Exercise 2.1
Page-2.12Question 1:
Compare the following fractions by using the symbol > or < or =:
(i) 79 and 813
(ii) 119 and 59
(iii) 3741 and 1930
(iv) 1715 and 119105
Answer 1:
First, we need to find the LCM of denominators in each case. After that, we will equate the denominators in order to compare the two fractions.
(i)
LCM of 9 and 13 is 117.
Now make both fraction equivalent with denominator as 11779=79×1313⇒79=91117813=813×99⇒813=72117we know91>72⇒91117>72117⇒79>813
(ii)
both fraction have same denominator as 9we know11>5⇒119>59
(iii)
LCM of 41 and 30 is 1230Now convert both fraction to their equivalent fractions with denominator as 12303741=3741×3030⇒3741=111012301930=1930×4141⇒1930=7791230we know1110>779⇒11101230>7791230⇒3741>1930
(iv)
LCM of 15 and 105 is 105.
Now convert fraction to its equivalent fractions with denominator as 1051715=1715×77⇒1715=119105
Question 2:
Arrange the following fractions in ascending order:
(i) 38,56,6824,13
(ii) 43,38,612,516
Answer 2:
(i)
LCM of the denominators 8, 6, 4 and 3 is 24.Now, convert all fractions into their equivalent fractions with denominator 24.38=38×33⇒38=92456=56×44⇒56=202468=68×33⇒68=182424=24×66⇒24=122413=13×88⇒13=824We know:8<9<12<18<20⇒824<924<1224<1824<2024⇒13<38<24<68<56
(ii)
LCM of the denominators 8, 12, 16 and 3 is 48.Now, convert all fractions into their equivalent fractions with denominator 48.43=43×1616⇒43=644838=38×66⇒38=1848612=612×44⇒612=2448516=516×33⇒516=1548we know15<18<24<64⇒1548<1848<2448<6448⇒516<38<612<43
Question 3:
Arrange the following fractions in descending order:
(i) 45,710,1115,1720
(ii) 27,1135,914,1328
Answer 3:
(i)
LCM of the denominators 5, 10, 15 and 20 is 60.Now, convert all fractions to their equivalent fractions with denominator 60.45=45×1212=4860710=710×66=42601115=1115×44=44601720=1720×33=5160We know:51>48>44>42⇒5160>4860>4460>4260⇒1720>45>1115>710
(ii)
LCM of the denominators 7, 35, 14 and 28 is 140.Now, convert all fractions to their equivalent fractions with denominator 140.27=27×2020=401401135=1135×44=44140914=914×1010=901401328=1328×55=65140We know:90>65>44>40⇒90140>65140>44140>40140⇒914>1328>1135>27
Question 4:
Write five equivalent fractions of 35.
Answer 4:
Five equivalent fractions of 35 are:
(i) 35=35×22⇒35=610(ii) 35=35×33⇒35=915(iii) 35=35×44⇒35=1220(iv) 35=35×55⇒35=1525(v) 35=35×66⇒35=1830
Question 5:
Find the sum:
(i) 58+310
(ii) 434+925
(iii) 56+3+34
(iv) 235+4710+2415
Answer 5:
(i)
58+310LCM of 8,10 is 40.⇒(5×5)+(3×4)40=3740
(ii)
434+925 or (4×4)+34+(9×5)+25⇒194+475LCM of 5,4 is 20.(19×5)+(47×4)20=28320
(iii)
56+3+34 LCM of 6,4 is 24.(5×4)+(3×24)+(3×6)24=11024
(iv)
235+4710+2415 or (2×5)+35+(4×10)+710+(2×15)+415⇒135+4710+3415LCM of 15,10 and 5 is 30.(13×6)+(47×3)+(34×2)30=28730
Question 6:
Find the difference of
(i) 1324 and 716
(ii) 6 and 233
(iii) 2125 and 1820
(iv) 3310 and 2715
Answer 6:
(i)
1324-716LCM of 24 and 16 is 48.(13×2)-(7×3)48=548
(ii)
233-6LCM of 3 and 1 is 3.(23×1)-(6×3)3=53
(iii)
1820-2125LCM of 20,25 is 100.⇒(18×5)-(21×4)100=6100=350
(iv)
3310-2715⇔(3×10)+310-(2×15)+715⇔3310-3715LCM of 10 and 15 is 30.(33×3)-(37×2)30=2530⇔56
Question 7:
Find the difference:
(i) 67-911
(ii) 8-59
(iii) 9-523
(iv) 4310-1215
Answer 7:
(i)
67-911LCM of 7 and 11 is 77.⇒67-911⇔(6×11)-(9×7)77⇔377
(ii)
8-59LCM of 1 and 9 is 9.⇒81-59⇔(8×9)-(5×1)9⇔679
(iii)
9-523⇔91-(5×3)+23LCM of 1 and 3 is 3.⇒91-173⇔(9×3)-(17×1)3⇔103
(iv)
4310-1215⇔(4×10)+310-(15×1)+215LCM of 10 and 15 is 30.⇒4310-1715⇔(43×3)-(17×2)30⇔9530⇔196
Question 8:
Simplify:
(i) 23+16-29
(ii) 12-312
(iii) 756-438+2712
Answer 8:
(i)
23+16-29LCM of 3.6 and 9 is 18.=23+16-29=(2×6)+(1×3)-(2×2)18=1118
(ii)
12-312=121-(3×2)+12LCM of 2 and 1 is 2.=121-72=(12×2)-(7×1)2=172
(iii)
756-438+2712=(7×6)+56-(4×8)+38+(2×12)+712LCM of 6,8 and 12 is 24.=476-358+3112=(47×4)-(35×3)+(31×2)24=14524
Question 9:
What should be added to 537 to get 12?
Answer 9:
Let x be the required fraction.
According to the question:
x+537=12⇒x+(5×7)+37=12⇒x=12-387⇒x=(12×7)-(38×1)7⇔467
Question 10:
What should be added to 5415 to get 1235?
Answer 10:
Let x be the required fraction.
According to the question:
x+5415=1235⇒x+(15×5)+415=(12×5)+35⇒x=635-7915LCM of 5 and 15 is 15.⇒x=(63×3)-(79×1)15⇔11015⇒x=11015⇔223
Question 11:
Suman studies for 523 hours daily. She devotes 245 hours of her time for Science and Mathematics. How much time does she devote for other subjects?
Answer 11:
Suman studies for 523hours daily. Therefore, we have
523hours =(5×3)+23=173hours
She studies science and mathematics for 245hours. Therefore, we have
245hours=(2×5)+45=145hours
Time devoted to other subjects = Total study time - Time devoted to science and mathematics
= 173-145=(17×5)-(14×3)15=4315hours
Question 12:
A piece of wire is of length 1234m. If it is cut into two pieces in such a way that the length of one piece is 514m, what is the length of the other piece?
Answer 12:
Let the length of second piece be x.
Total length of wire = Length of one piece + Length of second piece
1234=514+x⇒(12×4)+34=(5×4)+14+x⇒x=(12×4)+34-(5×4)+14⇒x=514-214⇔304⇒x=304⇔152
Question 13:
A rectangular sheet of paper is 1212 cm long and 1023 cm wide. Find its perimeter.
Answer 13:
Perimeter of rectangle = 2(length + width)
2×[1212+1023]=2×[(12×2)+12+(10×3)+23]=2×[(25×3)+(32×2)6]=2×[1396]=1393 cm
Question 14:
In a "magic square", the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic square?
411 | 911 | 211 |
311 | 511 | 711 |
811 | 111 | 611 |
Answer 14:
Sum along columns and rows:411+911+211=1511311+511+711=1511811+111+611=1511411+311+811=1511911+511+111=1511211+711+611=1511Sum along diagonals : 411+511+611=1511211+511+811=1511Since, all the sums in the square are equal along rows,columns and diagonals,it is a magic square.
Question 15:
The cost of Mathematics book is Rs 2534 and that of Science book is Rs 2012. Which costs more and by how much?
Answer 15:
Cost of mathematics book =Rs 2534=(25×4)+34=Rs1034Cost of Science book =Rs 2012=(20×2)+12 = 412=412×22 =Rs824We know 82<103=>824<1034Thus, Mathematics book costs more.Difference in the cost of Mathematics and Science book =cost of Mathematics book-Cost of Science book=1034-824= 214 = Rs 514So, Mathematics book costs more by Rs 514
Question 16:
(i) Provide the number in box and also give its simplest from in each of the following:
(i) 23× =1030
(ii) 35× =2475.
Answer 16:
(i) 23×x=1030x=1030×32=12
(ii) 35×x=2475x=2475×53=815
No comments:
Post a Comment