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Warm UpWarm

Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Da

y

Lesson QuizzesLesson

Quizzes

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Warm UpDivide.

12 24

34

16

1. 36 ÷ 3 2. 144 ÷ 6

3. 68 ÷ 17 4. 34 ÷ 11

5. 1!24 ÷ 64

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Problem of the Day

"n i#e #ream parlor has 6 fla$ors of i#e#ream% " &ish 'ith t'o s#oops #an ha$eany t'o fla$ors( in#lu&in) the same fla$ort'i#e% *o' many &ifferent &ouble+s#oop#ombinations are possible,

21

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Learn to 'rite rational numbers ine-ui$alent forms%

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rational number

relati$ely prime

Vocabulary

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" rational number is any number that #anbe 'ritten as a fra#tion ( 'here n 

an& d  are inte)ers an& d !% 

n

d 

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.he )oal of simplifyin) fra#tions is to ma/ethe numerator an& the &enominatorrelatively prime% Relatively prime 

numbers ha$e no #ommon fa#tors otherthan 1% 

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0ou #an often simplify fra#tions by &i$i&in)

both the numerator an& &enominator bythe same nonzero inte)er% 0ou #ansimplify the fra#tion to by &i$i&in)both the numerator an& &enominator by 3%

12 of the 15 boxesare shaded.

4 of the 5 boxesare

shaded.

The same total area is shaded.

121

4

=121

4

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Additional Example 1A: Simplifying Fractions

16

!

16 = 1 • 4 • 480 = 5 • 4 • 4

16 is a !ommon fa!tor.

1

168!

"ivide the n#meratorand denominator by 16.

16 ÷ 168! ÷ 16

"implify.

  ! for a  ! 1 for a  !

Remember#!a

aa

78

 78

78

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18  2

$1  2%

18 = 2 • $  2$ = 1 • 2$

There are no !ommonfa!tors.

18 and 2$ are relatively prime.18  2

"implify.

Additional Example 1: Simplifying Fractions

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1

2&

$ is a !ommon fa!tor.

2

3

1827

 18 ÷ 27 ÷ 

"ivide the n#meratorand denominator by $.

!"ec# $t %ut: Example 1A

"implify.

18 = % • % • 22& = % • % • %

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17

3

  1&$

35

 1& = 1 • 1&%5 = 5 • & 

There are no !ommonfa!tors.

1& and %5 are relatively prime. 17

3

!"ec# $t %ut: Example 1

"implify.

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De#imals that terminate or repeat are rationalnumbers%

.o 'rite a terminatin) &e#imal as a fra#tion(i&entify the pla#e $alue of the &i)it farthest tothe ri)ht% .hen 'rite all of the &i)its after the&e#imal point as the numerator 'ith the pla#e

$alue as the &enominator%

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%37

'. 5.3&

& is in the h#ndredths pla!e.37

1!! 

Additional Example 2: &riting 'ecimals as Fractions

Write ea(h de(imal a) a fra(tion in )imple)t form.

!%622

*. !.622

2 is in the tho#sandths

 pla!e.

622

1!!!

311!!

'implify by dividin( by the!ommon fa!tor 2.

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8%7

'. .&5

5 is in the h#ndredths pla!e.71!!

 8

 8 34

'implify by dividin( by the!ommon fa!tor 25.

Write ea(h de(imal a) a fra(tion in )imple)t form.

!"ec# $t %ut: Example 2

!%262

*. !.2625

5 is in theten)tho#sandths pla!e.

2621!(!!!

218!

'implify by dividin( bythe !ommon fa!tor 125.

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denominator numerator

.o 'rite a fra#tion as a &e#imal( &i$i&e thenumerator by the &enominator% 0ou #anuse lon) &i$ision%

numerator

denominator

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11

The pattern repeats.

1

%2

2

!

%!

2

11%

1 8

Additional Example (A: &riting Fractions as

'ecimalsWrite the fra(tion a) a de(imal.

.he fra#tion is e-ui$alent to the &e#imal 1%2%11

" repeatin) &e#imal #an be 'ritten'ith a bar o$er the &i)its thatrepeat% 5o 1%2222 1%2%

Writin+ ,ath

 

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This is a terminatin( de!imal.2! 7

%3!

The remainder is 0.

&2!

!7

1 !

!

!

!

%!

!6 !

1 ! !

Additional Example (: &riting Fractions as

'ecimalsWrite the fra(tion a) a de(imal.

.he fra#tion is e-ui$alent to the &e#imal !%3%72!

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1

The pattern repeats* sodra+ a bar over the 6 toindi!ate that this is arepeatin( de!imal.

1

%6

6

!

%!

6

15%

4

Write the fra(tion a) a de(imal.

!"ec# $t %ut: Example (A

.he fra#tion is e-ui$alent to the &e#imal 1%6%1

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4! This is a terminatin( de!imal.%2! 2

The remainder is 0.

%4!

!

1 !

!

!

%!

!8 !

8 !

2 !

!

!

! 2 !!

Write the fra(tion a) a de(imal.

!"ec# $t %ut: Example (

.he fra#tion is e-ui$alent to the &e#imal !%22%

4!

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5tan&ar& Lesson Quiz

-e))on ui//e)

Lesson Quiz for 5tu&ent esponse 5ystems

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)esson *ui+: ,art $

"implify.

1.  2. 

Write ea(h de(imal a) a fra(tion in)imple)t form.

3. !%27 4. !%62

5. Write as a &e#imal 2%16

1842

37

121

7

27 1!!

8

136

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.ommy ha& 13 hits in 4! at bats forhis baseball team% What is his battin)a$era)e, 9:attin) a$era)e is thenumber of hits &i$i&e& by the numberof at bats( e;presse& as a &e#imal%<

)esson *ui+: ,art $$

6.

!%32

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1. "implify .

'. 0. 

*.  D. 

)esson *ui+ for Student Response Systems

37

4

7

7

6

7

162

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2. "implify .

'. 0. 

*.  D. 

)esson *ui+ for Student Response Systems

46

4

6

4

243!

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3. Whi(h of the folloin+ repre)ent) the +ivende(imal a) a fra(tion in )imple)t form

!.43'. 0. 

*.  D. 

)esson *ui+ for Student Response Systems

 431!!

1!!43

43

1! 431!!!

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4. Whi(h of the folloin+ repre)ent) the +ivende(imal a) a fra(tion in )imple)t form

$!.&5'. 0. 

*.  D. 

)esson *ui+ for Student Response Systems

7

4

78

 1!

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5. Whi(h of the folloin+ repre)ent) the

+iven fra(tion a) a de(imal

'. 4%3

*. 4%6

0. %6

D. 6%

)esson *ui+ for Student Response Systems

51

%