# Multiplication

**Multiplication by 0**

Anything multiplied by 0 is 0.

5 X 0 = 0

**Multiplication by 1**

Anything multiplied by 1 is itself.

7 X1 = 7

**Multiplication by 2**

Double the number that is multiplied by 2.

8 X 2 = 16 (Double 8)

**Multiplication by 10**

Add a zero after the number multiplied by 10.

4 X 10 = 40 (Add a zero after the 4)

**Multiplication by 100.**

Add two zeros after the number multiplied by 100.

8 X 100 = 800 (Add two zeros after the 8)

**Multiplication by 11.**

Write the number multiplied by 11 twice.

7 X 11 = 77 (Write the 7 twice)

**Let's Test your knowledge:**

1. 7 X 0

2. 9 X 0

3. 4 X 1

4. 8 X 1

5. 2 X 3

6. 5 X 2

7. 9 X 2

8. 4 X 2

9. 9 X 0

10. 7 X 2

11. 2 X 6

12. 4 X 10

13. 8 X 10

14. 5 X 10

15. 9 X 10

16. 10 X 3

17. 5 X 100

18. 100 X 4

19. 100 X 9

20. 4 X 11

21. 11 X 7

22. 7 X 10

23. 8 X 11

24. 9 X 11

25. 3 X 100

## TAKING HALF

It will be helpful for multiplication and division if we can quickly take half of a number.

Take half of 20. You get 10.

Take half of 10. You get 5.

Take half of 40. You get 20.

Take half of 70. You get 35 - this one is a little trickier.

Take half of 30. You get 15.

Take half of 50. You get 25 (think about money, 50 cents is 2 quarters, half of 50 is one quarter or 25 cents).

Take half of 60. You get 30.

Take half of 80. You get 40.

## MULTIPLYING BY 5.

One way to multiply by 5 is to count by 5's. If you had 5 X 6 - you would count by 5's six times: 5, 10, 15, 20, 25, 30. This is a good strategy but if you know how to take HALF, you can get your answer quicker. Since 5 is HALF of 10, multiply your number by 10 and then take HALF.

So - 5 X 6 - THINK 6 X 10 = 60, take half, 30.

Try another one:

8X5 --> THINK 8 X 10,= 80, take half, 40.

This can get your answer much quicker!

Try some:

1. 5 X 3

2. 6 X 5

3. 5 X 5

4. 5 X 4

5. 8 X 5

6. 7 X 5

### Practicing your 5's:

1. 5 X 3

2. 5 X 9

3. 5 X 2

4. 5 X 4

5. 5 X 8

6. 5 X 1

7. 5 X 5

8. 5 X 6

9. 5 X 0

10. 5 X 7

11. 5 X 10

12. 5 X 11

## MULTIPLYING BY 9

To multiply by 9, there are a couple of tricks. First, the first (tens) digit of your answer is ONE LESS than the number you are multiply by. If you have 8 X 9, then your tens digit will be ONE LESS than 8 which is 7. If multiplying 6 X 9, then your tens digit will be 5; if doing 3 X 9, your tens digit will be 2. To find your ones digit, figure out what you need to add to the tens digit to get a sum of 9.

8 X 9

The tens digit will be 7.

Two more is needed to get from 7 to 9, so the answer is 72.

4 X 9

The tends digit will be 3.

Six more is needed to get from 3 to 9, so the the answer is 36.

**FINGER TRICK:** Another way to do it is to hold out both hands. Count from the finger on the farthest left hand side. Fold down the finger that corresponds to the number being multiplied by 9. So, if you have 9 X 5, fold down the fifth finger, this would be your thumb on your left hand. Count the number of finger (both hands) that fall to the LEFT of the folded finger, that is your TENS digit, then count the number of fingers to the RIGHT side of the folded finger, that is your ONES digit. So in 9 X 5, I have FOUR fingers to the LEFT of my folded down thumb and 5 fingers to the RIGHT of the folded down thumb, therefore the answer is 45.

If I have 9 X 8. I will count 8 fingers from the starting left-hand. This would have me fold down the middle finger on my RIGHT hand. I count the number of fingers to the LEFT of that finger and I get 7, to the RIGHT of the finger, I get 2 therefore my answer is 72.

### Practice your 9's

1. 9 X 2

2. 9 X 9

3. 9 X 6

4. 4 X 9

5. 5 X 9

6. 1 X 9

7. 9 X 0

8. 9 X 8

9. 7 X 9

10. 9 X 10

11. 11 X 9

## MULTIPLYING BY 4

**DOUBLE AND DOUBLE AGAIN**

Let's practice doubling a number twice.

If you have 4 and double it, you get 8. If you then double 8, you get 16.

If you have 9 and double it, you get 18. To double it again, you may have to write out the problem sometime if it cannot be done in your head:

18

__+18__

36

So, when you start with 9, double to 18, double again to 36.

If you have 6 and double, you get 12. Doubling 12 in your head is easier, just line up the 2's and add to 4. Line up the 1's and add to get 2. Your solution is 24. Practice the easier ones in your head until you get good at it.

Now, when you multiply by 4, you circle the number that is multiplied by the 4, double that number and double it again and you have your answer.

**3 X 4: Double 3 and get 6, double 6 and get 12. 3 X 4 = 12**

**7 X 4: Double 7 and get 14, double 14 and get 28. 7 X 4 = 28**

**8 X 4: Double 8 and get 16, double 16 (write it out on paper if you can't do this one in your head) and get 32. 8 X 4 = 32.**

Remember that if you have 9 X4 - you get to choose, do you want to use your 4's trick (double and double again) or use the 9's trick (fingers) - so do whatever is easier for you.

## MEMORIZING FACTS

We now have strategies for many different facts, but there are just a few that have to be memorized.

3's: There is no good trick for the 3's. **You can double it and then add one more if you like:**

3 X 6 = double 6 to 12 and add a 6 to get 18.

You can just use the other tricks for many of the facts.

For 6X6, 6X8 and 8X8, I try to remember either a little song or rhyme.

**6 times 6 is 36 and 6 times 8 is 48.**

**For 8 X 8,** you can either remember: Bend down touch the floor, 8 X 8 is 64.

Or Skate X Skate is Sticky Floor can help too.

**If you need to with 8's you can double 3 times too.**

8 X 7: Doulbe 7 to get 14, double 14 to get 28 and finally double 28 to get 56.

6 X 8 is a little easier for the Triple Double: Double once, 12, Double again 24, Double again, 48. (Those are easy enough to do in your head).

## Learning 12 FACTS

I don't believe in memorizing the 12 facts when it is so easy to multiply by 10 and by 2. You just need to do both and add together.

6 X 12: (6 X 10 ) + (6 X 2) = 60 + 12 = 72.

5 X12 = 50 + 10 = 60

8 X 12 = 80 + 16 = 96

Even for 11 X 12, you can multiply 11 by 10 - you get 110 and then add the double of 11, 22: 110 + 22 = 132.

### Practice your 12's:

1. 2 X 12

2. 8 X 12

3. 4 X 12

4. 9 X 12

5. 3 X 12

6. 0 X 12

7. 5 X 12

8. 6 X 12

9. 1 X 12

10. 7 X 12.

11. 10 X 12

12. 11 X 12

13. 12 X 12

## MULTIPLICATION CONCEPT

Don't forget as you work through learning your facts that you need to know the CONCEPT behind multiplication. There are 2 ways to think of multiplication:

1) Number of Groups and Number of Objects in each group.

One of the numbers tells you how many groups you have, the other number tells you how many objects are in that group. The total number of objects in the answer.

You can think about how many things in the real world come in groups. Each person has 2 eyes. Each dog has 4 legs. Each dozen eggs has 12 eggs. Each basketball team has 5 people playing.

Multiplication problems will state: There are 10 people, each person has 2 eyes, how many eyes in all? 10 "groups" with 2 "items" in each group: 10 X 2 = 20.

There are 6 dogs, each dog has 4 legs, how many legs in all? 6 "groups" with 4 "items" in each group: 6 X 4 = 24.

There are 8 baskets, each basket has 3 apples in it, how many apples in all? 8 groups of 3 or 8 X 3 = 24.

2) An Array - Imagine a rectangle shape with a certain number of objects across and then a certain number of objects down and filling in to form a rectangle. It you multiply the number across by the number down, you will have the total number in the array.

There are 6 row with 10 trees in each row, how many trees in all? This is an array with 6 across and 10 down, for a total of 6 X 10 = 60 trees.

There are 8 rows of cars with 8 cars in each row, how many cars in all? Again this makes an array (this time it is a square): 8 X 8 = 64.

It is easy to get a list of problems that are all multiplication, so to check that you understand the difference between the concept of multiplication, addition, and subtraction - here are a mixed set. Read each carefully and determine which operation to use and then write the number sentence and find the answer.

### Concept Problems

1. There are 5 apples in one basket and 9 apples in another basket, how many apples in all?

2. There are 5 baskets and each basket has 9 apples in it, how many apples in all?

3. There are 9 apples in a basket, I eat 3 apples, how many apples are left?

4. There are 7 candy bars on the table and 8 candy bars on the counter, how many candy bars in all?

5. There are 5 friends, each friend is carrying 4 candy bars, how many candy bars in all?

6. I have 15 candy bars and give 7 away to my friends, how many candy bars are left?

7. There are 9 rows of marbles and 6 marbles in each row, how many marbles in all?

8. Mike has 9 marbles and Sue has 6 marbles, how many more marbles does Mike have than Sue?

9. Lara has 9 marbles and jeff has 6 marbles, how many marbles are there in all?

10. Wes had 16 cards and givens 9 to his friend, how many does he have left?

11. Wes has 16 cards and his friend has 9 cards, how many more cards does Wes have than his friend?

12. Wes lines up his cards, he has 5 rows of cards and 8 cards in each row, how many cards does he have in all?