Properties, Multiplication, and Division Study Guide
Algebra – Properties
Multiplication:
You should know the following vocabulary words:
factor, product
You should be able to multiply and estimate a three-digit number by a two-digit
number and find a product.
234
x 32
7,488
Example word problems:
200
x 30
600
Division:
Dividend – the number that is being divided or broken up into pieces in a division
problem; it is usually the largest number in a division problem.
Divisor – the number that is doing the dividing or breaking up of the dividend in a
division problem
Quotient – the answer in a division problem
Remainder – part of the answer in a division problem that represents the leftover
amount when a dividend cannot be separated into an even number of groups.
a) 726  13 = 55 R11 c)
b)
a) 726 – dividend
b) 13 – divisor
c) 55 R11 – quotient and remainder
It’s good to add Rover (Remainder) and Cleo (Check) to the last suggestion.
You can get step by step instructions on how to divide and try some practice
problems at these sites:
http://www.coolmath4kids.com/long-division/long-division-lesson-1.html
http://www.mathsisfun.com/numbers/long-division-animation.html
http://www.khanacademy.org/math/arithmetic/multiplicationdivision/long_division/v/division-2 (there are multiple videos on this page and
practice problems, as well)
Here are a couple of sample question types for you to practice:
Which does NOT represent the following problem? Carl baked 162 muffins. If he puts 18 muffins in each box,
how many boxes will he need for all the muffins?
A.
B.
_____
18
162
162
18
_____
18
162
_____
C.
D.
Find the quotient. 260
A.
2
B.
12
C.
20*
D.
200
13
Daniel’s team is putting 856 pistachios into 8 plastic containers. If each container is to have the same
number of pistachios, how many pistachios will be in each plastic container?
A.
17 pistachios
B.
107 pistachios *
C.
117 pistachios
D.
217 pistachios
Roseann needs to solve 406
second step?
A.
Multiply 3
B.
Subtract 406
23.
C.
Subtract 406
230. *
D.
Divide 406
23. Her first step is 10
23 = 230. What would be reasonable for her
230.
30.
You will need to be able to successfully divide up to 4 digit-dividends by two-digit
divisors (example: 1204 ÷ 14)
Make sure you can answer word problems correctly
when the quotient involves remainders. Try this
sample problem.
Which story represents the problem?
A. Sewing Club has 18 members. They need to sew 740 vests. If each member sews the same number of vests, how
many will each member sew?
B. A train leaves downtown 18 times each day. If each train holds 740 passengers, how many passengers leave
downtown each day?
C. Last year, there were 740 students at Frost Middle School. This year, there are 18 more students. How many
students attend Frost Middle School this year?
D. Latoya has saved $740 for a television set. This is $18 more than the television set costs. What is the price of the
television set?
Mrs. LaRue needs to cut 600 inches of yarn into pieces that are each 14 inches long. How many full
pieces can she cut?
A.
43 pieces
B.
42 pieces *
C.
36 pieces
D.
12 pieces
Ways to estimate when dividing:
Division Compare – You should be able evaluate two division problems and
determine which has the greater quotient. Work through the sample
problem below by reviewing one set of steps you could use to solve it.
Can you think of your own strategy(ies)?
Which has a quotient greater than 600
A.
490 70
B.
50
C.
320
80
D.
500
90
80?
5
For 600  80, think: 80 X ? = some number close to 600
80 X 7 = 560 and 80 X 8 = 640, so 600  80 would be > 7, but < 8
For 490  70, think: 70 X 7 = 490, so 490  70 = 7
For 50  5, think: 5 X 10 = 50, so 50  5 = 10
For 320  80, think 80 X 4 = 320, so 320  80 = 4
For 500  90, think 90 X 5 = 450 and 90 X 6 = 540, so 500  90 would be > 5, but < 6
A quotient greater than 7-8 would be 10. The answer is B!
For division of area models please refer to workbook pages – 67, 68, 69, 70,
71, 72