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SCRIPT FOR MULTIPLICATION AND DIVISION II

Multiplication with a Pencil
Division with a Pencil
Division Leaving a Remainder


MULTIPLICATION WITH A PENCIL

If you have a pocket calculator, why in the world would you use pencil and paper to multiply? One answer is that you will not always have a calculator handy. Also there will be doors that will not open for you unless you can do paper and pencil math. Now you will learn to use your multiplication facts in making calculations with a pencil.

EXAMPLE 1: Kyle delivered 51 newspapers each day for 6 days. How many papers did he deliver in all?

THINK: Is this a combining problem? Is this addition or multiplication problem? Write the number question vertically.
COMPUTE: First, you do 6 x 1, and then you do 6 x 5 (50). 

     51 
    x 6 
    306
CHECK: Reread the question and check each step in your thinking and computation.

CHALLENGE 1: Fred went to the movies every day during the month of July, which has 31 days. The ticket for each movie cost $4. How much did he spend for tickets?

CHALLENGE 2: Make these multiplications with a pencil:

33 x 3 = ? , 60 x 9 = ? , 52 x 4 = ? , 74 x 2 = ? , 83 x 3 = ?, 100 x 5 = ?

EXAMPLE 2: Kyle's brother, Lyle, delivered 65 newspapers each day for 6 days. How many papers did he deliver?

THINK: Do you need to combine 6 sets of 65 papers? Write the number question vertically.
COMPUTE: Long way: Think of 65 as 60 + 5. First, you do 6 x 5 and write the product below. Next you do 6 x 60, and put the product below. Then you add the two partial products. 

    65 
    x6
    30
   360
   390
Short way: First, you do 6 x 5, which is 30. You put a 0 in the ones place, and carry the 3, which is 3 tens, over to the 10s place by writing it above the 6. Then do 6 x 6, which is 36, and add the carried 3 to 36 which makes 39 and write it below.
     3
     65 
    x 6
    390
  • CHECK by going through your calculation again.

    Compare each step of the long and short ways of multiplying.

    CHALLENGE 3: Gene bought 3 pairs of slacks on sale for $19 apiece. How much did the 3 pair cost?

    CHALLENGE 4: Make these multiplications with a pencil:

    25 x 5 = ? , 34 x 6 = ? , 47 x 4 = ? , 58 x 5 = ? , 66 x 7 = ? , 79 x 9 = ?

    EXAMPLE 3: Meg bought 16 dozen cookies for the school party. How many cookies is that?

    THINK: Do you need to combine 16 sets of 12? Write the number question vertically.
    COMPUTE: Instead of getting one product we get two partial products and add them together to get the final product. This shows once again that multiplication is just another way of adding. 

              1 
          12 
         x16 
          72 
         120  
         192
    CHECK your thinking and go through your calculation again.

    CHALLENGE 5: The baker bought 15 dozen eggs. How many eggs is that?

    CHALLENGE 6: Make these multiplications with a pencil:

    10 X 10 = ? , 15 X 15 = ? , 25 X 25 = ? , 33 X 66 = ? , 44 X 46 = ?

    Back to the Beginning

    DIVISION WITH A PENCIL

    [Go to and print out the division models.]

    If you need to find how many amounts (divisor) you can separate from another amount (dividend), use long division. You subtract "bunches" of the divisor at a time. You make the bunches with multiplication.

    EXAMPLE 1: Mrs. Jones has $12 to spend for meat, which is sells for $4 per pound. How many pounds can she buy?

    THINK: Do you need to find how many sets of 4 you can separate from 12? What is the number question?
    COMPUTE: Let's look at division model [a]. We separate one 4 at a time until there is nothing left and see how many 4s we separated. Model [b] shows how we can shorten the job by estimating how many 4s we can separate from 12 and multiplying 4 by the estimate. Here are the four steps in division:

    1. DIVIDE or estimate how many times we can separate the divisor from the dividend. How many 4s can you separate from 1? None, so move over to the right one place and estimate how many 4s can we separate from 12? Let's try 3.
    2. MULTIPLY the estimate by the divisor: 3 x 4 = 12
    3. SUBTRACT the product: 12 - 12 = 0
    4. BRING DOWN the next digit in the dividend, if there is one, which there isn't.
    CHECK: Remember that you can check division by multiplying the quotient by the divisor, and the product should equal the dividend.

    CHALLENGE 1: Mrs. Jones baked 24 cookies. If her fat son, Teddy, eats 6 cookies a day, how many days will the cookies last?

    CHALLENGE 2: Make these divisions with your pencil:

    18 ÷ 3 =? , 25 ÷ 5 = ? , 32 ÷ 4 = ? , 42 ÷ 6 = ? , 56 ÷ 8 = ?

    EXAMPLE 2: Mr. Jones gave $48 to his three grandchildren. Each received the same amount. How much was that?

    THINK: This is a different type of division problem than Example 1 where you separated dollars from dollars. In this example you can't actually separate children from dollars, so do you need to divide 48 into 3 parts and see how many dollars are in each part? What is the number question?
    We can look at the problem another way and find how many sets of $3 (1$ for each grandchild) you can separate from $48. What is the number question? The number question is the same. So, although this is a different type of division problem, you set it up in the same way.
    COMPUTE: Let's look at division model [c].

    1. DIVIDE or estimate how many times we can separate the divisor from the first digit in the dividend. How many 3s can you separate from 4?
    2. MULTIPLY the estimate by the divisor: 1 x 3 = 3
    3. SUBTRACT the product: 4 - 3 = 1
    4. BRING DOWN the next digit in the dividend, which is 8.
    5. Repeat the four steps.
    6. DIVIDE or estimate how many 3s we can separate from 18, which is 6.
    7. MULTIPLY: 6 x 3 = 18
    8. SUBTRACT: 18 - 18 = 0. If we estimated that we could separate 5 instead of 6, we would subtract 15 from 18 leaving 3. Since we could separate one more 3, we would cross out the 5 and write 6 above it.
    9. BRING DOWN: There is nothing more to bring down.
    CHECK: We check division with multiplication, so multiply 16 by 3 and the product should be 48.

    CHALLENGE 3: Arnie has $55. How many $5 movie tickets can he buy?

    CHALLENGE 4: Make these divisions with a pencil:

    42 ÷ 3 = ? , 60 ÷ 5 = ? , 76 ÷ 4 = ? , 80 ÷ 8 = ?

    Back to the Beginning

    DIVISION WITH A REMAINDER

    Often when we separate amounts from the dividend, there is a small amount left over that we call the remainder.

    EXAMPLE: Bryan has a $10 bill. Carnival tickets are $3 apiece. How many tickets can he buy? How much change should he get back?

    THINK: Do you need to find how many 3s you can separate from 10? What is the number question?
    COMPUTE: Let's look at division model [d]. We can separate three 3s from 10 which leaves a remainder of 1.
    CHECK: When you check a division with multiplication, you must add the remainder to the product: 3 x 3 = 9, 9 + 1 = 10

    CHALLENGE 1: Sally saw a book that sells for $2. How many of the books can she buy with a five-dollar bill, and how much change should she get back?

    CHALLENGE 2: Make these divisions with a pencil:

    9 ÷ 2 = ? , 11 ÷ 4 = ? , 13 ÷ 5 = ? , 16 ÷ 6 = ? , 17 ÷ 3 = ?

    CHALLENGE 3: Mr. Smith has 43 pictures that he wants to divide equally among his 3 children. How many pictures will each child receive, and what is the remainder?

    CHALLENGE 4: Make these divisions with a pencil:

    32 ÷ 3 = ? , 52 ÷ 5 = ? , 63 ÷ 4 = ? , 88 ÷ 5 = ? , 96 ÷ 7 = ?

    For further explanation of multiplication and division with practice drills go to Multiplying and to Division

    Back to the Beginning