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1.4: Whole Number Division

Difficulty Level: At Grade Created by: CK-12
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Practice Whole Number Division

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Did you figure out how many buckets of seafood Jonah will need?

Now that he knows how many pounds of seafood is needed, he will need to figure out how many buckets he needs to order. The seafood comes in 25 pound buckets. We know from the last Concept that Jonah will need to order 3,311 pounds of seafood. That will be enough to feed 43 seals for one week.

How many buckets should he 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.

Guidance

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.

72÷9=\begin{align*}72 \div 9 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

In this problem, 72 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 72?" If you said "8", you're right! 9 x 8 = 72, so 72 can be split into 8 groups of 9.

The answer to a division problem is called the quotient.

Sometimes, a number won’t divide evenly. When this happens, we have a remainder.

15÷2=\begin{align*}15 \div 2 =\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

Hmmm. This is tricky, fifteen is not an even number. There will be a remainder here.

We can use an “r\begin{align*}r\end{align*}” to show that there is a remainder. We can also divide larger numbers. We can use a division box to do this.

8)825¯¯¯¯¯¯¯¯¯¯¯\begin{align*}8 \overline{)825 \;}\end{align*}

Here we have a one digit divisor, 8, and a three digit dividend, 825. We need to figure out how many 8’s there are in 825. To do this, we divide the divisor 8 into each digit of the dividend.

\begin{align*}& 8 \overline{)825 \;} \qquad “How \ many \ 8’s \ are \ there \ in \ 8?”\\ & \qquad \qquad \ \ The \ answer \ is \ 1.\end{align*}

We put the 1 on top of the division box above the 8.

\begin{align*}& \overset{\ 1}{8\overline{ ) 825}}\\ & \underline{-8} \Bigg \downarrow\\ & \quad 02\end{align*}

We multiply 1 by 8 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 8’s are there in 2?” The answer is 0.

We put a 0 into the answer next to the 1. \begin{align*}& \overset{\ 10}{8\overline{ ) 825}}\\ & \underline{-8} \;\; \Bigg \downarrow\\ & \quad \ 025\end{align*}

Because we couldn’t divide 8 into 2, now we can bring down the next number, 5, and use the two numbers together: 25

“How many 8’s are in 25?” The answer is 3 with a remainder of 1. We can add this into our answer.

\begin{align*}& \overset{\ 103r1}{8\overline{ ) 825 \;}}\\ & \ \underline{ -8 \ \ }\\ & \ \ \ 025\\ & \ \ \underline{-24}\\ & \qquad 1\end{align*} We can check our work by multiplying the answer by the divisor.

\begin{align*}& \qquad 103\\ & \ \underline {\times \quad \ \ 8 \ }\\ & \qquad 824 + r \ \text{of} \ 1 = 825\end{align*}

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*}

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*}4\overline{ ) 469 \;}\end{align*}

Solution: 117 r 1

Example B

\begin{align*}18\overline{ ) 3678 \;}\end{align*}

Solution: 204 r 6

Example C

\begin{align*}20\overline{ ) 5020 \;}\end{align*}

Solution: 251

Now back to Jonah and the buckets of seafood.

If the seafood comes in 25 lb. 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 Jonah only orders 132 buckets. Therefore, Jonah needs to order 133 buckets. There will be extra fish, but all the seals will eat.

Vocabulary

Here are the vocabulary words used in this Concept.

Dividend
the number being divided
Divisor
the number doing the dividing
Quotient
the answer to a division problem
Remainder
the value left over if the divisor does not divide evenly into the dividend

Guided Practice

Here is a problem for you to solve on your own.

\begin{align*}25 \overline{)3075 \;}\end{align*}

Next, we divide twenty- five into 3075.

Division

Video Review

Here are a few videos for review.

Practice

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

1. \begin{align*}12 \div 6 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}13 \div 4 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}132 \div 7 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

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

5. \begin{align*}130 \div 5 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}216 \div 6 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}1161 \div 43 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}400 \div 16 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}1827 \div 21 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}1244 \div 40 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}248 \div 18 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}3264 \div 16 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}4440 \div 20 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}7380 \div 123 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}102000 \div 200 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

16. \begin{align*}10976 \div 98 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

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Color Highlighted Text Notes

Vocabulary Language: English

Dividend

In a division problem, the dividend is the number or expression that is being divided.

divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression $152 \div 6$, 6 is the divisor and 152 is the dividend.

Quotient

The quotient is the result after two amounts have been divided.

Remainder

A remainder is the value left over if the divisor does not divide evenly into the dividend.

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