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Unformatted text preview: Maths Study Sheet 5 Operations
with Decimals Addition and
EU btractien decimals dealing with operations part 2
— This UNIT censists at 4 Parts. Part Efren leek at the arithmetic eperatiens applied tn decimals. When yeu have werked threugh this Part, ynu will i have examined in detail the eperatinns nf additien, subtractien. multiplication
and divisien ef decimals Pie—requisites:
An understanding ef the fnur nperatiens in the arithmetic ef whele numbers.
Familiarity with Part 1 at this UNIT. Mest peeple use a calculater te carry nut the eperatiens described in this Part, and se it may be regarded as an eptinnal part. Hewever yeu may find it helpful
in deepen yeur understanding. In Part 1 we leaked at hew we multiply and divide. decimals by pewers ef it].
New we censider briefly the uperatiens ef additinn and subtractien, and than
general multiplicatien and diyisien ef decimals. A calculater can be used in check all the calculatinns in this Part. Decimal peints sheuld be aligned and all digits placed carefully in their appre— priale pusitien in the units, tenths. hundredths, pesitien. Then the rules fer
addingi subtracting whnle numbers apply. Examples:
{i} Add 5.?2 and 0.1534 {ii} Subtract 0.034 [rem 5.12
{i} 5.?2 {ii} 5.120 [11:34 + magi, 6.354 5.0845 Multi pIicatiDn (a) in multiply a decimal by a whale nuniben plate the units digit tif the
multiplier under the last figure [if the iiiultipliearul and tarry nut
multiplication as usual. Example: 5.12 H 3 5.12 multiplieand
31 multiplier Answer F15 : 3.6 Line Lil tleeimal ptiinte Example : 5.12. 1": 1?: 51 I ’t "I thii; ltt t'ilHtlll {it multiplying by Hi
1*?! ftﬁi the; is; restult tit multlplying by 3 .55 55.“ adding, giyea result ut' multiplying by 13 line ul‘tleeimnl pninte {h} in multiply a decimal by a decimal. A5; in plaee the unite digit at the multiplier under the last figure tit the
multiplieantl. The line tit points to be tnllnwed is that at the multiplieand. Example
5 ' 12
_ ...3'4
15 I Fiﬁ multiplying by Ti
"'  3'04 8 multiplying hy {Lil 1‘? I 40 8 adding; Tn uItElETtit'dltd tl’tiH line tit teething it may be helpful tn note that
till it 4 — 20.48 and 5.12 E 0511:3111 be thought til a5
4 Ill
i.e. 5.12 I l +10: 20.48 +10  lll~lti th
pi
ltd
:e An alternative Many penple tie a calculatien such as the last example in the felletving, way: method _
Calculate 51 2 a 34 (retrieving the decimal peints] te give the answer 137403.
New find the tetal number ef decimal places in the multiplicantl and multiplier.
5.12 3. 4
l T
1?. decimal places + 1 decimal place : 3 decimal places
Inserting 3 decimal places inte the abeve answer gives
5.12 a 331 = 11408
the justiﬁcatien ler this is illustrated beltnv:
5.12 e “m at:
a 3.4 t “l — 34
17.408 "'" l *
+ {IUD a 1m 74%
Hr lll'llll
DiViSiDn 'Ie divide a decimal by a whtile number, the decimal peints in the dividend and qttetient sl‘teultl be aligned. Fatra acres ma}r need to be added he the dividend.
Example ?3.8 + 5
a aem needs te he addch J
rllvlser '* 5: 3813 “" divitlcntl 14 76 *l etietienl (answer)
line if peints
l‘lv’e have written F38 as T330 which has the same value. 'l'ci divide a decimal lav a decimal. first we vvrite the divisien line in the term eF a
fractinn _ _ 0.03
Example 0.05 + 0.5 _ —
0.5 Neal multiply numerator and denominator by 10 or 100 or 1000. (as required) to
make the denominator a whole number. 0.03 0.3
— = multi 1 Fin 1: ' 10
0.5 5 P 3 g 3
Then 5 0.30 adding an extra zero to 0.3 to make 0.30
0.06 So 0.03 : 0.5 = 0.06
Example 7.5 + 0.15 = —— = ——— multiplying by 100 For harder eaaitiples you may prefer to use a calculator. EXEfCise 1. Find the sum of 0.09, 0.032 and. 51?. 2. Subtract 1.24 from 9.1. 3. Use one of the methods described in the UNIT to multiply:
{1'} 10.6 a 0.2 {ii} 15.26 a 0.04
{iii} 3?.8 a 1.3 {iy} 14.0 a 1.05
4. {i} 20 + 0.? {ii} 0433 + 0
(iii) 0.0?0 + 3.? {iv} 001 + 0.10
5. A car is timed on a journey between two bridges on a motorway which are 1.6 km apart. If the stopwatch records 1.2 min. what is the speed of
the car in km Eh? Solutions 1. 0.002 2. 0.00
3. {i} 3.72. {a} 0.0104 {00 £19.14 00;. 1554(0)
4. a} 40 {ii} 0.054 (iii) 0.02 {iy} 3000 00 kmr'h EJI ...
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This note was uploaded on 03/16/2011 for the course ECON 1003 taught by Professor Dr.mcdonald during the Spring '11 term at University of the West Indies at Mona.
 Spring '11
 DR.MCDONALD

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