All ACT Math Resources
Example Questions
Example Question #1 : How To Divide Negative Numbers
Solve for :
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:
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:
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:
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:
Starting at and adding
is the same as subtracting
.
.
Example Question #1 : How To Add Negative Numbers
Solve:
Adding to
is the same as subtracting
from
.
.
Example Question #1623 : Act Math
Add
Starting at and adding
is the same as subtracting
.
.
Example Question #1 : Number Line
How many integers are there between and
(not including
or
)?
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?
18
-18
4
10
18
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?
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:
All ACT Math Resources
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