GRADE 6 FLORIDA. Division WORKSHEETS

Transcription

1 GRADE 6 FLORIDA Division WORKSHEETS

2 Mental division stategies invese opeations As we know, multiplication and division ae invese opeations. 8 9 = 7 This means they do the evese of each othe: 7 9 = 8 We can use ou knowledge of the times tables to help us answe division questions. Complete these fact families: a 8 = 4 b 8 = 3 c 7 = = 3 8 = 4 7 = d 9 = 7 e 5 = 5 f 8 = = 5 5 = 96 8 = Use you knowledge of multiplication to help you mentally solve these poblems. Some will have emaindes. a 36 3 = c = e 5 6 = g 68 = b 63 7 = d 0 0 = f 37 8 = h 3 = What do we do when thee ae emaindes? We have to guess, check, and impove. 7 5 =? 5 6 = 30 Too high 4 5 = 0 Too low, thee ae 7 left ove 5 5 = 5 Thee ae left ove so 7 5 = 5 3 Ty these: a 4 cupcakes ae shaed evenly among you and 7 fiends. How many whole cakes does each peson eceive? b How do you ecommend shaing the emainde? c 0 pencils need to be put into packets of. How many full packs can be made? How many pencils ae left ove? Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS..

3 Mental division stategies split stategy Division poblems become easie if you split the numbe to be divided into ecognizable facts. Look at the poblem 68 Can we divide 68 into multiples of? One option is 60 and 8. These ae both easily divided by We do this, then we add the two answes togethe = 34 O, with two even numbes, we can keep halving until we get to known numbe facts: Þ 8 3 Þ 64 6 Þ 3 8 = 4 Use the split stategy to divide these numbes: a 8 b 5 5 c = + = + = Choosing a stategy, solve these poblems. Ty and do them in you head. You can also make notes as you go, as in the example above! a 68 6 = b 84 4 = c 6 = d 68 8 = e 96 = f 744 = 3 Choose a stategy and solve these: a 848 packs of Smaties ae thown into the audience at an end of yea school concet. If the teaches bought enough Smaties fo each child to eceive 8, how many audience membes ae thee? b You class of 4 ended up doing extemely well at the Smatie toss. Not only wee you positioned well, you had a show no mecy appoach which esulted in the class scoing 6 of the Smaties. On aveage, how many was this pe student? c Afte the concet, you class feels bad that you squashed so many kindegatenes in you quest fo the Smaties. You decide to give 90 of them to the 8 little ones. How many does each kindegatene get? Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS..

4 Mental division stategies using factos Factos ae numbes you multiply togethe to get to anothe numbe: facto facto = whole numbe Knowing the factos of numbes is helpful when solving multiplication and division poblems. Complete these facto activities: a List all the factos of the following numbes. The fist one has been done fo you. 36, 36,, 8, 3,, 4, 9, b Geneate sets of factos fo each numbe. The fist one has been done fo you Facto tees help us wok out the factoization of numbes. Pime factos ae the factos that can be divided no futhe, except by themselves and one. Pactice pime factoization by completing these facto tees: a 50 b 8 c = 50 = 8 = 6 3 Find the answe to these: a What ae the common factos of 4 and 60? b What is the geatest common facto (GCF) of 75 and 5? c What is the geatest common facto of 36 and 63? Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 3

5 Mental division stategies using factos When we ae dividing by digit numbes we can split the diviso into two factos. This makes the poblem easie. Then we do the division in two steps: and ae factos of 8. 6 = 08 We divide 6 by = We then divide 08 by = 4 Fo each poblem, find a pai of factos you can wok with and solve these poblems: a 564 b 6 4 = = = = = = c d 98 8 = = = = = = 5 These poblems have been woked out aleady but thee ae wong answes. Mak the ones that have been woked out coectly. If eos have been made, cicle whee it all began to go wong: Check each line a 9 = 6 3 and 4 ae factos of b 88 4 = 4 and 6 ae factos of 4 caefully! It s OK to make notes as you go. 9 4 = = = = 4 c = 56 5 and 8 ae factos of = = 57 d = 7 3 and 0 ae factos of = = 7 Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 4

6 Mental division stategies divisibility ules Divisibility tests tell us if a numbe can be divided evenly by anothe, with no emainde. These ae handy ules to know: A numbe can be divided by if the ones digit is even. 4 A numbe can be divided by 4 if the last digits fom a numbe that can be divided by 4. 5 A numbe can be divided by 5 if the ones digit is 0 o 5. 0 A numbe can be divided by 0 if the numbe ends in a zeo. 00 A numbe can be divided by 00 if the numbe ends in zeos. 6 A numbe can be divided by 6 if it is divisible by both and 3. 3 A numbe can be divided by 3 if you add all the digits and the sum is divisible by 3. 9 A numbe can be divided by 9 if you add all the digits and the sum is divisible by 9. Test these ules. Cicle the numbes that match the stated ule. a Divisible by b Divisible by 5 c Divisible by , , , ,5 6,56,56 7,890 3,547 d Divisible by 0 e Divisible by 3 f Divisible by 00 4, , ,436 3,56 6,730 87,490, ,800,609 3, ,600 Each of the numbes below has one o moe missing digits. Add the digits needed to make the statements tue. Fo some of the numbes, moe than one choice of digit would wok. a 54 is divisible by 4. b, 5 is divisible by 9. c,35 is divisible by 3. d 3,4 0 is divisible by 6. e 45,67 is divisible by 0. f 678,9 is divisible by 00. g 56,85 is divisible by 6. h 5,4 is divisible by 5. Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 5

7 Mental division stategies dividing by multiples of ten Dividing a whole numbe by 0 makes it smalle by one place value: 80 0 = 8 Dividing by 00 makes a numbe smalle by place values: = 0.8 Dividing by,000 makes it smalle by thee place values: 80,000 = 0.08 Solve these poblems by moving the appopiate numbe of place values: a = b = c 550,000 = d,000 0 = e, = f,000,000 = g 6 0 = h 6 00 = i 6,000 = We divide by a multiple of 0 such as 0 o 40 in two pats. Look at : = OR = Solve these poblems: a = b = c = d 8, , = e 9, , = f,000 00, = 3 Use doubling o epeat doubling to help you get to an easie poblem: a 65 5 = = Doubling is a useful stategy to use to get me to multiples of ten. Look at 5 5. If I double both numbes I can divide 450 by 0. Much easie! b 75 5 = = c,50 5 = = d = = = e = = = Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 6

8 Long division The poblem 84 divided by 5 can be solved using long division. Long division contains fou steps:. Divide. Multiply 3. Subtact 4. Bing down Divide: 5 8 =. Multiply: 5 = 5 3. Subtact: 8 5 = 3 4. Bing down: the comes down, foming 3, and begins the pocess again. Now you have a new division poblem 5 3. Divide: 5 3 = 6. Multiply: 6 5 = Subtact: 3 30 = 4. Bing down the 4 to ceate 4 and a new division poblem 5 4. Divide: 5 4 = 4. Multiply: 5 4 = 0 3. Subtact: 4 0 = 4 4. Bing down: thee is nothing moe to bing down so 4 is you emainde. So we wite 4 afte the whole numbe. Wam-up with these: a b c Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 7

9 Long division Divide these 3-digit numbes: a b c 6 6 d e f Mnemonic devices allow you to emembe impotant infomation: Dad Mom Siste Bothe can help you emembe the ode of long division: Divide Multiply Subtact Bing down Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 8

10 Long division 3 Look at these wod poblems and decide if they ae asking you to divide. If they ae, solve the poblem. If not, name the pocess you would use to solve them: a 50 kids go to the local pool on a hot summe s day. Each kid dives off the diving boad 9 times. How many dives ae thee altogethe? b The lifeguads come to the pool and hand out 750 fee balloons. How many kids ae thee if they each get 3? c The ice ceam shop is packed and sells ice ceams befoe lunch and 45 afte lunch. How many ice ceams do they sell in total? Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 9

11 Long division d Of the 95 kids at the pool, one fifth ae planning to come back the next day. How many ae coming back? 4 The mnemonic device Dad, Mom, Siste, Bothe helps us emembe the steps of long division. Can you wite you own mnemonic device fo long division? Gade Gade 6 6 DIVISION DIVISION MAFS.6.NS.. 0