# 1.3: Whole Number Multiplication

**At Grade**Created by: CK-12

**Practice**Whole Number Multiplication

Have you ever wondered how much fish a seal can eat?

Jonah loves his job, especially because he gets to help feed the seals who live at the zoo. There are 25 female and 18 male seals for a total of 43 seals. One day, Ms. Guttierez, Jonah’s supervisor at the zoo, asked him to help her place the order for the week’s seafood. Jonah began to do some calculations. Each seal eats an average of 11 lbs. of seafood each day. The seafood comes in 25 lb. buckets. Jonah is puzzled. He doesn’t know how much food to order for one week. He doesn’t know how many buckets will be delivered. Jonah needs help.

**In this Concept, you will learn how to help Jonah figure out his fish problem.** **How many pounds of seafood will they need to feed all of the seals for one week?**

### Guidance

Now that we have learned about addition and subtraction, it is time for multiplying whole numbers.

**Addition and multiplication are related.** Hmmm... What does that mean exactly?

\begin{align*}5 \times 6 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

You can use your times tables to complete this problem using mental math, but let’s look at what we **MEAN** when we multiply 5 by 6. \begin{align*}5 \times 6\end{align*} means that we are going to need five groups of six.

****** | @@@@@@ | ###### | $$$$$$ | &&&&&& |
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We could think of this another way too. We could add 5 six times.

\begin{align*}5 + 5 + 5 + 5 + 5 + 5 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

Wow, that is a lot of work. It is easier to use our times tables.

\begin{align*}5 \times 6 = 30\end{align*}

When multiplying larger numbers, it will help you to think of multiplication as just a short cut for addition.

**What about vocabulary for multiplication?**

5 and 6 are ** factors** in this problem.

**What is a** *factor***?**

**A** *factor***is the name of each of the two values being multiplied.**

30 is the ** product** of the factors 5 and 6.

**What does the word product mean?**

**The** ** product** is the answer to a multiplication problem.

**Now let’s take what we have learned and look at how to apply it to a few more challenging problems.**

\begin{align*}567 \times 3 = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

If you think about this like addition, we have 567 added three times. That is a lot of work, so let’s use our multiplication short cut.

**First, let’s line up our numbers according to place value.**

To complete this problem, we take the digit 3 and multiply it by each digit of the top number. The three is called the ** multiplier** in this problem because it is the number being multiplied. Since 7 is the first number in the upper row, we start by multiplying it by our multiplier, 3:

\begin{align*}7 \times 3 = 21\end{align*}

We can put the 1 in the ones place and carry the 2 (which is really two tens) to the next column over, where it can be added to the other tens after the next multiplication step.

\begin{align*}& \quad 5^267\\ & \underline {\times \quad \ \ 3}\\ & \qquad \ \ 1\end{align*}

Next, we multiply the 3 by 6 and add the two we carried. Leave the 0 in the tens place and carry the two.

\begin{align*}& \quad ^25^267\\ & \underline {\times \quad \quad 3}\\ & \quad \quad \ 0 1\end{align*}

Next, we multiply the 3 by 5 and add the two we carried.

\begin{align*}& \quad ^25^267\\ & \underline {\times \qquad 3}\\ & \quad 1,701\end{align*}

**Our product is 1,701.**

**Now let's look at one with more digits.**

\begin{align*}234 \times 12 =\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, we need to line up the digits according to place value.

\begin{align*}& \qquad 234\\ & \underline {\times \quad \ \ 12}\end{align*}

Our ** multiplier** here is 12.

12 has two digits. We need to multiply each digit of the top number by each digit of the number 12. We can start with the 2 of the multiplier.

\begin{align*}& \qquad 234\\ & \ \underline {\times \quad \ 12}\\ & \qquad 468 \quad Here \ is \ the \ result \ of \ multiplying \ the \ first \ digit \ of \ the \ multiplier.\end{align*}

Next, we multiply the 1, which is in the tens place, by each digit. Because we are multiplying by a number in the "tens" place, we start the second row of numbers with a zero so that the answer to the multiplication is kept in the correct place value for the addition we will do next. Here is what this looks like.

**Our product is 2,808.**

**You could multiply even more digits by more digits.**

You just need to remember two things.

- Multiply each digit of the multiplier one at a time.
- Add in a zero for each digit that you have already multiplied.

Now let's practice. Multiply the following whole numbers.

#### Example A

\begin{align*}456 \times 9 = \underline{\;\;\;\;\;\;\;}\end{align*}

**Solution: 4,104**

#### Example B

\begin{align*}321 \times 18 = \underline{\;\;\;\;\;\;\;}\end{align*}

**Solution: 5,778**

#### Example C

\begin{align*}562 \times 248 = \underline{\;\;\;\;\;\;\;}\end{align*}

**Solution: 139,376**

Now back to Jonah and the seafood order.

We know from the problem that each seal eats an average of 11 lbs of seafood per day. We could do repeated addition here, add 11 forty-three times once for each seal. Boy that is a lot of work. When we have a repeated addition problem, our short cut is to multiply.

\begin{align*}& \qquad \quad 43\\ & \ \underline {\times \qquad 11}\\ & \qquad \quad 43\\ & \ \underline {+ \quad \ 430}\\ & \qquad \ 473\end{align*}

**Jonah needs 473 pounds of seafood to feed all of the seals for one day.**

That's great, but we need to feed all the seals for ONE WEEK! Once again, we could use repeated addition, but multiplication is so much quicker. There are 7 days in one week, so we can multiply 7 by the total pounds of seafood for one day.

\begin{align*}& \quad \ \ \ \ \ 473\\ & \ \underline {\times \quad \ \ \ \ \ 7}\\ & \quad \ \ \ \ 3311 \quad \text{pounds of seafood for one week}\end{align*}

**Okay, we have helped Jonah with half of his problem. Now we know how much seafood he needs for one week.**

### Vocabulary

**Here are the vocabulary words used for this Concept.**

- Factor
- the numbers being multiplied in a multiplication problem

- Product
- the answer to a multiplication problem

- Multiplier
- the number you multiply with

### Guided Practice

Multiply the following values.

\begin{align*}214 \times 362 = \underline{\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

**Answer**

What about when we multiply three digits by three digits? First, you will multiply the first digit of the multiplier by each of the three digits of the top number. Second, you will multiply the second digit of the multiplier by all three digits of the top number. Don’t forget that placeholder zero! Third, you will multiply the third digit of the multiplier by all three digits of the top number. Use two zeros since you are now multiplying by a number in the "hundreds" place.

\begin{align*}& \qquad \quad \ \ 214\\ & \ \ \underline {\times \qquad \ 362}\\ & \qquad \quad \ \ 428 \quad Here \ is \ the \ result \ of \ multiplying \ by \ 2.\\ & \qquad \ \ 12840 \quad Here \ is \ the \ result \ of \ multiplying \ by \ 6. \ Notice \ we \ had \ to \ carry \ and \ add \ in \ a \ zero.\\ & \underline {+ \qquad 64200} \quad Here \ is \ the \ result \ of \ multiplying \ by \ 3. \ Notice \ we \ had \ to \ add \ in \ two \ zeros.\\ & \qquad \ 77,468\end{align*}

**Our product is 77,468.**

### Interactive Practice

**Multiplication**

### Video Review

These videos will help you with multiplying whole numbers.

Khan Academy Basic Multiplication

James Sousa Example of Multiplying Whole Numbers

### Practice

Directions: Use what you have learned to solve each problem.

1. \begin{align*}34 \times 8 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}67 \times 12 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}34 \times 87 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

4. \begin{align*}124 \times 9 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

5. \begin{align*}345 \times 11 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}6721 \times 9 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}8723 \times 31 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}9802 \times 22 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}345 \times 123 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}617 \times 234 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}534 \times 78 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}834 \times 228 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}1134 \times 68 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}2434 \times 218 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}6734 \times 208 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

16. \begin{align*}8934 \times 1238 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

17. \begin{align*}2334 \times 3408 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

factor

Factors are the numbers being multiplied to equal a product. To factor means to rewrite a mathematical expression as a product of factors.Multiplier

The multiplier is the number you multiply with.Product

The product is the result after two amounts have been multiplied.### Image Attributions

Here you'll learn how to multiply whole numbers.

## Concept Nodes:

factor

Factors are the numbers being multiplied to equal a product. To factor means to rewrite a mathematical expression as a product of factors.Multiplier

The multiplier is the number you multiply with.Product

The product is the result after two amounts have been multiplied.