Unit 2Math 6

Lesson 7

Math 6 7-1

Tiger SalamanderThe tiger salamander is common in southern Alberta. You can identify this salamander by the netlike pattern on their skin. This salamander has a broad head and a stout body. These salamanders live on ground and like the water.

The north-western salamander is found in Alberta as well. It has a golden brown colour to its body. These salamanders prefer the water but also dwell on land.

Many people keep salamanders as pets in aquariums. They have to study what the amphibians eat, how to create the proper environment and how to care for their health.

Nina has salamanders in an aquarium at home. Two times the number of her tiger salamanders is 18.

You can write an equation for the following situation.

In words: Two times the number of salamanders is 18.

Variable: n = number of salamanders

Equation: 2n = 18

Writing a Multiplication or Division Equation

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Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

7-2

Objectives for this LessonIn this lesson you will explore the following concepts:

Develop and justify equations that illustrate the commutative property of multiplication

Identify the unknown in a problemRepresent the problem with an equationCreate a problem for a given equation

Multiplication and Division EquationsA multiplication equation has the operation of multiplication on one side:

In words: Six times a number is eighteen.

Equation: 6n = 18

ReflectionReflection

Howwouldyoufindthenumberofsalamandersnowthat you know the equation?

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

5

5

35

35n

5 35n =

Math 6 7-3

The commutative property of multiplication allows you to write the equation in different ways:

6n = 18 OR n(6) = 18

The value of n is the same for both of these equations.

The commutative property of multiplication allows you to multiply numbers in any order. Using this property, the product will remain the same.

4 x 3 = 3 x 4

A division equation has the operation of division on one side:

In words: A number divided by six is four.

Equation:

Example 1

Writeanequationfor:Fivetimesanumberequalsthirty-five.

Identify the numbers:

Five times a number equals thirty-five.

Identify the variable:

Five times a number equals thirty-five.

Identify the symbols:

Five times a number equals thirty-five.

n6 = 4

Use any letter

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

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The left side of this equation can be written as 5n or n 5 due to the commutative property of multiplication.

The equation is: 5n = 35

There are many ways to write multiplication equations that have the same meaning for the variable.

With division equations this is not true.

A number times three is fifteen

n . 3 = 15 3n = 15

15 = n . 3 15 = 3n

ReflectionReflection

Why are there less ways to write a division equation than a multiplication equation?

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

Math 6 7-5

Example 2

Write an equation for the sentence:

Identify the numbers:

The quotient of a number and five is six .

Identify the variable:

The quotient of a number and five is six .

Identify the symbols:

The quotient of a number and five is six .

The equation is: b 5 = 6

Whentwovaluesfollowthewordsthequotientofyouwilldividethefirstvalueby the second value.

Another way to express division is using a fraction bar:

b divided by 5 is: b5

This is a very common way to write division once you begin to use variables.

This applies to the following numbers in order.

5

5

5

6

6

6

b

b

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

Math 6 7-6

Lets PracticeLets Practice

Word ProblemsThere are many strategies you can use to solve word problems. It is good to use multiple strategies when problem solving. For this lesson you will not solve the problem. You will write equations for these word problems. You will write an equation with a variable to represent the solution. It is not about getting the solution right now.

Example 3

Write an equation for the following word problem.

The width of a wall is three times its height. The width of the wall is 327 metres. What is its height?

Use a picture model:

Height

HeightHeight Height

Width

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

327 = 3 h

7-7

This model shows you that the width is 3 times as long as the height.

Usethefirstsentencetowriteawordmodel:

The width of a wall is three times its height.

An equation is: 327 = 3h

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

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For 1 4: There are three shelves on the bookcase with the same number of books on each shelf. There are 15 books in all.

1. ZachandLianeachwriteanequationforthissituation.Whoiscorrect?

Zach: 3n = 15 Lian: = 15n3__OR

Lets PracticeLets Practice

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

Math 6 7-9

2. Explainyouranswertonumber1.

3. Writethecorrectanswerinoneotherway.

4. Write a situation to match the incorrect answer.

For 5 16: Write an equation for the sentence.

5. Twelvetimesanumberisthirty-six.

6. Anumberdividedbyeightisten.

7. Theproductofanumberandthreeisfifty-four.

8. Thequotientofanumberandfiveisseventeen.

9. Eighttimesanumberissixty-four.

10. Fourteentimesanumberisforty-two.

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

h5 = 6

7-10

11. Elevenequalsanumberdividedbysix.

12. Eighteenistheproductofanumberandsix.

13. Anumberdividedbyseveniseight.

14. Eleventimesanumberisonehundredtwenty-one.

15. Thirtyisthequotientofanumberandthree.

16. Twelve is the product of two and a number.

For 17 18: Write a sentence for each equation.

17. 4m = 12

18.

19. AlyssaandDakshaareplantingtulipbulbs.Thetulipbulbsforthecommunitycentreflowerbedscost$150.00.Thebulbscomeinbagsof6andcost$7.50perbag.Writeanequationtofindthenumberofbagstheybought.

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

Math 6 7-11

20. Mr.Daviescommutes2.5hourstothecityandhomeeachday.Lastmonth hecommutedfor42.5hours.Writeanequationtofindthenumberofdays hecommutedtothecitylastmonth.

21. LastweekMrs.Sharmaworked42hours.Sheworkedfivedaysandthe samenumberofhourseachday.Writeanequationtofindthenumberof hourssheworkedeachday.

22. Cameronboughtsomeballoonsforaparty.Therearetwentypackagesof balloons.Thereare24balloonsineachpackage.Writeanequationtofind the number of balloons that Cameron bought.

23. Pedrobought4boxesofcerealforsomeamount.Thecostperboxwas$3. WriteadivisionequationtofindtheamountofmoneyPedrospenton his cereal.

24. ZachandNinamadeadisplayintheschoolwindow.Theycutapieceof ribboninto42equalpieces.Eachnewpiecewas15cmlong.Writean equation for the original length of the ribbon.

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

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For 1 5: Solve each equation and check.

1. k12=13

2. v7.1=12.4

3. 5=b2

Mixed ReviewMixed Review

Lesson 7: Writing a Multiplication or Division Equation

Unit 2Math 6

Math 6 7-13

4. 72=f65

5. 2.8=g3.9

02-7 Writing a Multiplication or Division Equationworkbook.pdf