Math 9 Numeracy– Unit 6.8
-Unit 6 Review
6.8 – Unit 6 Review
Remember that an integer is simply a whole number. There are both positive and negative numbers on a number line. When you draw a number line, the positive numbers are to the right of a zero and the negative numbers are to the left.
On a number line, it is the zero that separates positive numbers from negative numbers. If two numbers are the same distance from zero, but on different sides of the zero, they are called opposites. Understanding the concept of opposites is VERY important in math.
If opposites are combined, the result will always be zero.
Your turn….
Directions: Write the opposites of each number in the space provided.
When adding, subtracting or even multiplying or dividing positive and negative integers, a simple trick can often make things easy for you.
Whenever you see a combination of + or – signs together it is often easy to think of combining the two signs together as one according to this pattern;
Simply put… two signs that are the same are positive and two signs that are different are negative.
Adding Integers
When you add integers you must;
- find the number on the number line
- if the second number is positive, move to the right
- if the second number is negative, move to the left
Your turn…
Directions: Add the following positive and negative integers. Use the following number line to help you.
Your turn…
Directions: Solve the following subtraction of positive and negative numbers. The first three have been done for you.
Multiplying and Dividing Pos/Neg Integers
Multiplying and dividing integers is really quite simply as long as you remember that when you multiply or divide integers that have the same sign, your answer will always be positive, and if you multiply or divide integers that have different signs, then your answer will always be negative. For example;
Your turn…
Multiply the following positive and negative numbers the first three have been done for you.
Now divide the following positive and negative numbers. The first two have been done for you.
Variables and Algebraic Equations
A variable is a letter that represents an unknown number for example if given the algebraic equation x + 3 = 5 , x is the variable and in this instance, equals “2”. To solve this equation in an algebraic fashion you would work top to bottom, keep the equal sign aligned and work first to isolate the x so that in the end you end up with (in this example) x = 2.
It is important that you remember to treat your equation as having two sides, a left and a right, separated by an equals sign ( = ). Your equals sign is like a teeter-totter and in order to keep everything balanced, whatever you do to one side of the equals sign you MUST do to the other side.
Your turn…
Solve the following equations. SHOW ALL YOUR WORK FOR FULL MARKS!!!
Writing and Solving Algebraic Equations
Because many word problems make use of algebraic expressions, it is important to familiarize yourself with some of the language used to express algebra. For example;
Your turn…
Directions: Translate each word problem into an algebraic expression. The first one has been done for you.
Directions: Solve each of the following questions as directed.
- Shale gives 10 CDs to his brother. Now Shale has 35 CDs left.
- Write an equation that you could use to find out how many CDs Shale had to start with, and then solve the equation in an algebraic fashion SHOWING ALL YOUR WORK!!!
- Write an equation for each sentence, and then solve the equation in an algebraic fashion SHOWING ALL YOUR WORK!!!
- Seven more than a number is 18
- Six less than a number is 24
- Five times a number is 45
- A number divided by six is 7
- Three more than four times a number is 19
- Steph bought 14 DVDs of the Johans Brothers for $182. Assuming that each DVD was the same price, what was the individual cost of each DVD?
BEDMAS
Order of operations means just what it sounds like; the order in which we solve our mathematical operations within an algebraic equation.
It is important to do our mathematical operations in the proper order to go about it wrong will only result in a wrong answer. The simplest way in which we can remember this order is by using the acronym, B.E.D.M.A.S. where each letter represents a different operation and the order in which we solve them is in the order in which we spell B.E.D.M.A.S.
If you try to solve an equation like you are reading a book (solving operations as they appear left to right), you run the risk of getting the wrong answer.
Your turn…