Multiplication

Multiplication

We will be going over the multiplication charts from 1-12 and breaking down techniques, strategies, as well as skills to do further multiplication.​

Multiplication is the practice of or an operation of multiplying two or more numbers together to get a product or end result.

​What is multiplication?

​Multiplication Terms

Multiplicand- The number being multiplied (the first number).

Multiplier- The number "doing the multiplying."

Product- The number at the end of the equation.

Equation- A mathematical statement containing a product, an equal sign, an operation symbol and values/expressions.

x- The symbol used for a multiplication equation.

More Multiplication Terms

Multiple- The end result or the product of when two (whole) numbers are multiplied together.

Example: Multiples of 13 would include 13, 29, 42, 55, 68...

Factor- A number that is multiplied by another number, also known as a factor too, to get the product.

Example: Factors of 8 would include 1, 2, 4, and 8.

Times Tables

The common numbers that would be used for times tables are 1-12. Here are the important numbers or "factors" for each number set:

1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

Important Numbers (Continued)

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108

Important Numbers (Continued)

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120

11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

​Tips and Tricks with 1-12

• When it comes to multiples of 9, think of it as counting down from 9 to 0 and then restarting for the number in the ones place,

• When it comes to multiples of 8, think of it as multiples of 4 except skipping one multiple each time. So you would first start off with 8 for multiples of 8 but with multiples of 4 it would start with 4, then goes to 8. You would then skip four then you'd have your first multiple, which is 8.

​Tips and Tricks with 1-12 (Continued)

Let's go more into depth about the trick with 8:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28...

Multiples of 8: 8, 16, 24, 32, 40, 48...

*Notice how 4 and 8 share the same multiples of 8, 16, as well as 24? Every other multiple in the set of 4 belongs to the set of 8.

​Tips and Tricks with 1-12 (Continued)

• Multiples of 11 from 1-9 are just counting from 1-9 except with two of the same number/the number being duplicated

• Multiples of 10 is just counting from 1-12 but adding a 0 at the end of a number

• Multiples of 12 is the same as multiples of 2 for the number in the ones place (this does vary however)

Multiple Select

Which of the following numbers are a multiple of 10? (Select all that apply)

• 26

• 20

• 39

• 120

Multiple Select

Which of the following numbers are a factor of 9? (Select all that apply)

• 9

• 36

• 3

• 1

Multiple Choice

What is 8 x 6?

• 64

• 72

• 48

• 32

Multiple Choice

What is 5 x 10?

• 50

• 55

• 40

• 80

Multiple Choice

What is 4 x 11?

• 55

• 89

• 22

• 44

Multiple Choice

What is 9 x 7?

• 54

• 72

• 63

• 45

Further into Multiplication

​Multiplying Outside of 1-12

It might seem a little uncomfortable after having to move towards multiplying with different numbers outside of the 1-12 pairs but do not fret! All you need to do is remember the tips and tricks as well as how you would work out the numbers from your familiar pairs. Multiplying numbers outside of the 1-12 pairs is no different than multiplying numbers inside the 1-12 pairs. Let's take a look at an example of multiplying a single digit number with a two-digit number.

​Illustration of 13 x 8 going through the problem step by step together.

​Let's try another problem!

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​Illustration of 18 x 5 going through the problem step by step together.

You try the next problem on your own!

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​Illustration of 15 x 9 seeing if she can go through the problem by herself with a little bit of guidance if needed.

You try the next problem on your own!

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​Illustration of 26 x 4 seeing if she can go through the problem by herself with a little bit of guidance if needed.

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Further into Multiplication

​Multiplying with 2+ Digit Numbers

If you are given an equation with two two-digit numbers such as 26 x 48 or 10 x 10 or something like that, you can assume that your answer will be a three-digit number or more. If it is a single digit number being multiplied with a double-digit number, then your answer will be a two-digit number.

Further into Multiplication (Continued)

​Steps to Solving the Problems

1. Set up your equation with a two-digit number at the top, the other two-digit number at the bottom, the multiplication sign at the left, and a line at the bottom of the full equation.

2. Start with multiplying the number in the ones place at the bottom with both digits at the top from right to left, placing the answers beneath the line.

Steps to Solving the Problems (Continued)

3. Once you have your answers or new numbers beneath the line move beneath the new numbers and place a zero in the ones place.*

   1. Referring to step two, if you multiplied the ones place number with any of the top numbers and got a two-digit number, place the digit of that number on top of the number next to the top number in the ones place (add that number to the answer you get from multiplying the bottom ones place number to the top number in the tens place).

Steps to Solving the Problems (Continued)

4. Repeat step two except place the new numbers underneath the numbers in the "third row."

5. Add all of the numbers together and you will have your answer.

The steps might sound a little confusing so let's go over a few practice problems.

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​Illustration of 35 and 24 going through the problem step by step together.

Let's try another problem!

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​Illustration of 128 and 37 going through the problem step by step together

You try the next problem on your own!

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​Illustration of 86 and 23 seeing if she can go through the problem by herself with a little bit of guidance if needed.

You try the next problem on your own!

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​Illustration of 345 and 48 seeing if she can go through the problem by herself with a little bit of guidance if needed.

You try the next problem on your own!

Summary

• Multiplication is the practice of or an operation of multiplying two or more numbers together to get a product or an end result

• Some important multiplication terms include a product, a multiplicand, a factor, a number multiplied by another number to receive a product, and a multiple, the product from two numbers being multiplied together

• Each individual number from the multiplication tables of 1-12 has its own individual set with important multiples to note

Summary (Continued)

• There are some common multiples between different sets of numbers from the 1-12 multiplication sets, easy tricks such as skipping numbers to get particular multiples, duplicated numbers, counting down in the ones place, counting up with a zero in the ones place, etc.

• Multiplying numbers outside of the 1-12 multiplication sets is simple if you succeed or do well with the numbers inside the 1-12 multiplication sets

Summary (Continued)

• When multiplying with 2+ digit numbers you have to remember that you will either end up with a two-digit product, or a three-digit product (it could vary and be more than a three-digit product)

• After multiplying the number in the bottom's ones place by the numbers on top of it make sure to bring down a zero and continue as followed

END OF DAY 1

Day 2

In this portion of the slideshow you will be learning about greatest common factors and least common multiples.

Definition: The smallest or lowest multiple shared between two numbers.

Least Common Multiple

Definition: The greatest or largest factor shared between two numbers.

Greatest Common Factor

Terms to Know

Term Breakdown

​Greatest Common Factor

As mentioned from the previous lesson, a factor is a number multiplied by another number to receive a product. But instead of just looking at factors, here's an example of how GCFs would be set up:

4: 1, 2, 4

8: 1, 2, 4, 8

Term Breakdown

​Greatest Common Factor (Continued)

4: 1, 2, 4

8: 1, 2, 4, 8

*Take note that out of all the common factors that 4 and 8 share the largest common factor is 4, making that the GCF.

Let's look at another one.

Term Breakdown

​Greatest Common Factor (Continued)

12: 1, 2, 3, 4, 6, 12

24: 1, 2, 3, 4, 6, 8, 12

*Take note that out of all the common factors that 12 and 24 share the largest common factor is 12, making that the GCF.

Let's look at the second term.

Term Breakdown (Continued)

Least Common Multiple

A multiple is the product from two numbers being multiplied together. When looking for the least common multiple you would want to find the first common multiple out of the two sets that is the lowest.

Let's take a look at a few examples.

Term Breakdown (Continued)

Least Common Multiple (Continued)

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

*Take note that out of all the common multiples that 4 and 5 share, the smallest common multiple is 20.

Let's look at another multiple.

Term Breakdown (Continued)

Least Common Multiple (Continued)

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

7: 7, 14, 21, 29, 35, 42, 49, 56, 63, 70

*Take note that out of all the common multiples that 6 and 7 share, the smallest common multiple is 42.

Let's take a look at some practice problems for both terms.

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​Illustration of 9 and 12 going through the problem step by step together (GCF).

​Let's try another problem!

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​Illustration of 10 and 5 going through the problem step by step together (GCF).

You try the next problem on your own!

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​Illustration of 48 and 36 seeing if she can go through the problem by herself with a little bit of guidance if needed (GCF).

You try the next problem on your own!

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​Illustration of 60 and 10 seeing if she can go through the problem by herself with a little bit of guidance if needed (GCF).

Let's try practicing least common multiples.

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​Illustration of 3 and 20 going through the problem step by step together (LCM).

Let's try another problem!

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​Illustration of 15 and 20 going through the problem step by step together (LCM).

You try the next problem on your own!

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​Illustration of 4 and 60 seeing if she can go through the problem by herself with a little bit of guidance if needed (LCM).

You try the next problem on your own!

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​Illustration of 14 and 8 seeing if she can go through the problem by herself with a little bit of guidance if needed (LCM).

Summary

• GCF- The largest common factor shared between two numbers.

• LCM- The smallest common multiple shared between two numbers (if the multiples in each set are ordered from smallest to biggest it is usually the first common multiple spotted).

END OF MULTIPLICATION SLIDESHOW