Download Multiplication and Division of Integers Study Guide

Multiplication and Division of Integers Study Guide
Rules for Multiplication and Division: IT IS THE SAME FOR BOTH!!!
negative (x) or (÷) negative is positive
positive (x) or (÷ )positive is positive
negative (x) or (÷) positive is negative
positive (x) or (÷) negative is negative
 If you multiply or divide same signs, the answer will be positive
Examples:
1. – 3 x -5 = +15
Same signs so answer is (+)
2. -15 ÷ -3 = +5
Same signs so answer is (+)
 If you multiply or divide different signs, the answer will be negative.
Examples:
1. -5 x 4 = -20
Diff. signs will have (-) answer
2. -20 ÷ 4 = -5
Diff. signs so answer is (-)
You try:
1.
8 x 2 = __________
5. -35 ÷ (-7) = ___________
2.
-4 x -3 = _________
6. 12 x ( -4) = ___________
3.
-20 ÷ 2 = _________
7. -55 ÷ ( -1) = ___________
4.
-6 x 5 = __________
8. 18 ÷ ( -3) = ___________
Evaluate: Substitute the variable with the given value and then simplify.
13r when r = (-2)
f / (-15) when f = -45
Word Problems: Applications of Integer Multiplication and Division
A group of hitch hikers is descending a mountain at a rate of 400 feet per hour.
What is the change in the elevation of the hikers after 6 hours?
Solve.
The population of a small town is changing at the rate of -120 people per year. How long will it
take for the change in population to be - 960 people?
The temperature outside was 10 degrees. The wind chill made it feel like – 15 degrees. What is
the difference between these two temperatures?
Multiplying Fractions:
To multiply fractions you multiply the numerators and denominators.
Don’t forget to check to see if you can cross reduce before multiplying.

3 10
x =
5 21

2
12
5
52
x
x x
=
5
26
48 100
Multiplying Fractions by Whole Numbers or Mixed Numbers.
Remember to put whole number over one first.
Remember to convert all mixed numbers into improper fractions BEFORE you multiply!!
Check for cross cancelling before multiplying.
Then multiply numerators and then denominators.
4
2
21
x (- ) =
7
45
- 25 x
3
=
5
3
-4
7
1
x 5 =
12
2
8
1
x (-2 ) =
15
68
Applications of Multiplying Fractions
3
1
In a classroom, of the students are wearing blue jeans and
of those students are wearing T5
2
shirts. How many students are wearing jeans and a T-shirt?
2
cups granulated sugar.
5
1
How many cups of sugar are needed if only of the recipe is being made?
2
A muffin recipe calls for 4
a.
b.
How many cups of sugar are needed if only
5
of the recipe is being made?
6
Dividing Fractions
To divide fractions, multiply by reciprocal of divisor.
NOTE: KCF = Keep (first number) then Change (÷ to x) then Flip (second number)
Then follow multiplication rules above.

7
8

=
8
14

4
12
 7
21
Dividing Mixed Numbers and Whole Numbers
Remember to put whole number over one first.
Remember to convert all mixed numbers into improper fractions BEFORE you KCF!!
Keep Change Flip. Then check for cross cancelling before multiplying.
Then multiply numerators and then denominators.
9
4
 2 =
21
7
-3
6
8
 2 =
13
26
3
4
 -5=
7
Applications of Dividing Fractions
2
9
A bag of onions weighs 1
pounds. If the average onion weighs
pound, how many are in
16
16
the bag?
Mixed Application of Fraction Concepts
If a bag of chocolate contains 6 pieces and a box of graham crackers contains 10 crackers, how
many packages of each are needed for 30 campers to evenly divide the food with none left over?
a. 3 bags of chocolate,
5 boxes of crackers
c. 5 bags of chocolate,
3 boxes of crackers
b. 6 bags of chocolate,
10 boxes of crackers
d. 2 bags of chocolate,
1 boxes of crackers
Multiplying Decimals by Decimals
To multiply decimal numbers:
1. Multiply the numbers just as if they were whole numbers.



Line up the numbers on the right - do not align the decimal points.
Starting on the right, multiply each digit in the top number by each digit in
the bottom number, just as with whole numbers.
Add the products.
2. Place the decimal point in the answer by starting at the right and moving a
number of places equal to the sum of the decimal places in both numbers
multiplied.
Dividing Decimals by Decimals
Dividing is the most challenging of our four basic operations. In fact, you have to use
subtraction and multiplication in order to divide, and you also have to be pretty good
at rounding and estimating! Many students have trouble with division, perhaps
because most problems don't come out nice and even--you really have to use your
mental muscle when dividing. Fortunately, we have calculators to make the job
easier--but that doesn't mean you shouldn't learn how to do it yourself! It's easy to
push a wrong button on the calculator, and you always need to know when the
answer it's giving is reasonable.
Dividing decimals is almost the same as dividing whole numbers, except you use the
position of the decimal point in the dividend to determine the decimal places in the
result.
To divide decimal numbers:
1. If the divisor is not a whole number:


Move the decimal point in the divisor all the way to the right (to make it a
whole number).
Move the decimal point in the dividend the same number of places.
2. Divide as usual. If the divisor doesn't go into the dividend evenly, add zeroes
3.
4.
to the right of the last digit in the dividend and keep dividing until it comes
out evenly or a repeating pattern shows up.
Position the decimal point in the result directly above the decimal point in the
dividend. [Show Me. Show and highlight the decimal point in the quotient,
between the 4 and 9]
Check your answer: Use the calculator and multiply the quotient by the
divisor. Does it equal the dividend?
Let's work through an example.
Find this quotient:
First show the division like this:
Now move the decimal point one place to the right, which makes the divisor a whole
number. Also move the decimal point in the dividend one place to the right:
Divide as whole numbers. 65 goes into 169 two times with 39 left over:
To continue dividing, add a zero to the right of the decimal point in the dividend.
Then bring down the zero, and add it to the end of 39, making it 390
65 goes into 390 six times. We write a 6 above the zero in the quotient and put the
decimal point just above the decimal point in the dividend:
To check our answer, we multiply the quotient by the divisor and make sure it equals
the dividend: