Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #3 : Number Lines

Find the inequality that corresponds to the following number line.Inequality

Possible Answers:

Correct answer:

Explanation:

Inequality

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 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.

Possible Answers:

Correct answer:

Explanation:

Thus, in increasing order:

Example Question #3 : Number Lines

Find the inequality that corresponds with this number line.

Number line

Possible Answers:

Correct answer:

Explanation:

When looking at the number line,

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.

Possible Answers:

Correct answer:

Explanation:

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.

Possible Answers:

Correct answer:

Explanation:

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:

Possible Answers:

Correct answer:

Explanation:

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?

Possible Answers:

Add, square, multiply, divide

Multiply, divide, add, square

Add, multiply, divide, square

Multiply, add, divide, square

Add, square, divide, multiply

Correct answer:

Add, square, multiply, divide

Explanation:

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?

Possible Answers:

Square, multiply, add, subtract

Multiply, add, square, subtract

Multiply, square, add, subtract

Add, square, multiply, subtract

Square, add, multiply, subtract

Correct answer:

Add, square, multiply, subtract

Explanation:

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.

Possible Answers:

Correct answer:

Explanation:

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:

Possible Answers:

Correct answer:

Explanation:

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:

 

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