply, divide, square
Multiply, add, divide, square
Add, square, divide, multiply
Add, square, multiply, divide
By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a division. Since there are no more grouping symbols, square next. The multiplication is done next, as multiplications and divisions are performed in left-to-right order.
In summary: Add, square, multiply, divide
Example Question #4 : Operations And Properties
Suppose you know the value of , and you want to evaluate the expression:
In which order would you carry out the four operations in the expression?
Square, multiply, add, subtract
Multiply, add, square, subtract
Multiply, square, add, subtract
Add, square, multiply, subtract
Square, add, multiply, subtract
Add, square, multiply, subtract
By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a subtraction. This is the correct order in the absence of grouping symbols.
In summary: Add, square, multiply, subtract
Example Question #5 : Operations And Properties
Simplify the expression.
The order of operations is parenthesis, exponents, multiplication, division, addition, subtraction (PEMDAS).
First, we will evaluate the parentheses. Within the parentheses, we need to solve the exponent, then multiply,
Now that the parenthesis is evaluated, we need to multiply.
Finally, we add and subtract. We can arrange the terms in any order.
Example Question #2 : Order Of Operations
Simplify:
Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:
Certified Tutor
Certified Tutor