Download Multiplication and Division Study Guide

Multiplication and Division Study Guide
Multiplication
 When you multiply (x), you add the same number over and over again. The numbers that you multiply are
called factors. The answer when you multiply is called the product.
 Example:
A horse has 4 legs. If I see three horses in a field, how many legs are there?
1. You can solve this problem by skip counting. Skip count three times by the number of legs on each horse:
4,
8, 12
2. You can solve this problem using repeated addition. Add the number of legs on one horse three times.
4 + 4 + 4= 12
3. You can also solve the problem using multiplication!
3
x
4 = 12
number of number of legs total number
horses
on each horses
of legs
o 3 x 4= 12 is the multiplication sentence for this problem. 2 and 3 are factors, and 12 is the product.
 ARRAY: An array is a group of objects in a square or rectangular shape. In an array the number of rows
is one factor, and the number of objects in each row is the other factor. The total number of objects in
the array is the product.
There are 2 rows of stars, with 4 stars in each row.
The multiplication sentence for this array would be:
2
x
4 =
8
2 rows
4 in each total number
row
of stars
 Multiplication Properties
Identity Property of Multiplication
The Identity Property of Multiplication says that when you multiply a number by 1, the product is that same
number. Example: 1 x 3= 3, 1 x 9= 9, 1 x 10,000= 10,000, 4 x 1= 1
Commutative Property of Multiplication
The Commutative Property of Multiplication says that the order of the factors in a multiplication sentence does
not change the product. Example: 8 x 3 = 3 x 8
24 = 24
Ms. Ivers Multiplication and Division Study Guide
Associative Property of Multiplication
The Associative Property of Multiplication says that when you multiply three numbers, it doesn t matter how you
group the numbers, the product will always be the same. Parentheses () are used to show which two numbers you
will multiply first. Example: (2 x 5) x 3 = 2 x (5 x 3)
10 x 3 = 2 x 15
30 = 30
Division
 When you divide a number or set of things, you break it into equal groups. The number you are dividing is
the dividend. The number you are dividing by is the divisor. The answer when you divide is the quotient.
If something is left over, that number is the remainder.
 Example:
If I have 12 cookies, and 4 friends, how many cookies will each of my friends get?
1. Solve with a division number sentence:
12
total number
of objects
(DIVIDEND)
12
4
=
3
number of
number in
groups
each group
(DIVISOR)
(QUOTIENT)
4 = 3, This means that each of my friends will get 3 cookies!
2. Division is simply repeated subtraction. Start with the total number of objects in the set, and subtract
the number of groups you are putting the objects into. Continue subtracting until you can t subtract
anymore. Count the number of times you subtracted to find your answer. Example:
12 4 = 8 (1 time)
8 - 4 = 4 (2 times)
4 - 4 = 0 (3 times)
3. Division problems can also be solved using equal sharing. Using the total number of objects in the set, place
one object in each group that you are dividing by. Repeat until no objects are left.
Ms. Ivers Multiplication and Division Study Guide