Download Notes for Lesson 1-6: Multiplying and Dividing Real Numbers

Notes for Lesson 1-6: Multiplying and Dividing Real Numbers
1-6.1 - Multiplying and Dividing signed numbers
When you multiply or divide signed numbers the signs of the numbers you are multiplying or dividing
determines whether the product or quotient is positive or negative.
To Multiply or Divide signed numbers:
a) Multiply or divide the integers
b) If both numbers have the same sign, your product or quotient is positive If the two numbers have
different signs, your product or quotient is negative
Examples: Multiply or Divide
8 x for x  
12  5
60
5
4
11(4)
44
 5
8  
 4
40
 or  10
4
1-6.2 - Dividing by fractions
Vocabulary:
Reciprocals - Two numbers whose product is 1
Multiplicative Inverses - A number and its reciprocal
When dividing by a fraction, we multiply by the reciprocal.
Examples: Divide
4  8
  
5  15 
4  15 
  
5  8
60
3
1
or or 1
40
2
2
1
4
4 37
 
1 4
4 4
 
1 37
16

37
4  9
3
  9
4
3
9
 
4
1
3
1
 
4
9
3
1
or
36
12
6 x for x  7
6  7 
42
1-6.3 - Properties of Zero
Remember when you multiply or divide with zero special things will happen.
Multiplication by Zero - The product of any number and zero will always be zero
Division by Zero - When the divisor is zero, the answer is undefined
Zero divided by a number - When zero is your divisor, the answer is always zero
Examples: Multiply or Divide
a0  0
0
0
6
12
 undefined
0
1-6.4 Simplifying square root expressions
Since the square root is the same number multiplied together, a square root can have 2 possible solutions a
positive and negative.
For example: √25 could be 5 since 5*5 = 25 but also -5 since -5 * -5 = 25 also.
Usually we only use the positive square root but there are time we need to use the negative or consider both as
possible solutions. For those times, we will use the – sign in front for the opposite of the square root. Or we
will use the ± sign to show we want both.
Examples: −√121 = −11
±√16 = 4 𝑎𝑛𝑑 − 4 𝑜𝑟 ± 4
1-6.5 - Application
A hot-air balloon is taken for a 2.5-hour trip. The wind speed (and the speed of the balloon) is 4.75 mi/h. The
balloon travels in a straight line. How many miles away from the liftoff site will the balloon land?
4.75(rate)  2.5 time   11.875 miles