Decimals New

7/25/2019 Decimals New

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3. Decimals and fractions

Adding and Subtracting Decimals

To add decimals, follow these steps:

Write down the numbers, one under the other, with the decimal

points lined up

Put in zeros so the numbers have the same length

Then add using column addition, remembering to put the

decimal point in the answer

That's all there is to it - just remember to line up the decimals, then add normally.

Subtracting

To subtract, follow the same method: line up the decimals, then subtract .

Do these operations:

a)3, ! ",#$ ! %& '

b)($,& ! 3,""# ! ",) '

c)3","% * ,3$ '

d)%#,("3 ! ($ ! +,#& '
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e)#,"&( * 3+,) '

f)%"" * +(,"& '

g)&,#) ! ",(( ! 3,%( '

h)%#,)) * %%,&&& '

i)(,""% * +& '

ultipl-ing Decimals

.ow to ultipl- Decimals

/ust follow these steps:

ultipl- normall-, ignoring the decimal points0

Thenput the decimal point in the answer * it will have as man- decimal

places as the two original numbers combined0

1n other words, 2ust count up how man- numbers are after the decimal point

in bothnumbers -ou are multipl-ing, then the answer should have that man-

numbers after itsdecimal point0

Do these operations:

a)3+,"( ",3# '

b)3,# #,"+ '

c)(,)) " %%3 '

d)",3(# ",&$ '


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e)+,$ %(% '

f)$,#$ " $ '

g)",#$ ",""% '

h)",""3& 3,"#$ '

i)",+ " +% '

Dividing Decimals

Dividing a Decimal umber by a !hole umber

To divide a decimal number by a whole number:

"se Division ignoring the decimal point

Then put the decimal point in the same spot as the dividend

#$ample:

The answer is %,&

Dividing b- a Decimal 4umber

ut what if you want to dividebya Decimal umber(

The tric) is to convert the number you are dividing by to a whole number first,

byshifting the decimal point of both numbersto the right:


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4ow -ou are dividing by a whole number, and can continue as

normal0

1t is safe to do this if -ou remember to shift the decimal point of both

1Solve these operations:

a)#3,$( : ",3 '

b)3,#%$%(( : $,(# '

c)#,)# : ",3+ '

d)3,#( : ,+ '

e)%,$("& : (#,& '

f)%#" : ","$( '

g)",##"& : ",""+) '

h)3 """,$ : #& '

i)#3,&$ : $ '

2Wor5 out these divisions:

a))+ : %"" ' b))+ : % """ '


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c))+ : %" '

d)3,($ : % """ '

e)3,($ : %" '

f)3 ($ : %" """ '

g)$$,% : %"" '

h)$$,% : %" """ '

i)$$,% : % """ '

26 #3$ : %"" '


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37oo5ing at the results, tr- to do the following divisions:

%%# : ( ' #& #&$ : + ' (,$ 3,+ : ",) ' (

a)%%# : (" ' d)#&$ : +" ' g)3,+

:","") '

b)%%# : ("" ' e)#&$ : +"" ' h)3,+ : ) '

c)%%# : ( """ ' f)#&$ : + """ ' i) 3,+

: )" '

Combined operations with decimal numbers.

8emember the order of operations

a0 9*",6 9*,(6 9*%),$6 * 9*%3,$6;

b0 9*(,%6 9*3,+6 * 9%&,3 ! #,6

c0 ),# &,& * 9%$,( * %(6

d0 (,9*+,36 * 9*$,6 %%,#

e0 %#,) * ,% ! 9*#,#6 %$,$

f0 9*&,#6 9*(6 ! %$,$ ! 9*%3,%6

g0 9*%&6 ! 9*%%,#6 ! %$, * 9*%%6


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h0 &,+ 9*+,#6 9*%+,(6 * 9*%+,)6;

i0 9*%#,)6 ! 9*%,&6 * #,) * 9*%3,36;


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.ow do we ?nd3=$of #"@

ethod % is to ?nd%=$of #", then multipl- b- 30

%=$of #" is #" $ ' (0

We need3=$of #", so we multipl- ( b- 30

3=$of #" ' ( B 3 ' %#0

ethod # is to multipl-3=$b- #"

3=$B #" ' 93 B #" 6: $ ' +" : $ ' %#


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Convert Decimals to


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$ $

$

'

%$

'

3

%"" #" (

$ $

Epress as a fraction:

a6 "0&$ b6 ",#$ c6 %,#

d6 #,( e6 %#,$ f6 #%,+

g6 3,+ h6 #(,# i6 $",#

To convert a


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4/5=

1/2=

6/8=

3/4=1/5=

3/6=

1/4=

6/12=

2/8=

'0uivalent ractionsEquivalent Fractionshave the same value, even though they may

look dierent.

These fractions are reall- the same:

%

#

'

#

(

'

(

&

hy are they the sameGecause when -ou multipl- or

divide boththe top and bottom b- the same number, the fraction

5eeps its value0

1/2 2/ /!

' '

implifying ractions

To simplif- a fraction, divide the top and bottom b- the highest

numberthat

can divide into both numbers eactl-0

The wa- to simplif- a fraction is dividing both the top and bottom ofthe fraction until -ou canHt go an- further 9tr- dividing b- #,3,$,,000

etc60


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Eample: Simplif- the fraction#(=%"&:

# # 3

#(

'

%#

'

+

'

#

%"& $( # )

# # 3

Simplif-

*dding and Subtracting +ractions


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There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same

Step 2: Add or subtract the top numbers (the numerators), put the answer oer

the denominator

Step 3: Simplif! the fraction (if needed)

#$ample %:

%

4

%

( (

Step 1. The bottom numbers the denominators are already the same. o straight

to step /.

Step 2. *dd the top numbers and put the answer over the same denominator:

%

4

%

5

% ! %

5

#

( ( ( (

Step 3. Simplify the fraction:

#

5

%

( #

0n picture form it loo)s li)e this:

1/4 11/4 2

2/4 21/2


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Example 2:

1/2 31/6

Step 1. The bottom numbers are different. See how the slices are different si4es(

!e need to ma)e them the same before we can continue, because

we can'tsubtract them li)e this:

1/2 31/6 2 (

To ma)e the bottom numbers the same, multiply the top and bottom of the first

fraction 1/2 by3li)e this:

B 3

%

'

3

# +

B 3

*nd now our 5uestion loo)s li)e this:

3/6 I 1/6


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The bottom numbers the denominators are the same, so we can go to step /.

Step 2. Subtract the top numbers and put the answer over the same denominator:

3

J

%

'

3 J %

'

#

+ + + +

0n picture form it loo)s li)e this:

3/6 31/6 2

2/6

Step 3. Simplify the fraction:

#

'

%

+ 3

Add:


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Subtract:

6ultiplying +ractions


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There are3 simple steps multiply fractions

1.Multiply thetop numbers( thenumerators ).

2.Multiply the bottomnumbers(thedenominators) .

3.the fraction if needed .

#$ample:

%

B

#

# $

Step 1. 6ultiply the top numbers:

%

B

#

'

% B #

'

#

# $

Step 2. 6ultiply the bottom numbers:

%

B

#

'

% B #

'

#

# $ # B $ %"

Step 3. Simplify the fraction :

#

'

%

%" $
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Dividing +ractions

Step %0 ultipl- crossing the numbers 9numerator denominator, and

denominator numerator6

Step 30 Simplif- the fraction 9if needed6


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#$ample:

%

:

%

'

% B +

'

+

# + # B % #

+

' 3

#

4ow -ou:


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Calculate:

And now:


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Solve these operations:

Calculate:


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Wor5 out and simplif-:

ultipl- and reduce:


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Calculate and reduce:

Divide and simplif-:

Wor5 out:


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Wor5 out:

Calculate:


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#7D 87#9:';

%0 A group of people were standing in line0 3=&of the people were

bo-s and %=(of the people were girls0 .ow much of the group

was made up of bo-s and girls@ .ow much of the group was not

bo-s or girls@

#0 /ane and /err- were counting the months until their birthda-s0

/ane said 3=(of the -ear would pass before it was her birthda-0

/err- said he onl- needed to wait %=3of the -ear0 .ow much

longer did /ane have to wait than /err-@

30 Gill ran around #=3of the trac50 /osh ran around$=+of the trac50

.ow much farther did /osh run than Gill@


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(0 A bo of paper clips fell on the Koor0 Gett- pic5ed up #=$of the

paper clips and /oanne pic5ed up 3=%"0 .ow man- of the paper

clips did the- pic5 up altogether@ .ow man- were still on the

Koor@

$0 ThereLs a bag with #( balls, the white balls are %=( of them0 .ow

man- white balls must 1 add to get the white balls the half of

the total@

+0 A car has been around #+ minutes0 1n this time it has traveled

#=3 of its wa-0 .ow long will it ta5e to cover all the wa-, going

alwa-s at the same speed@

0 A ball hitting the Koor bounces to 3=& of the height that it is

dropped0 1f it is dropped from %"#( cm, how high will it get after

the third bounce@


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&0 1n a forest of pine trees the- felled its 3=$, shortl- after there

was a ?re, in which $= of the remaining pine burned0 .ow

man- pines survived@

)0 The famil- of Mscar spends one third of his budget on housing

and one ?fth in suppl-0 What fraction of budget is left for other

epenses@ .is monthl- income is ##3$ Euros0 .ow much willthe- pa- for the housing@

%"0 A c-clist has to travel %& 5m from a town to another one0

1f he has travelled #=3 of the total, how man- 5m are left -et@

%%0 Ever- step of Eva measures about 3=$ of meter0 .ow

man- steps are there in si 5m@


28/30

%#0 A compan- wants to bottle +" liters of orange 2uice, if

each bottle has a capacit- of #=3 of liter, how man- bottles do

the- need@

%30 The relationship between the width and height of a

traditional screen is (=30 Calculate what measure is high one

screen whose width is %%# cm0

%(0 There are #( hours in a da- and scientists tell us that we

should sleep for 3=& of the da-0 .ow much time should we spend

sleeping@

%$0 The 4ational .istor- useum has collected %#$ dinosaurs0

Neorge has collected 3=$ of this amount0 .ow man- dinosaurs

has Neorge collected@


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%+0 r urrin is %+"cm tall and his brother Tom is =& as tall

as him0 .ow tall is Tom@

%0 The weather forecaster sa-s that it is #"" C in 7ondon but

onl- =%" as hot in 4ew Oor50 .ow hot is it in 4ew Oor5@

%&0 S5ateboards cost 3+ each in m- local store0 The

shop5eeper sa-s if 1 bu- one 1 can bu- another for onl- =) of

the normal price0 .ow much would a second s5ateboard cost@

%)0 Gill- collected #$+ con5ers but lost F of them on his wa-

to school through a hole in his bag0 When he arrived at school

how man- con5ers did Gill- have left@


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#"0 There are #$ pupils in the class, 3=$ of the pupils support

Chelsea and the remainder support Arsenal0 .ow man- pupils

support Arsenal@

#%0 The local shop normall- sells ars bars for (" pence0 The

shop5eeper sa-s 1 can bu- them for %=( less than the normal

price0 .ow much can 1 bu- a ars bar for

Documents

Decimals New