Lesson 6 Introduction Divide hole Numbers - PC\|MAC
Lesson 6
Introduction
Divide Whole Numbers
5.NBT.6
Use What You Know
In the last lesson, you learned how to find products of two- and three-digit factors.
Now you will learn how to divide with two-digit divisors.
There are 345 fifth graders enrolled at Wilson Middle School and 15 fifth-grade
classrooms. How many students are in each class if each class has the same number
of students?
a. What multiplication equation can you use to solve 345 4 15?
b. Multiply 15 by multiples of 10. Fill in the blanks.
15 3 10 5 ???
15 3 20 5 ???
15 3 30 5 ???
c. Now estimate the quotient. The quotient will be between which two tens?
d. If 15 3 20 5 300, what number is left after you subtract this product from 345?
e. Divide what is left by 15. ??? 4 15 5 ???
f. Use the information above to find 345 4 15. Explain your thinking.
42
Lesson 6 Divide Whole Numbers
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Find Out More
On the previous page, you used the relationship between multiplication and division
along with properties of operations to divide.
You can also use an area model to show division. It is similar to an area model for
multiplication. You can think of division as finding a missing factor. The dividend is the
product, the divisor is the known factor, and the quotient is the unknown factor.
The area model shows 345 4 15.
20
?
(15 3 20 5 300)
15
345
15
1
3
5 23
(15 3 3 5 45)
345
2 300
45
2 45
45
0
Start with the greatest place and find the quotient place by place. On the previous page,
you estimated the quotient to be between 20 and 30. So, 20 is the greatest ten that can
be in the quotient.
? Start by multiplying 15 by 20.
? Subtract the product from the dividend, 345.
? Write the difference, 45, in the next section of the model.
? Think: 15 3 ? 5 45. Multiply 15 by 3 and subtract this product from 45.
? The difference is 0, so there is nothing left to divide.
Reflect
1 How is dividing with an area model similar to multiplying with an area model?
How is it different?
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Lesson 6 Divide Whole Numbers
43
Lesson 6
Modeled and Guided Instruction
Dividing by Two-Digit Numbers
Learn About
Read the problem below. Then explore different ways to divide by a two-digit divisor.
A grocery store only sells eggs by the dozen. There are 12 eggs in 1 dozen eggs.
If there are 624 eggs in stock, how many dozens of eggs are there?
Model It
You can use the relationship between multiplication and division to
estimate the quotient in a division problem with a two-digit divisor.
624 4 12 5 ? and 12 3 ? 5 624
Multiply 12 by multiples of 10. Make a table.
Number of dozens
10
20
30
40
50
60
Number of eggs
120
240
360
480
600
720
Since 624 is between 600 and 720, the quotient is between 50 and 60.
Model It
You can use an area model to solve a division problem with a
two-digit divisor.
?
50
(12 3 50 5 600)
12
44
624
Lesson 6 Divide Whole Numbers
12
624
2 600
24
1
2
5 52
(12 3 2 5 24)
24
2 24
0
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Connect It
Now you will record the calculations from the model as
partial quotients.
2 How many hundreds are in the dividend? ???
How many groups of 12 are in 600? ???
This partial quotient is written above the bar.
What equation in the area model shows this?
???????????????
3 Why is 600 subtracted from 624?
52
2
50
12?q¡¤¡¤¡¤¡¤
624??
2 600
24
2 24
0
quotient
partial quotient
partial quotient
4 How does the area model relate to finding the second partial quotient?
5 Explain how to use the partial quotients to find 624 4 12.
6 Describe how to divide using partial quotients.
Try It
Use what you just learned about dividing by a two-digit divisor to solve
these problems. Show your work on a separate sheet of paper.
7 An elementary school has 1,134 seeds. The seeds will be planted in 27 rows.
Each row will have the same number of seeds. How many seeds will be planted
in each row? ???????????????
8 Nathan writes an essay with a total of 583 words. Every line of his essay has 11 words.
How many lines long is Nathan¡¯s essay?
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Lesson 6 Divide Whole Numbers
45
Lesson 6
Practice
Guided Practice
Dividing Whole Numbers
Study the example below. Then solve problems 9¨C11.
Example
Each package has 21 pieces of chalk. How many packages can be
made with 1,701 pieces of chalk?
Look at how you could show your work using partial quotients.
81
1
80
21?q¡¤¡¤¡¤¡¤¡¤¡¤
1,701??
2 1,680
21
2 21
21 3 80
Why is 80 a good
number to use as a
first partial quotient?
Pair/Share
21 3 1
0
81 packages
Solution
How can you use
multiplication to
check that the quotient
is correct?
9 A water cooler holds 1,284 ounces of water. How many more 6-ounce
glasses than 12-ounce glasses can be filled from a full cooler?
Show your work.
You can first estimate
how many glasses of
each size can be filled.
Pair/Share
Solution
46
Lesson 6 Divide Whole Numbers
Explain how you found
your estimate.
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