ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Divide Negative Numbers

Solve for :

Possible Answers:

Correct answer:

Explanation:

Begin by isolating your variable.

Subtract  from both sides:

, or 

Next, subtract  from both sides:

, or 

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

 or 

Example Question #1 : How To Divide Negative Numbers

Solve the following equation:

Possible Answers:

Correct answer:

Explanation:

The rule for dividing negative numbers is the same as for multiplying negative numbers.  

If both numbers are negative, you will get a positive answer.  

If either number is positive, and the other is negative, you will get a negative answer.  

Therefore:

Example Question #1 : How To Divide Negative Numbers

Choose the answer which best solves the following equation:

Possible Answers:

Correct answer:

Explanation:

To solve, first put the equation in terms of :

First multiply the x to both sides.

Now divide by 12 to solve for x.

Here, because one of the numbers in the equation is positive, and the other is negative, the answer must be a negative number:

Example Question #1621 : Act Math

Add:   

Possible Answers:

Correct answer:

Explanation:

Simply the signs before solving. A positive sign multiplied with a negative sign will convert the sign to a negative, and a negative multiplied with a negative will convert the sign to a positive.

Example Question #1622 : Act Math

Solve: 

Possible Answers:

Correct answer:

Explanation:

Starting at  and adding  is the same as subtracting .  .

Example Question #1 : How To Add Negative Numbers

Solve: 

Possible Answers:

Correct answer:

Explanation:

Adding  to  is the same as subtracting  from .

Example Question #1623 : Act Math

Add 

Possible Answers:

Correct answer:

Explanation:

Starting at  and adding  is the same as subtracting .

Example Question #1 : Number Line

How many integers are there between  and  (not including  or )?

Possible Answers:

Correct answer:

Explanation:

Since we are not including  or  in the count, the number of integers is given by the equation:

 

If negative numbers are difficult for you to understand you can think of it this way. Since both values are negative and we are looking for the amount of integers between them we can solve the problem by subtracting 2 from 17 and then another one since we don't want to include the endpoints.

Example Question #1 : Graphing An Inequality With A Number Line

On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?

Possible Answers:

18

-18

4

10

Correct answer:

18

Explanation:

The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.

|14- (-4)| = |14+4| = |18| = 18

Example Question #2 : Graphing An Inequality With A Number Line

Which of the following is a graph for the values of  defined by the inequality stated above?

Possible Answers:

Ineq21

Ineq24

Ineq22

Ineq23

Ineq25

Correct answer:

Ineq21

Explanation:

To begin, you must simplify so that you "isolate" , (i.e. at least eliminate any coefficients from it). To do this, divide all of the members of the inequality by :

Now, this inequality represents all of the numbers between 13 and 32.  However, it does include  (hence, getting a closed circle for that value) and does not include  (hence, getting an open circle for that value). Therefore, it looks like:

Ineq21

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