Unit 1: The Number System
Review Material
The unit 1 test will be on the application of the following skills and concepts:
Rational Numbers
Rational numbers can be expressed as one integer divided by another. Rational numbers either terminate or
repeat.
Absolute Value
Absolute value is the distance from zero.
We need to use the absolute value when finding the distance between two points. This is because distance must
be positive, but differences can be positive or negative. Taking the absolute value makes the number positive.
Opposites
Opposites are numbers that are the same distance from zero. Their sum is always zero.
Comparing and Ordering Rational Numbers
Positive numbers are larger than negative numbers.
Positive numbers that are further from zero are larger.
Negative numbers that are further from zero are smaller.
Operations with Rational Numbers
Addition
Adding numbers with the same sign: add the absolute value of the numbers and keep the original sign.
Adding numbers with different signs: subtract the smaller absolute value from the larger absolute value. If the
positive number has the larger absolute value, the answer is positive. If the negative number has the larger
absolute value, the answer is negative.
Subtraction
Same-change-change
Keep the first number the same- change subtraction to addition- change the number to its opposite
Solve as an addition problem.
Multiplication
Multiply the two numbers
If the numbers have the same sign, the answer is positive.
If the numbers have different signs, the answer is negative.
*Note: this applies to two numbers (-2)(-3)(-1) is negative.
(-2)(-3) is positive since a negative times a negative is positive. Now we have a positive times (-1) which is
negative since a positive times a negative is negative.
Divison
Divide the two numbers
If the numbers have the same sign, the answer is positive.
If the numbers have different signs, the answer is negative.
Dividing by zero:
You cannot divide by zero. Look at the example 13 ÷ 0.
We can rewrite this as multiplication: 0 x _____ = 13
But zero times anything is zero so there is no number that when multiplied by zero will equal 13.
Expressing fractions as decimals:
Use long division to express fractions as decimals
The decimals will terminate or repeat. We show repeating decimals by placing a bar above the repeating
number(s).
Fractions
Adding and Subtracting
A common denominator is needed to add and subtract fractions.
Once you have a common denominator, add or subtract the numerators. Put the answer over the denominator.
The denominator remains the same.
Multiplying
Multiply the numerators and multiply the denominators.
Put the product of the numerators over the product of the denominators
Dividing
Same-change-flip
Keep the first fraction the same- change division to multiplication- flip the second fraction
Then solve as multiplication
Mixed numbers
Turn mixed numbers into improper fractions to add, subtract, multiply or divide
Multiply the denominator by the whole number. Then add the numerator. Put the answer over the original
denominator.
Order of Operations
Parenthesis - Exponents - Multiplication and Division (left to right) - Addition and Subtraction (left to right)
Word Problems
Review your classwork and homework for examples