1. Copyright © Ed2Net Learning, Inc. 1 Dividing with Decimal Remainders Grade 4

2. Copyright © Ed2Net Learning, Inc. 2 Warm Up Divide: 1. 42 ÷ 4 2. 25.93 ÷ 8 3. 23 ÷ 40 4. 77.76 ÷ 15 5. 84.21 ÷ 13

3. Copyright © Ed2Net Learning, Inc. 3 Let’s first review what we learnt about division in the previous session before proceeding further. There are four terms which describe the four numbers in a division problem. Dividend. Divisor. Quotient. Remainder. Dividend = Divisor X Quotient + Remainder. 8 quotient 5)43 40 dividend divisor 3 remainder

4. Copyright © Ed2Net Learning, Inc. 4 This can be represented on the number line as follows: Multiplication is repeated subtraction. So, 4.5 ÷ 3 = 1.5 1 0 2 34 1.5 5 You can count backward in groups of 1.5. There are 3 jumps of value 1.5 from 4.5 to 0. Find 4.5 ÷ 3. 4.5

5. Copyright © Ed2Net Learning, Inc. 5 Expressing the quotient as a decimal Divide 17 by 5. 5 17 3 -15 2 There are no more digits in the dividend. Place a decimal point and bring it up to the quotient. 5 17.0 3.4 -15 20 Add a 0 onto the remainder. Continue dividing. Add a 0 onto each remainder until the division is exact. If the division is not exact, round off the quotient to the required number of decimal places. -20 00 Review

6. Copyright © Ed2Net Learning, Inc. 6 Review The dividend less than the divisor Divide 7 by 8. The dividend 7 is less than the divisor 8. 8 7.0 0.875 -64 60 Place a decimal point and bring it up to the quotient. Add a 0 onto the dividend. Start dividing. Add a 0 onto each remainder until the division is exact. If the division is not exact, round off the quotient to the required number of decimal places. - 56 40 - 40 00

7. Copyright © Ed2Net Learning, Inc. 7 Review When the dividend is a decimal, and the divisor a whole number Divide: 7.64 ÷ 2 Place the divisor (2) before the division bracket and place the dividend (7.64) under it. Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole number. STEP 1: 2 7.64

8. Copyright © Ed2Net Learning, Inc. 8 Review To divide a decimal by a whole number, divide as you would for whole numbers. 2 7.64 3.82 -6 16 Place a decimal point in the answer so that it lines up with the decimal point in the Dividend. -16 004 -4 0 If after dividing you have a remainder, add a zero to the dividend and continue to divide until there is no remainder or the decimals recur. STEP 2:

9. Copyright © Ed2Net Learning, Inc. 9 Review Divide: 8.66 ÷ 4 We can find the solution as follows: 4 8.66 2.165 -8 06 -4 26 -24 20 -20 00 Note: We added a trailing zero to 8.66 when 4 would not divide into 2. Adding a trailing zero (or zeros) to a decimal number does not alter its value.

10. Copyright © Ed2Net Learning, Inc. 10 Let’s start When we are given a long division to do, sometimes there will be numbers left over. These are known as Remainders. We can use the long division process to work out the answer to a number of decimal places. Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole number. If the divisor has a decimal in it, we can make it a whole number by moving the decimal point the appropriate number of places to the right.

11. Copyright © Ed2Net Learning, Inc. 11 Divide: 5 ÷ 12. Round to the nearest hundredths place. Note: Since we must round to the hundredths place, we will carry the answer out 1 place beyond the hundredths place.) 12 5 Place the numbers in the division equation format. The dividend 5 is less than the divisor 12. Place a decimal point and bring it up to the quotient. 12 5.00 0.4 - 48 20

12. Copyright © Ed2Net Learning, Inc. 12 5.000 0.416 - 48 20 - 12 80 Add a 0 onto the dividend. Start dividing. The remainder is not zero, so add another zero to the dividend. - 72 8 The remainder is still not zero. The remainder continues to be 8. This is a repeating decimal. We need our answer rounded to the nearest hundredths place, so we are ready to round. 0.416 rounded to the nearest hundredths place is 0.42

13. Copyright © Ed2Net Learning, Inc. 13 4 233.4 Place the numbers in the division equation format. Begin the division with 4 into 23 (since 4 cannot go into 2). This gives us 5 with a remainder of 3. 4 233.4 5 - 20 3 Divide: 233.4 ÷ 4 We will see another problem:

14. Copyright © Ed2Net Learning, Inc. 14 Now bring down the next 3, so we must divide 33 by 4. This gives us 8 with a remainder of 1. 4 233.4 58 - 20 33 - 32 14 Now bring down 4, so we must divide 14 by 4. Here, 4 occurs in the dividend after the decimal, so we put a decimal in the quotient after 8. This gives us 3 with a remainder of 2. 4 233.4 58.3 - 20 33 - 32 14 - 12 2

15. Copyright © Ed2Net Learning, Inc. 15 If after dividing you have a remainder, add a zero to the dividend and continue to divide until there is no remainder or the decimals recur. Now bring down the next 0, so we must divide 20 by 4. This gives us 5 with a remainder of 0. 4 233.40 58.35 - 20 33 - 33 14 - 12 20 - 20 00

16. Copyright © Ed2Net Learning, Inc. 16 BREAK

17. Copyright © Ed2Net Learning, Inc. 17

18. Copyright © Ed2Net Learning, Inc. 18 Assignments 1) 23 ÷ 16 2) 13 ÷ 15 Divide. Round to the nearest hundredths place: 3) 67 ÷ 9 4) 7 ÷ 8

19. Copyright © Ed2Net Learning, Inc. 19 6) 246.8 ÷ 9 7) 685.53 ÷ 11 5) 355.67 ÷ 13 Divide. Round to the nearest thousandths place: 8) 513.56 ÷ 45

20. Copyright © Ed2Net Learning, Inc. 20 9) Tina bought 6 ice creams for $15.9. Find the cost of one ice-cream.

21. Copyright © Ed2Net Learning, Inc. 21 10) Four tanks can store 550 liters of water. If the capacity of the tanks is equal, then what is the capacity of one tank?

22. Copyright © Ed2Net Learning, Inc. 22 Very Good! Let's Review When we are given a long division to do, sometimes there will be numbers left over. These are known as Remainders. We can use the long division process to work out the answer to a number of decimal places. Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole number. If the divisor has a decimal in it, we can make it a whole number by moving the decimal point the appropriate number of places to the right.

23. Copyright © Ed2Net Learning, Inc. 23 Review 4 233.4 Place the numbers in the division equation format. Begin the division with 4 into 23 (since 4 cannot go into 2). This gives us 5 with a remainder of 3. 4 233.4 5 - 20 3 Divide: 233.4 ÷ 4 We saw the following problem:

24. Copyright © Ed2Net Learning, Inc. 24 Review Now bring down the next 3, so we must divide 33 by 4. This gives us 8 with a remainder of 1. 4 233.4 58 - 20 33 - 32 14 Now bring down 4, so we must divide 14 by 4. Here, 4 occurs in the dividend after the decimal, so we put a decimal in the quotient after 8. This gives us 3 with a remainder of 2. 4 233.4 58.3 - 20 33 - 32 14 - 12 2

25. Copyright © Ed2Net Learning, Inc. 25 Review If after dividing you have a remainder, add a zero to the dividend and continue to divide until there is no remainder or the decimals recur. Now bring down the next 0, so we must divide 20 by 4. This gives us 5 with a remainder of 0. 4 233.40 58.35 - 20 33 - 33 14 - 12 20 - 20 00

26. Copyright © Ed2Net Learning, Inc. 26 You have done a nice job. See you in the next session.