5th Grade Topic 22 Study Guide
Test Date_____________________
For this test students will need to be able to:
*estimate quotients
*describe mental strategies to solve division problems *solve 2 digit by
3 digit long division problems
hour/price per gallon
*determine what to do with remainders
*determine price with a fraction discount
*determine rate per
*determine ratio
Estimate quotients and describe a mental strategy to solve
3470 divided by 50
1. Round 3470 to nearest hundreds…decide if it is compatible…think: What is a
friendly/compatible number (divided evenly) with 5? Answer 35
2. Change 3470 to 3500
3500 divided by 50
3. Use the cross off zero strategy: Cross off any matching zeros on either side of the division
sign.
3500 divided by 50
350 divided by 5
4. Ignore the extra zero for a moment
350 divided by 5 ……and just divide 35 divided by 5 = 7
5. Add the zero back on to your quotient/answer
70
Solve two digit divisor division problems
4138 ÷ 17
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Place the divisor before the division bracket and place the dividend (4138) under
it.
17)4138
Examine the first digit of the dividend(4). It is smaller than 17 so can't be divided
by 17 to produce a whole number. Next take the first two digits of the dividend
(41) and determine how many 17's it contains. In this case 41 holds two
seventeens (2*17=34) but not three (3*17=51). Place the 2 above the division
bracket.
2
17)4138
Multiply the 2 by 17 and place the result (34) below the 41 of the dividend.
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2
17)4138
34
Draw a line under the 34 and subtract it from 41 (41-34=7). Bring down the 3
from the 4138 and place it to the right of the 7.
2
17)4138
34
73
Divide 73 by 17 and place that answer above the division bracket and to the right
of the two.
24
17)4138
34
73
Multiply the 4 of the quotient by the divisor (17) to get 68 and place this below the
73 under the dividend. Subtract 68 from 73 to give an answer of 5. Bring down the
8 from the dividend 4138 and place it next to the 5
24
17)4138
34
73
68
58
Divide 58 by 17 and place that answer (3) above the division bracket and to the
right of the four.
243
17)4138
34
73
68
58
Multiply the 3 of the quotient by the divisor (17) to get 51 and place this below the
58 under the dividend. Subtract 51 from 58 to give an answer of 7.
243
17)4138
34
73
68
58
51
7
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There are no more digits in the dividend to bring down so the 7 is a remainder.
The final answer could be written in several ways.
243 remainder 7 or sometimes 243r7 or as a mixed number 243 7/17.
5th graders are now expected to write the remainder as a fraction.
What to do with remainders
Depending on the situation you will do one of the following with the remainders.
Use the division stories we did in class to help you understand which to choose.
1. Round Up – round the quotient/answer up in situations like…”How many cars will be
needed to take 23 people on the field trip when each car holds 5 people?” 23 divided
by 5 is 4 with a remainder of 3. Those extra 3 people still need to go, so round 5 to 6.
6 cars will be needed.
2. Drop it – drop the remainder in situations like…”There are 62 students in the
Football League. How many teams of 6 can they make?
62 divided by 6 is 10 with a remainder of 2. We can’t make a team with only 2 people
so we drop the remainder.
3. Share it – do this is situations like when the remainder can be split up and shared.
Determine rate per hour /price per gallon
How much per hour would you be getting paid if your total payment was $34.00 and
you worked 6 hours?
Divide to solve this problem.
34.00 divided by 6 is $5.66 so you would be getting paid $5.66 per hour
Sam bought 14 gallons of gas and it cost him $26.00. What is the price per gallon
that he paid for gas?
Divide to solve this problem : 26.00 divided by 14 is $1.85, so he paid $1.85 per gallon.
Determine price with a fraction discount
I bought a game for $49.99. My friend got the same game for 1/3 off! How much did
she pay?
This is a 2 step process….First divide, then subtract
49.99 divided by 3 is $16.66
Subtract this quotient from the original price.
49.99
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The price she paid is $33.33
16.66
33.33
Determine ratio
I am making a necklace. Each necklace needs 2 glass beads and 5 wooden beads.
Complete the chart to show how many wooden beads I will use for each necklace.
Glass beads
Wooden
beads
1 necklace
2
5
2 necklaces
4
3 necklaces
6
Multiply the number of beads by the number of necklaces…
5 beads x 2 (for 2 necklaces) = 10 beads
5 beads x 3 (for 3 necklaces) = 15 beads
5 beads x 4 (for 4 necklaces) = 20 beads
5 beads x 5 (for 5 necklaces) = 25 beads
4 necklaces
8
5 necklaces
10