Properties, Multiplication, and Division Study Guide

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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.

234 200 x 32 x 30 7,488 600

Example word problems:

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/multiplication- division/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. _____ 18 162

B. 162 18 _____

D. 18 162 _____

Find the quotient. 260 13

A. 2

B. 12

C. 20*

D. 200

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 23. Her first step is 10 23 = 230. What would be reasonable for her second step? A. Multiply 3 230.

B. Subtract 406 23.

C. Subtract 406 230. *

D. Divide 406 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 80?

A. 490 70

B. 50 5

C. 320 80

D. 500 90

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