3rd Grade Math

Multiplication and Division

Unit 1


You should try to memorize multiplication, so that you don't have to draw out dots every time!

Multiplication

  1. Multiplication is adding numbers together a specific number of times.

  2. For example, 5 x 3 is 5 added together 3 times. So 5 x 3 = 5 + 5 + 5 = 15.

  3. There are three parts to multiplying, the first number is the factor, the second number is also called a factor, and your answer is the product.

  4. Let's start off with 12 x 4 (these two numbers are being multiplied together and are your factors).

  5. When multiplying, the first factor in the problem is seen as the number of groups and the second factor is the number of objects in each group. An easy way to read that is "there are 12 groups of 4 pieces." In other words, add 12 together 4 times.

  6. 12 x 4 = 12 + 12 + 12 + 12 = 48.

Try Watching These Videos to Watch Multiplication in Action!

Watch this video to see how division works!

Division

  1. Division is the opposite of multiplication.

  2. Where multiplication is the combining of groups and objects in each group, division is the separating between groups and the objects in each group.

  3. When dividing, the first number is your dividend and the second number is your divisor. In 12/4, 12 is your dividend and 4 is your divisor.

  4. You can read division as "How many times does my divisor fit into my dividend?" So for 12/4, how many times does 4 fit into 12? It fits 3 times so 12/4 = 3.

Watch the videos below for more help with multiplication and division!

What is the relationship between multiplication and division?

What is the relationship between 90 ÷ 9 = ___ and 9 × ___= 90?

  1. Ninety divided by nine is equal to blank.

  2. Thinking of that as a multiplication question, nine multiplied by blank is equal to ninety.

  3. So whatever the blank is, when you multiply it by 9 you should get 90.

  4. Another way to think about it is what times 9 will get you 90?

  5. Because 9 x 10 is 90, 90/9 is also 10. This is because 9 fits into 90 ten times.

Need more help? Watch this video!

Your Turn!

Once you understand division and multiplication, see if you can answer these questions!

Try to find the relationship between these multiplication and division problems!

11. ___ x 9 = 27 and 27 ÷ ___ = 9

12. 100 ÷ 4 = ___ and 4 x ___ = 100

13. 6 x ___ = 36 and 36 ÷ 6 = ___

14. 81 ÷ ___ = 3 and 3 x ___ = 81

15. ___ x 16 = 48 and 48 ÷ 16 = ___

Play these games for more practice with multiplication and division!

Order of Operations and PEMDAS

Please Excuse My Dear Aunt Sally = Parentheses, Exponents, Multiplication, Division, Addition, & Subtraction

For all math problems that involve more than one operation you must follow the order of ...

  1. Parentheses

  2. Exponents

  3. Multiplication or Division (whichever comes first, from left to right)

  4. Addition or Subtraction (whichever comes first, from left to right)

What's an example of PEMDAS?

Use the drop down arrow to walk through an "order of operations" problem!

"What would that look like?"

Please remember that not all problems will be this long, I just wanted to include all operations. :)

(3 + 22) x 4 + (93 - 43) ÷ 3 x 2 - (19 x 5)

Ok this problem looks like a beast, BUT remember to breathe and you can do this! Break it down into steps and tackle it task by task. You're smart and completely capable of doing anything. Now let's do this together!!

REMEMBER PEMDAS! (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction)

TIP!! Underline or highlight what you're to start with to help organize your work.

Start with the PARENTHESES. Let's simplfy the 3 parentheses that we have.

Simplify by adding 3 and 22 together.

  1. (3 + 22) x 4 + 6 x (93 - 43) ÷ 3 x 2 - (19 x 5)

3 + 22 = 25

25 x 4 + 6 x (93 - 43) ÷ 3 x 2 - (19 x 5)

Go to the second parentheses and subtract 43 from 93.

  1. 25 x 4 + 6 x (93 - 43) ÷ 3 x 2 - (19 x 5)

94 - 43 = 50

25 x 4 + 6 x 50 ÷ 3 x 2 - (19 x 5)

Almost done with all of the Parentheses! Multiply the factors in these parenthesis together!

  1. 25 x 4 + 6 x 50 ÷ 3 x 2 - (19 x 5)

  2. 19 x 5 = 95

25 x 4 +6 x 50 ÷ 3 x 2 - 95

Now that we don't have any more parentheses, let's move on to MULTIPLICATION AND DIVISION!

Multiply left to right.

  1. 25 x 4 + 6 x 50 ÷ 3 x 2 - 95

25 x 4 = 100

100 + 6 x 50 ÷ 3 x 2 - 95

SKIP over the addition and go to the next multiplication operation.

  1. 100 + 6 x 50 ÷ 3 x 2 - 95

6 x 50 = 300

100 + 300 ÷ 3 x 2 - 95

Now Let's Divide!

  1. 100 + 300 ÷ 3 x 2 - 95

300 ÷ 3 = 100

100 + 100 x 2 - 95

Next, Multiply!

  1. 100 + 100 x 2 - 95

100 + 200 - 95

Now that we don't have any multiplication or division left, let's ADD and SUBTRACT!

  1. 100 + 200 - 95

100 + 200 = 300

300 - 95

Final Step!!! Subtract!

  1. 300 - 95 = 205

205 is the answer!! Amazing job, I knew you could do it!

Try these games for more practice with mixed equations and order of operations!