Introduction
Did you figure out how many buckets of seafood Alex and Nate will need?
Now that they know how many pounds of seafood is needed, they will need to figure out how many buckets they need to order. The seafood comes in 25-pound buckets. We know from the last Concept that Alex and Nate will need to order 3,311 pounds of seafood. That will be enough to feed 43 seals for one week.
How many buckets should they order? Given that it comes in 25-pound buckets, will there be any seafood left over? This Concept will show you how to divide whole numbers. It is exactly what you will need to solve this problem.
Guided Practice
You have learned how to add, subtract and multiply. The last operation that we will learn is division.
First, let’s talk about what the word “division” actually means. To divide means to split up into groups. Since multiplication means to add groups of things together, division is the opposite of multiplication.
\begin{align*}63 \div 9 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
In this problem, 63 is the number being divided, it is the dividend. 9 is the number doing the dividing, it is the divisor. We can complete this problem by thinking of our multiplication facts and working backwards. Ask yourself "What number multiplied by 9 equals 63?" If you said "7", you're right! 9 x 7 = 63, so 63 can be split into 7 groups of 9.
63 ÷ 9 = ?
Ask: What times 9 = 63?
9 X 7 = 63
63 ÷ 9 = 7
The answer to a division problem is called the quotient.
Sometimes, a number won’t divide evenly. When this happens, we have a remainder.
\begin{align*}17 \div 3 =\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}
Hmmm. This is tricky, seventeen is not an even number. There will be a remainder in the quotient.
17 ÷ 3 = ?
Ask: What times 3 gets close to 17, but not over 17?
5 X 3 = 15
We can use an “\begin{align*}r\end{align*}” to show that there is a remainder. The quotient to this problem is 5 r. 2.
We can also divide larger numbers. We can use a division box to do this.
\begin{align*}5 \overline{)725 \;}\end{align*}
Here we have a one digit divisor, 5, and a three digit dividend, 725. We need to figure out how many 5’s there are in 725. To do this, we divide the divisor 5 into each digit of the dividend.
We put the 1 on top of the division box above the 7.
\begin{align*}& \overset{\ 1}{5\overline{ ) 725}}\\ & \underline{-5} \Bigg \downarrow\\ & \quad 22\end{align*}
We multiply 1 by 5 and subtract our result from the dividend. Then we can bring down the next number in the dividend. Then, we need to look at the next digit in the dividend. “How many 5’s are there in 22?” The answer is 4.
Next, we multiply the 4 by 5 to get an anwer of 20. Then we subtract 20 from 22 to find our next number in the dividend. The answer is 2.
In order to complete the problem where all place value digits have a value in the quotient, we need to bring down the 5 in the dividend.
"How many 5's are in 25?" The answer is 5. Our quotient for 725 divided by 5 is 145.
We can check our answer by multiplying the quotient, 145, by the divisor, 5, and see if it equals the dividend, 725.
Our work checks out.
Let’s look at a problem with a two-digit divisor.
\begin{align*}& \overset{\ \hspace{2 mm} 2}{12\overline{ ) 2448}} && ``How \ many \ 12's \ are \ in \ 2? \ None.''\\ & \ \underline{-24} \Bigg \downarrow && ``How \ many \ 12's \ are \ in \ 24? \ Two. \ So \ fill \ that \ in.''\\ & \qquad \ 4 && \ Now \ bring \ down \ the \ "4".\\ \\ & \overset{\ \hspace{4 mm} 20}{12\overline{) 2448}} && ``How \ many \ 12's \ are \ in \ 4? \ None, \ so \ we \ add \ a \ zero \ to \ the \ answer.''\\ && &``How \ many \ 12's \ are \ in \ 48?''\\ && &Four\\ && &There \ is \ not \ a \ remainder \ this \ time \ because \ 48 \ divides \ exactly \ by \ 12.\\ \\ &\overset{\ \hspace{6 mm} 204}{12\overline{ ) 2448}}\end{align*}
We check our work by multiplying: \begin{align*}204 \times 12\end{align*}.
\begin{align*}& \qquad \quad 204\\ & \ \underline {\times \qquad \ 12}\\ & \qquad \quad 408\\ & \ \underline {+ \quad \ 2040}\\ & \qquad \ 2448\end{align*}
Our answer checks out.
We can apply these same steps to any division problem even if the divisor has two or three digits. We work through each value of the divisor with each value of the dividend. We can check our work by multiplying our answer by the divisor.
Now let's practice by dividing whole numbers
Example A
\begin{align*}3\overline{ ) 357 \;}\end{align*}
Solution:
Example B
\begin{align*}8\overline{ ) 4668 \;}\end{align*}
Solution:
Example C
\begin{align*}20\overline{ ) 5020 \;}\end{align*}
Solution:
Now back to Alex and the buckets of seafood.
If the seafood comes in 25-pound buckets, how many buckets will he need?
To complete this problem, we need to divide the number of pounds of seafood by the number of pounds in a bucket. Notice, that we divide pounds by pounds. The items we are dividing have to be the same.
Let’s set up the problem.
\begin{align*}& \overset{\ \ \ \hspace{2 mm} 132}{25\overline{) 3311 \;}}\\ & \ \ \underline{-25}\\ & \quad \ \ 81\\ & \quad \underline{-75 \ }\\ & \qquad \ 61\\ & \quad \ \ \underline{-50}\\ & \qquad \ \ 11\end{align*}
Uh oh, we have a remainder. This means that we are missing 11 pounds of fish. One seal will not have enough to eat if Alex only orders 132 buckets. Therefore, Alex needs to order 133 buckets. There will be extra fish, but all the seals will eat.
Here are two problems for you to solve on your own.
\begin{align*}5 \overline{)4035 \;}\end{align*}
Next, we divide five into 4035.
Answer
\begin{align*}12 \overline{)2820 \;}\end{align*}
Next, we divide twelve into 2820.
Answer
Interactive Practice
Division
Video Review
Here are a few videos for review.
James Sousa Example of Dividing Whole Numbers
Practice Set
Directions: Use what you have learned to solve each problem.
1. \begin{align*}14 \div 7 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
2. \begin{align*}15 \div 2 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
3. \begin{align*}172 \div 6 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
4. \begin{align*}224 \div 8 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
5. \begin{align*}630 \div 5 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
Choose the correct answer.
6. Which number is divisible by 2?
a. 3,405 b. 3,407 c. 3,409 d. 3,406
7. Which number is divisible by 3?
a. 2,688 b. 2,689 c. 2,690 d. 2,692
8. Which number is divisible by 5?
a. 6,709 b. 6,710 c. 6,711 d. 6,712
Choose the missing number.
9.
9,549 ÷ 9 = _______________
a. 579 b. 1,061 c. 791
10.
___________ ÷ 8 = 248
a. 6,245 b. 1,984 c. 2,231
Write a division equation to match the chart. Include the quotient.
11.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
26 | ||||||||||||
39 | ||||||||||||
52 | ||||||||||||
65 |
12.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
32 | |||||||||||||||
48 | |||||||||||||||
64 |
Solve the following word problems. Don't forget the label.
13. Mr. Williams has 160 rubber stamps and wants to give an equal number to each of his 9 students. If Mr. Williams gives the same number of stamps to each student, how many stamps will be left over?
__________________________
14. The farmer wants to plant 37 tomato plants. If he puts 7 plants in each full row, how many tomato plants will be in the partially filled row?
__________________________
15. The media center has 611 magazines at the end of the school year that need to be organized for storage. Each box holds 8 magazines. How many magazines will be in the partially filled box?
_________________________
For 16-20, solve the equations.
16. \begin{align*}216 \div 6 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
17. \begin{align*}1161 \div 43 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
18. \begin{align*}400 \div 16 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
19. \begin{align*}1827 \div 21 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
20. \begin{align*}1244 \div 40 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
21. Which two numbers in the list have a quotient of 18?
23 5 90 36 ________________________
22. Which two numbers in the list have a quotient of 15?
6 45 26 3 39 ________________________
23. Which two numbers in the list have a quotient of 19?
133 3 76 4 38 95 ________________________
Review
- To divide means to split up into groups.
- Division is the opposite of multiplication.
- 63 is thd dividend, and 9 is the divisor in this multiplication problem. \begin{align*}63 \div 9 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}