Math 5
Unit 1
Lesson 11
Division
Camping
Vacations do not always involve cars and hotels or airplanes.
More people are discovering a love for the road by camping while
travelling long distances. They pack tents, air mattresses, and
sleeping bags. For cooking, gas stoves or campfires are used.
Campers can go hiking, or swimming, or have campfires when
they stop at a campground for the night.
There are many popular places across Canada to stop and camp.
Canada’s national parks are beautiful places to visit. In Alberta the
national parks are Banff, Elk Island, Jasper, Waterton Lakes, and
Wood Buffalo National Park.
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Math 5
Unit 1
Lesson 11: Division
It is 4 391 kilometres from Quebec to Banff National Park. Cameron’s
uncle and aunt plan to camp while they drive from Quebec to Banff to
visit Cameron’s family. They will drive for 5 days.
Alberta
British
Columbia
Banff
Manitoba
Ontario
Saskatchawan
Quebec
Que
bec
Regina
Winnipeg
Thunder
Bay
Montreal
Ottawa
Reflection
How many kilometres will they travel each day
if they travel for 5 days?
Objectives for this Lesson
In this lesson you will explore the following concepts:
• Divide 3-digit numbers by 1-digit numbers
• Find and interpret remainders in division problems
• Solve division problems
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Math 5
Unit 1
Lesson 11: Division
Dividing Numbers
Given two numbers, called the divisor and the dividend, we are able
to find the number of times the divisor is contained in the dividend.
Another way of putting this is that when we divide, we are to find what
number times the divisor will equal the dividend. This answer is called
the quotient.
Dividend
40 ÷ 5 = 8
Divisor
Quotient
Division is considered the inverse operation of multiplication. If you
multiply 4 x 8 you get 32. If you start with the answer 32 and divide by
the 4 or the 8 you will get the other number:
4 x 8 = 32
32 ÷ 4 = 8
32 ÷ 8 = 4
Using multiplication, you can check your answers to the division problems
to see if you are correct.
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Math 5
Unit 1
Lesson 11: Division
You will use your basic multiplication facts to 9 x 9 a lot for division. You
may also have to work with remainders. When you divide 12 ÷ 5 you
cannot get a perfect answer. 5 will divide into 12 twice but that leaves a
remainder of 2 as shown in the picture below.
12 ÷ 5 = 2 R 2
You read this statement as “2 remainder 2.” It means that you can make
2 groups of 5 from the 12 but there will be 2 left over.
You will sometimes have to use remainders in the process of long
division.
Example 1
105 ÷ 7 = ?
Find the answer using long division.
1. Set up your division problem as:
7g105
quotient
divisorg dividend
2.You cannot divide 7 into the 1 of the hundreds place. You will need to
divide 7 into the tens place. Ask yourself: How many 7s are in 10? You
should think 1.
1
7g105
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Lesson 11: Division
3. Now multiply 1 x 7 to get the product 7. Write this below the tens.
1
7g105
7
4. Now subtract the 7 from the 10.
1
7g105
-7
3
5. Bring down the ones of the dividend.
1
7g105
7
35
6.Divide 7 into the 35. Write the answer above the ones. Multiply 5 x 7
to get the product 35. Write this below the 35 and subtract.
15
7g105
7
35
-35
0
The difference here is 0 so that means there is not a remainder. 105
divides into 7 equal parts of 15 without anything left over.
7.Check the quotient using multiplication. Remember, it is the inverse
operation of division, meaning that if you multiply the quotient and the
divisor you should get the dividend.
15 x 7 = 105
This means your answer checks.
105 ÷ 7 = 15
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Lesson 11: Division
Example 2
138 ÷ 6
1. Write your problem in division form.
6g138
2.6 doesn’t divide into 1 so divide 6 into 13. It goes in 2 times.
2 x 6 = 12. Write the 12 below the 13.
6g138
2
12
3. Subtract 12 from 13 and bring down the 8 from the ones place.
6g138
2
-12
18
4.Divide the 18 by 6. 6 goes into 18, 3 times. 3 x 6 = 18 so write that
below the 18.
6g138
23
-12
18
18
0
5. Subtract 18 – 18. The remainder is 0.
6. Check by multiplying the quotient by the divisor.
1
23
x6
138
138 ÷ 6 = 23
Go online to watch the Notepad Tutor: Long Division 1-Digit
Divisor by 3-Digit Dividend.
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Math 5
Unit 1
Lesson 11: Division
Long Division with Remainders
At times you may not get 0 after subtracting at the end. If that is the
case you will have a remainder. Answers with remainders look like this:
Quotient
Meaning
25 R 3
25 Remainder 3
34 R 1
34 Remainder 1
The process for long division does not change, just the result. Remember,
having a remainder means that the divisor does not go into the dividend
evenly. The remainder is the number that is left over after dividing the
dividend into equal parts based on the divisor.
Let’s Explore
Exploration 1: What Remains?
Materials: Unit 1, Lesson 11, Exploration 1 page from your Workbook, About 200 counters
(dry beans will work), Pencil
1. Take 185 counters. Divide the counters into two equal groups.
2. How many counters are in each group?
3. How many counters are left out when you make two equal groups?
4. Write the answer to the problem 185 ÷ 2 in remainder form.
5. Divide the 185 counters into three equal groups.
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Math 5
Unit 1
Lesson 11: Division
6. How many counters are in each group?
7. How many counters are left out when you make three equal groups?
8. Write the answer to the problem 185 ÷ 3 in remainder form.
9.How many equal groups can you make with 185 that will have no
remainder?
10. Take 150 counters. Divide the counters into 7 equal groups.
11. 150 ÷ 7 = ___?
The process for long division is the same with remainders. The following
example will help you see how it ends.
Example 3
158 ÷ 7
1. Write your problem in division form.
7g158
2. Divide 7 into 15. 2 x 7 = 14. Write that below the 15.
2
7g158
14
3. Subtract 14 from 15 and bring down the 8 in the ones place.
2
7g158
14
18
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Lesson 11: Division
4.Divide the 18 by 7. There is no number that you can multiply 7 by to
get 18, so you will have to get as close as you can. 2 x 7 = 14 will
work. Write 2 x 7 = 14 below the 18.
22
7g158
14
18
14
5. Subtract 18 – 14. The remainder is 4.
22
7g158
14
18
14
4
6. Write the answer with the remainder:
22 R 4
7. C
heck by multiplying the quotient by the divisor. Take the remainder
and add it back to your product. If you get the dividend it is correct.
154 + 4 = 158.
Since this is the dividend, our answer is correct.
1
22
x7
154
158 ÷ 7 = 22 R 4
Let’s Practice
• In your Workbook go to Unit 1, Lesson 11 and complete 1 to 15.
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Lesson 11: Division
Using Remainders
Remainders are used all the time. They are not numbers that can be
discarded in real world problems. Think of this situation:
Mrs. Joyce’s fifth grade class will take a field trip next week. The vans
they rent will hold 8 people each. There are 30 people going on the trip.
How many vans will they need to rent?
You can divide to get the number of vans:
3
8g30 3 R 6
24
6
There will be 3 vans with 8 people in each. The remainder is the number
of people that will be left over after the 3 vans are filled. So do you only
need 3 vans? No! This answer leads us to two options for the situation:
Option 1: You will have to rent one van for the extra 6 people that
don’t fit in the first three vans. That means you will need
to rent 4 vans.
or
Option 2: You rent only 3 vans, leaving 6 people out.
You will have to analyze remainders to determine what may be done with
the numbers in a real world context.
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Lesson 11: Division
Example 4
The hockey team has ordered trophies for the end-of-season banquet.
There are 158 awards and each box holds 8 awards. How many awards
will be in the partially filled box?
1. What are you looking for?
The number of awards in the last box
2.How can you find it?
Each box holds 8 so divide 158 by 8
and look for the remainder.
3. Write a number sentence
158 ÷ 8
4. Divide
19
8g158
8
78
72
6
5.Analyze the answer:
The quotient 19 tells us we have 19 boxes
of 8. The remainder 6 is the number of
trophies in the partially filled box.
There will be 6 trophies in the last box.
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Math 5
Unit 1
Lesson 11: Division
Let’s Practice
• In your Workbook go to Unit 1, Lesson 11 and complete 16 to 21.
Go online to watch the Notepad Tutor: Division with Decimals
(3-Digit by 1-Digit Natural Number Divisor).
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