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. 1-121
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 Manitoba British Columbia Banff Saskatchawan Ontario Quebec Quebec 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 1-122
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. 1-123
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: quotient divisorgdividend 7g105 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 1-124
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 1-125
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. 2 6g138 12 3. Subtract 12 from 13 and bring down the 8 from the ones place. 2 6g138-12 18 4. Divide the 18 by 6. 6 goes into 18, 3 times. 3 x 6 = 18 so write that below the 18. 23 6g138-12 18 18 0 5. Subtract 18 18. The remainder is 0. 6. Check by multiplying the quotient by the divisor. 1 23 x 6 138 138 6 = 23 Go online to watch the Notepad Tutor: Long Division 1-Digit Divisor by 3-Digit Dividend. 1-126
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:, 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. 1-127
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 1-128
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 h e c k 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 x 7 154 158 7 = 22 R 4 Let s Practice In your Workbook go to, Lesson 11 and complete 1 to 15. 1-129
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 24 6 3 R 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. 1-130
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? 2. How can you find it? 3. Write a number sentence 4. Divide 5. Analyze the answer: The number of awards in the last box Each box holds 8 so divide 158 by 8 and look for the remainder. 158 8 19 8g158 8 78 72 6 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. 1-131
Let s Practice In your Workbook go to, 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). 1-132