og ath ety MATHEMATICS Class 4 PUNJAB CURRICULUM AND TEXTBOOK BOARD,{All righia easerved with tha Punjab Curriculum ond Texibeck Boord. Lahore. No part of thie boat con be copied, translated, reproduced or used for ‘Proparation of test papers, guide book, hay notes and halp bok, ate 2g Contents [Ra fa ie Rees | 1 Numbers 1 2 Addition and Subtraction 22 3 Multiplication and Division 46 # Factors ond Multiples: 74 5 | Fractions 95 6 Decimals and Fractions 127 7 Measurements 140 8 | Geometry 165 9 Information Handling | 180 ‘Auithoes: Rabia Aatom Sobio Sajjad Nakai: coo Spam Editar Muhommad lahfag Boig 8.8.8 (1d), Sciance Education Project. Lahore Reviewers: Prof. Or. Foroog Ahmad Dr. Saif-ullah Dean of Science Govt. Ialoma Coll Civil Lines, Ube Muhommad Akhtor Shirani Board, Li. oaid, Lbi Action: Supervision: Muhammed Akhtar Shira Composing Madina Mehmood & Layout Setting: Muhommad Roshaan Director Manuscripts: Dr. Mobeen Akbar likastrotor: Sophia Khan PUBLISHED BY: MAKTABA DANIAL, LAHORE PRINTED BY: QUDRAT ULLAH PRINTERS, LAHORE DATE OF PRINTING EDITION IMPRESSION NOOF COPIES PRICE March 2018 v a 16,500 85i-CHAPTER 1: NUMBERS 1.1 Numbers up to 1 million Hl I block = lone Groupof 15 bodke scl ten : Ahmad has 26 blacks . How many tens and ones are in 26? ee ee 2 = so MM 56 = 2 tens bones 26=20+6 In words, we read and write it as twenty six When we group 10 tens together, we get 1 hundred. How many hundreds, tens and ones are there in 2417 24-1 There are 2 hundreds, 4 tens and | one in 241.Look at these coins. The number on each coin shows its value. @ Ona 10 ‘ts ‘100 Hundred Let's write 241 according to the place value of its digits. 241 = Qhundreds + 4 tens +1 ones = 200 + 40 +1 In words, we read and write It as two hundred and forty one. “uy Identify hundreds, tens and ones in the following numbers and complete the table.Group of 10 hundreds = 1 thousand = 1 000 There are 3 254 students in Ali's school. ads There are 3 thousonds 2 hundreds § tens and 4 ones in the number 3.254. Digit 3 is in the thousands place Ithas avalue of 3000 Digit 2 is in the hundreds place Ithasavalue of 200 Digit Sis in the tens place Ithasavalueof 50 Digit tis in the ones place It has a value of 4 3254 = 3000+200+50+4 In words, we read and write it as three thousand, two hundred and fifty four There are three thousand, two hundred and fifty four students in All's school.Can you read and write a number with 5 thousands 6 hundreda 2 tens and 4 ones? S thousands 6 hundreds 2 tens 4 ones a. 5624 5 624 =5 000 + 600 +20+4 In words: Five thousand, six hundred and twenty four In Figures: 5 624 The achool library has 12 635 books. let Look at the place value chart. Ten Thousands| Thousands | Hundreds Tens Ones ee”*%ee 5 1 [a¥2 6 3 There are | ten thousands, 2 thousands, 6 hundreds, 3 tens and 5 ones. 12 635 = 10 000 +2 000 + 600 +30+5 In words: Twelve thousand, six hundred and thirty five In Figures: 12 635 Identify the place value of all digits in 93 465. There ore. ten thousands, thousands, hundreds, tens and ones 93 465 = 90 000 +. +400 +Group of 10 ten thousands = 100 000 100 000 is written and read as one hundred thousand. Identify the place value of each digit in number 215 678. 215 678 2hundred lten thousands 6 hundreds 7 tena 8 ones thousands thousand : 215 678 = 200 000+ 10 000 +5 000 +600+ 70+ 8 In words: Two hundred and fifteen thousand, six hundred and seventy eight. In figures: 215 678 If we have 10 hundred thousands, we get 1 000 000. ‘e000 ito 0 1.000 000 is written and read as one million. We will leave a second space between hundred thousands ond millions.Table shows distance between moan and earth in kilometres. Can you read ond write the number in words and Figures? There are 3 millions, 4 hundred thousands, 5 ten thousands, | thousand, 9 hundreds, 8 tens and 2 ones in this number. We read and write it as: In words: Three million, four hundred fifty one thousand, nine hundred and eighty two. In Figures: 3 461 982, Let's lok at the place value of each digit in the number 3 451 982_ Digit © is in the ces place Ithas a value of 2 000 000 Digit 4 Is inthe hundred thousendsplace = Ithasavaluecf 400 000 Digit § Is In the ten thoumeneds place Ithascvalueof 50000 Digit | is In the thousands place Tt has a value of 1000. Digit’? is in the hundreds place It hos o value of 900. Digit 8 Is in the tens place It has a value of ‘80. Digit 2 Is In the omes place It hos o value of 2. 3451 982 = 3000 000 +400 000 +50 000 +1 000+900 +80+2Identify the place value of all digits in 124 756. There ore. hundred thousands.. ten thousands,, thousands, hundreds, tens and ones. Complete the place value table for 9 871 203 and write it in 9.000 000 +. + + +200 4+0+ rite 935 432 in words Write five million, three hundred eighty two thousand, four hundred and thirty three in figures. Group of 10 millions = 10 000 000 There are 25 450 605 people in a city. Let's write the number according to the place value of its digits. Hundred | Tan | Thousands Ws on Om 25 450 605 =20 000 000 + 5 000 000 + 400 000+ 50 000 + 0+600+045 In words: Twenty five million, four hundred and fifty thousand, six hundred and Five. a Ten MillionsGroup of 10 ten millions = 100 millions =100 000.000 Let's identify place value of each digit in the number 523 129 728. There are § hundred millions, 2 ten millions, 3 millions, | hundred thousands, 2 ten thousands, 9 thousands, 7 hundreds, 2 tens and & ones. 523 129 728 = §00 000 000 + 20 000 000 +3 000 000 + 10¢ 000 + 20 000+9000 + 700+ 20+8 Lot's read and write the number. In words: Five hundred and twenty three million, one hundred and twenty nine thousond, seven hundred ond twenty eight. In Figures: 523 129 728 Complete the place value table for the number 182 246 342. Von [Thoteanda| Hundeede| Tene | a Write 182 246 342 in words.Exercise 1.1 ACTIVITY Ahmad has some digit cards. He can make different 5-digit numbers. Write down any five numbers he can make. ae | 3 1. Write the place value of underlined digits. a) 72 —10_ 9) 9991324 b) 367 ——— h) 7036904 c) 2397 ——— 1) 80719369 d) 8910 —— j) §8724098 eo) 47613 —__k)_ 625391 175 f) 612731_____ )_ 709020 168 2. Write each of the following number In words. 2) 63 “Swnythres b) 415 ce) 6314 d) 19412 eo) 583614 Ff) 24447193) h) 33 690 132 65 498 876 390 790 080 Write the following numbers in figures Five hundred and forty three. Nine thousand, two hundred and fifteen. Seventy one thousand, two hundred and nine. Nine hundred eighty one thousand, five hundred and sixty three. One hundred thirty thousand, four hundred and twenty one. Five hundred thirty two thousand, one hundred and one Seven million, five hundred seventy six thousand and fifty four. ee Nine million, eight hundred six thousand, five hundred and eighty five. Nineteen million, eight hundred seventy three thousand, five hundred and twenty ane, Thirty one million, two hundred fifty six thousand, seven hundred and twenty one. Six hundred and fifty three million, two hundred and seventy two thousand, four hundred and thirteen.4, °) b) °) d) °) 5. °) b) 5) a) °) f) a) h) In the number 845 296 000, The digit[ is in the millions place. The place value of the digit 8 is | 3 The place value of the digit 2is[—‘- Thedigit 9 isinthe[ |place. The digit[_]is in the thousands place. Complete the following: 5814=5000+ +1044 12718 = 10000 + ____+700+10+8 2303 820 = __ +300 000+ 3000+______+20 8517 342=8000 000+ __—s +10 000 + +300 +4042 6532 171=______ + 800 000 + 30 000+____+ 100 +704 25479 600=20 000 000 + +400 000 +70 000 EID 937 164.563 =30 000 000 +____ ese +60000+4000+_ ss #6049 354 176321 =__ +o i re1.2 Number line am 0123466 78 910 3 “es Ali and Sara are holdinga banner to show a number line The number line shows numbers from left to right ——— In order from smallest to greatest with equal spaces. You can see that every number thot appears on the right is greater than call numbers on its left. Let's circle number 5 on the number line. 2084 Boe 7 809° 10 5 Is greater than every number that is on Its left and & is smaller than every number that is on ite right, Now, look at the number line below. Ahmad skips over 2 spaces to go to 2. o 2 4 6 8 10 12 4 Let's find number 3 on the number line. Since, number line shows numbers in order with equal spaces in between, the line marked between 2 and 4 shows the number 3. When we have to go to bigger numbers on the number line, we can always skip over equal spaces,Identify number 5 on the following number line. 0 3 9 12 15 ed 5 is.one less than 6 Count one step: backward. 5 is 2 more than 3, Count on two steps forward. Show 15, 20 and 30 on the number line. To show these numbers we can draw any number line that goes te of least 30. Let's skip count by 5. —_— ttt ttt Oo 5 2 30 36 10 , , , We have represented all three numbers on the number line. Represent 20, 40 and 50 on the following number line. ee al Identify the value of the number where the butterflies are sitting. 0 10 20 30 40 50 60 «++ Since, numbers and the vertical lines an a number line are equally spaced, one line between O and 10 means a 5. The first butterfly is sitting at 15 The second butterfly is sitting otExercise 1.2 1. Draw the number lines and represent the following numbers. a) 24ond6 O 1 2 8 4 5&5 6 7 8B b) 5, 10 and 16 ec) 10 and 25 4) 4,8and 20 e) 20and 40 f) 30,40 and 60 2. Identify the value of the number where the frogs are sitting a) i+ 2 0 1 2 3 4 5 6 7 8 9 10 b) eee BE ge, 0 10 20 30 40 50 Co) of. , 5 2, , . 0 10 20 30 40 50 d) «4 # + ¥ +—+_+__+4 # $e 0 8 16 24 32 401.3 Comparing and ordering numbers Ahmad hos 22 toffees ond All has 15 toffees. Who has more? 22 is greater than 15. We can also compare numbers by comparing the digits in the highest place value only. 2 is greater than |. So, 22 is greater number thon 15. We can also write itas 22 >15. So, Ahmad has mare feffees. Which number is greater, 198 or 3287 Let's compare the digits in the highest place value. 3 hundreds is greater than 1 hundred. So, 328 is greater than 198. We can also write It as 328 > 198. Which number is smaller, 63 163 or 98 163? Let's compare the digits In the highest Le] value. 6 ten thousands is smaller than 9 ten thousands. So, 63 163 is smaller son fa 98 163. We can also write it oa: 63 163 < 98 163.Which number is greater, 47 463 111 or BB 445 622? Ten Mill Let's compare the digits in the highest place value. 8 ten millions >4 ten millions. So, 88 445 622 > 47 453 111 Compare the numbers and write >" or "<" in the middle. 4369 [| 863 234 ses[_ Jers 679 «23-187 346 [] 207 400) Compare 7 198 and 7 283. Let's compare the digits in the highest place value. Both numbers have 7 thousands. So, we move 8n [Fiusanddlondied Which number is greater, 32 984 312 or 32 935 O11? Let's compare the digits in the highest place value. Digits in ten millions place, millions ploce and hundred thousands place are same In both numbers. So, we compare digits in ten thousands place: 8 ten thousands > ten thousands. So, 32 984 312 > 32935 011(Compare the following numbers and write ">" or “<* in the middle. weve] 12489 en Sara has 12 marbles and Anum has 9 marbles. Who has more marbles ? SSSGSG8 06606 12 9 120 ~=> 9 12 is greater than 9. So, Sara has more number of marbles. Which number is smaller, 1 219 or 3257 Let's compare digits in the highest place value. Thousand Hundred | The number 325 has no thousands. 1 =a There ore 0 thousands In 325. 9 Remember we can write as many zeroes os we want on the left side of a number. O thousands is smaller than | thousands. Se, 325 < 1 219. Which number is greater, 1 324 660 or 32 100 789 7 There ara 0 ten millions in 1 324 660. 3 ten million > O ten million. So, 32100 789 > 1324 660. Compare the numbers and write ">" or “<" in the middle. a 12 29776 [eso ur vie00 [Janet 21876 ses[_}e00 701Ordering numbers There are four schools in a city with differant number of students School A School B School C School 0 9.000 7500 2800 3000 Which school has the most number of students? Which school hos the least number of students? 9 000 is the greatest number. School A has the most number of students. 2 800 is the smollest number. School C has the least number of students. Can you order these numbers? Let's arrange the numbers from smallest to greatest. Write smallest number first and greatest number at the end. If we write the smallest number first and the greatest number at the end, It is called increasing order or ascending order 9.000 3000 2800 We can also arrange the numbers from gractest to smallest. Write the greatest number first and the smallest number at the end, If we write the greatest number first and the smallest number at the end, it is called decreasing order or dencending order.Can you arrange the following numbers in ascending order? 56 248.910, 9 286 344 and 56 382 193 Hundred ae housanda| 2 a 2 4 3 3 Let's start from the highest place value. 5 Ten millions > 0 ten millions. So, 9 286 344 is the smallest number. Now, we compare 56 248 910 and 56 382 193 Ten millions place is same and one millions place is also the same. So, we move to hundred thousands place. 3 hundred thousands is greater than 2 hundred thousands. So, 56 382 193 > 56 248.910 Let's arrange these numbers in ascending order. Write the smallest number first and the greatest number at the end. wing 9 286 344 56 248 910 563821934) Se Arrange these numbers in ascending order = 246989 435123 289909 } Arrange these numbers in descending order 24653900 78542121 12432 677a a4 () 1806 b) 6890 [_] 6017 °) 23765 (_] 12.789 d) 1345 (} 13.345 e) 132302 [|] ¥a24i1 f) 2645 7a9([_] 3942000 k) 99654323 [_] 99.894 121 ) 321684213 [_] 921 654379 2. Arrange the following numbers in ascending order. a) 238. M41 634 b) 6157 3164 2157 3] 53 231 23451 99 BOY d) B46 123 914 675 871 462e) f) 3) 0) b) ¢) 4) ) 9) 1423431 6 163 540 6879 892 eo 236 211999 111 232 000 321342 121 a 25 432 419 999 123 156 100 234 456 Arrange the following numbers in descending order. 238 141 634 a 6157 3164 2167 ee 85 205 12 285 99 000 816816 110 819 962 321 3171 623 § 000 701 3.762 189 11235 686 22544 000 34 343 765 34125 131 99 123 200 248 156 000CHAPTER 2: ADDITION AND SUBTRACTION 2.1 Simple addition Ahmad has 15 marbles. Sara has 12 marbles. How many marbles do they have in total? To know the total, we will add 15 marbles and 12 marbles. Ahmad SS SSSS SSSSG6 Sara SSSSSSSSESSESSE Yau can count the total marbles. There ore 27 marbles in total. We add numbers by writing them according to the place value of their digits. >. First, we odd ones of the numbers. 6+ 2=7 ag Ber | @ 1+ 1=2 5 6 2 ee 2 it The sum of 15 and 12 is 27. ‘Add the following numbers: 1 2 +3 1All spent Rs. 321 on Eid. Sora spent Rs. 54 on Eid. How much money did both spent on Eid? To know the total, we will add 321 and 54 Recall that we can always put a zero on the left side of o number without changing Its value. =. First. we add ones. 3 2 l+4=5. * Next, we add tens. 2+5 57. Next, we add hundreds. — 34053. ede) a Ali and Sora.spent Rs. 375 in totol, Add the following numbers:Let's add 6 137 and 2 622. We will write both numbers according to the place value of their digits and follow the following steps. 6 1 3 6 1 7 + 2 6 2 9 6 a: gt 1 3 + 2 2 2 + 6 2 fn a Gea - The answer is 8 759. + no a ny Add the following numbers: on +n nmWhat is 43 152 + 12 446? Let's write both numbers according to the place values of their digits and follow the same steps to odd them. ‘Add the following numbers: 13 674 32 881 67100 +64 221 + 27 117 +22 190 Follow the same steps you have learnt and add the following numbers. Remember we start adding from the right side. 613 4651 231 871 31211 + 262 138 # 8 Be bet +712 704 oeExercise 2.1 1, Add the given numbers. 0) b) 30 611 + 16 +237 4) 6112 e) 7 + 3660 +1 a i2 pO bf 2 5 OO 8 Qe sity Oeotagi dedi +61 404 + 64135 4372464 2. Line up the following numbers according to the place value of their digits and odd them. a) 16+22= | Se | b) 617+140 = [——-_) ec) 223646763 = c=) d) 41618+14160= ( e) 13617+10141= [2.2 Addition with regrouping There are 16 red flowers and 8 yellow flowers in a garden. What Is the total number of floware? See ee ee ee ee eS 6068888 You can count total number of flowers. There are 24 flowers in total. Let's write both numbers according to the place value of their digits and » them. o~. we odd ones. — B+6=14 We will regroup 14 into 10 and +. 14 ones = 1 ten 4 ones. Let's carry 1 ten to the tene column. » Next, we add tens. o i + 8 2 4 1+1=2 The total number of flowers is 24.Can you now add 937 and 237 Let's write both numbers according to the place value of their digits. Recall that we can always put o zero on the left side of a number without changing Its value, » First, we add ones. 9 3 7+3=10 We will regroup 10 into 10 and 0. 10 ones = 1 ten O ones 0 ' @ Let's take | ten to the tens column, areors - Next. we add tens. 9 7 + 0 3 We have 1 more ten now. So 3+24+1=6 » Neti a add Nanas. 940=9 The answer is 960, ‘Add the following numbers:A toy shop has 4 255 different toys in one section ond 4 360 toys in another section. How many toys are there in total? To know the total, we will add both numbers. Thera are 8 615 toys in total. Find the sum of the following numbers: 499 87 3090 +63 6 1 +1931Let's now add 91 819 and 33 276. @ © @ Find the sum of the following numbers: 13 649 32 081 71 544 * #4 ea + §6 884 + oe 772 Follow the same steps you have learnt and add these numbers. 673 338 752 + 112 047 + 176 956 819 218 315 + 341 270Exercise 2.2 1, Add the given numbers. 2) 36 b) 55 ) 182 + 79 + 16 +139 9 65 *) go009 6381 + +7269 +1531 2. Find the sum of the following numbers. a) 6734 b) 17316 tO 4. MITE s) d) peas 63174 etn 3 5 +20 935 3. Line up the following numbers according to the place value of their digits and add them. a) 55429 = a ») | 91462 = aay 2) 2804150 = C4 ) §ie+i4o9= ( ») 41 850+ 20311 = (4 aD2.3 Addition problems in daily life Sara has 92 blue toffees. Ali hos 18 red toffees. How many toffees are a) i : Lins Gon ti tT oe * a|- «© Pakistan scored 350 runs on the first day of a cricket test match and b) ‘ 215 on the second day. How many runs were scored in total? c) The shopkeeper sold 450 oranges in the morning and 375 orangas in the evening. How many oranges did he sell altogether? Anam scored 8 789 in level 1 of her computer game. She scored 7 480 3) in level 2. What Is her total score? There are two schools in a town. 2 450 children go to one school and *) 8 910 children go to the other school. How many children go to koth schools? a2.44 Mental addition .et's find the sum of 22 and 56. iplit the numbers according to the place value of their digits. 22= 2042 16= 50+6 Hence, 22 + 56 =78 at's find the sum of 350 and 415. iplit the numbers according to the place value of their digits. 150 = 300+ 50 15 = 400+ 1045 Add the following numbers: is+5= [] TO+41= ad | a+io= [| 50+18= EF] = eS 70440 = [ 280 +10= 30+36= [| 350+ 400 =2.5 Simple subtraction Sara bought 23 biscuits. She ate 11 of them. How many does she have left? SESLESSESSPSSSSsS SSESSESESS There are 12 biacuite left. We find the difference between two numbers by writing them according to the place value of their digits. = TB te we sat oe 2-151Asad has 125 coins. He gave away 13 coins. How many coins are left? ‘o find out number of coins left, we will subtract 13 from 125. Yecall that we can always put a zero on the left side of a number without thanging its value. Asad has 112 coins. Find the difference of the following numbers: 9 3 430 Sa 722 10A worker packed 2 317 shirts. If he has to pack 7 348 shirts in total, how many shirts are still left to pack? To know thot, we will subtract 2 317 from 7 348. 7 4 8 — : 7 0 3 2. The answer is 5 031 shirts | now oo 4 @ 3 1 3 4 8 i 7 5 Oo 3 1What is 79 562 - 72 5407 Let's line up both numbers in vertical columns and follow the same steps. 7 9 5 6 2 rm id 2 5 4 Oo 0 7 Oo 2 2 The answer is 7 022. Find the difference between the following numbers: 93 638 64 651 6 32 Ly @b 6 le 22040 e012 E210 & Follow the same steps and find the difference between the following numbers. 913 487 Gor 251 935 430 -112 261 +-210140 -721 000Exercise 2.5 1. Subtract the given numbers. a) 8 4 b) BATS ) 7 =a 5 - o0o48 -204 da) 26s e) 836 f) 699 Bit 615 543 2. Calculate the difference between the given numbers. 9) 4604 b) 43436 6) ise doe - 3001 -4 0122 -65135 413876 *) 81760 7989001 - 14918 -61700 -93 75000 9) 25846 h) 58764 ) 760901 * O20 2 ~21702 - SO0O4002.6 Subtraction with regrouping Let's find the difference between 23 and 6. We cannot subtract 6 from 3. So, we will borrow 1 ten from the tens side. Now, we have l3ones. 13-6 =7 Then, we subtract tens. 1 7 After borrowing, we are left with 1 tens. 1-0= Subtract the following numbers:Find the difference between 292 and 165. Let’s write both numbers according to the place value of their digits. 6 First we subtract ones, We cannot subtract 5 from 2. So, we will borrow | ten from. the tens side, 12 - 5 = 7 7 ey Next we subtract tens. We have 8 tens left. 2 @) ©, a-6=2 = if 5 2 @ Next we subtract hundreds. 8 2 hundreds — 1 hundred =1 hundred () 4 De = 6 6Now. let's find the difference between 63 158 and 57 462. oy lay 107 lg 8 The anewer is § 696. Find the difference of the following numbers: 712654 86 361 63 168 - 50641 - 67 420 ~ 48093 Follow the same steps and subtract the following numbers. 784859 620705 635 529 ~ 629-379 i 1-F 402 = 8.82 7:17Exercise 2.6 1. Subtract the following numbers: - a) 441 b) 824 2) 675 - 3650 ~6569 =~3.95 4d) 2887 e) 4761 f) 5462 -1578 -2687 -1376 | 2. Find the difference of the following numbers: a) 9B467 b) 37510 — eee? - 198861 3. Line up the given numbers and find their difference: a) 958 - 682= (______) b) 4698-3400 c) 5 183~ 2661 4) 6897-4910 e) 45125-1003 = ——) f) 70800-14783 = C—_—_] i2.7 Subtraction problems in daily life a) b) e) 4) *) There were 54 marbles in a jor. Sara took 32 marbles out. How many marbles are left in the jar? 5 3 a> 2 2 2 54 32 All is reading @ book that has 423 pages. He has read 167 pages. How many pages are left to read? Asad got 1050 rupees from his father. He spent 312 rupees. How much money does he have left? There were 680 books in a school library, 250 were borrowed by the students. How many books are left? A factory made 9 450 footballs and sold 8 750 of them. How many footballs are left?2.8 Mental subtraction Let's find the difference between 28 ond 44. Count on from 28 to 30. Hold the 2 in your head. 30 to t4is 10 +4 = 14. Add the 2 in 14. 14 + 2 = 16 is the answer. Find the difference between 130 and 50. Count from § to 13. 13-5 =8. So, 130 — 50 =80 Subtract the following numbers: 67-10 = 24-8 = 23-12= 78-25 = 44-32 = a7-27 = 350 - 270= 820 - 580= JUuBUULCHAPTER 3: MULTIPLICATION AND DIVISION 3.1 Multiplication There ore two groups of 4 balls each, How many balla are thera in total? 4 *¢'4 = 8 There are ° groups. Each group has 4 balls. 2 x4 = 8 We say 2 times | equals 8. We con also write it os, 2 —— Multiplier X 4——+Multiplicand 8——-Multiple We say that the product of 2 and 4 is 8. There are 3 boxes with 7 apples in each box. How many apples are there in total? Se ee There are 3 boxes. Each box has 7 apples. 3 times 7 equals 21.The product of 7 and 3 is 21. 3 x 7 2 1 Let's quickly revise tables of 7, 8 and 9.Ali, Sara and Ahmad have 12 coloured pencils each. How many coloured pencils do they have altogether? There are 3 children. Each one of them has 12 coloured pencils. Let's find what 12 times 3 is. 12x3=? The product of 12 and 3 is 36. There are 36 coloured pencils altogether. Multiply the following numbers: 4 3 x 2Fatima reads 4 pages of a book every day. How many pages will she read in 24 days? Let's multiply 24 by 4. Fatima will read 96 pages. Find the product of the following numbers: 14 x 5 3 x no xLet's multiply 452 by 4.txercise 3.1 1. Complete the following: 2. Colculate the product of the given numbers. «) 13 b 20 «e 10 4) 11 x 2 x 4 x 8 x 7 e) 15 fA 3 6 g) 5 9 4h) 8 2 x 5 x 2 x3 x 3 ) 222 y 234 671 J rit x 3 x2 x1 x 6 m> 680 n) 841 o) 4178 Pp) 230 x2 x 6 x 2 x33.2 More about multiplication Recall that 10 times 1 ie 10. What is 10 times 37 x10 @60 — 60@ 3 30 10 times 3 is 30. Multiply 13 by 10. ® (o@) 000 = @@@ 13 130 Let's multiply 3 by 20. We will break 20 Into 2 and 10. 3 X20 = 3X?x10 @ = 6x10 = 60 $0.3 x20=60shopkeeper hos 12 boxes. Each box has 13 books. How many ooks are there in total? at's find the product of 12 and 13. 1,2 x 1 3 3 can be split into 3 and 10. + Ve will multiply 12 by’3 first ond then by 10 and add our products. Lecall the multiplication rules. 1 2 1 2 x 3 x 1.0 6 ie a) Step 1 Step 2_ 3°46 3 +1 2°90 16 6 12 x13 =156Let's multiply 26 by 14. Multiply the first number by ones place of second number, Sp | @, 6 * pol 1 oP 4 Multiply the first number by the tens place of the second number. Step 2 2 i 1 L 0 2 6 6 4 4 0 ‘Add the products from step 1 and step 2. one x ie 6 4 4 oO y + air ala ol- Multiply the following numbers: 13 3 23 BeckA book coats 31 rupees. What is the cast of 127 such books? Let's multiply 127 by 31 127 ¥31=? = ae = =oExercise 3.2 1. Multiply the given numbers. 23 3 2 4 0 1 4 x 23 x2 2 x 11 x 1 2 26 3°65 261 3 x3 1 x5 6 x6 2 x 6 2. Find the product of the following numbers. 639 548 312 423 xX 1 x 20 x 23 x 313. Find the product of the following numbers 211 321 614 1103 x 32 x AE. x 31 x 21 Challenge Let's try 4 192 x 123.3.3 Multiplication problems in daily life 2) 5) <) a) e) Sara bought four books to read. If each book has 32 pagas, how many pages will Sara read in total? 32 x4=7 3 x -n 12 9] we There are 9 mangoes in a box, How many mangoes are there in 32 boxes? Ahmad ond Ali eat 11 toffees every day. How many toffaes will they eat in 7 days? There are | 272 children in a school. If every child has 7 books, how many beoks are there in total? re . Aman sold some packets of balloons with 25 balloons in each packet. If h sold 13 packets, how many balloons did he sall altogether?3.4 Division There are § biscuits in a box. Ahmad tokes 2 biscuits out, There ore 6 biscuits left. 8-2=6 Sora tokes 2 biscuits out, There ore + biscuits left. 6-2=4 Ali also takes 2 biscuits out. There ore 2 biscuits left. 4-252 Anam also takes 2 biscuits out, There are O biscuits left. 2-2=0 We can subtract 2 four times till we are left with 0. This is called repeated subtraction, Count the mangoes. Subtract 2 till you are left with 0. 10- 2=__ 8-2=__ —- 2 =. —-2=— —-25 We can subtract 2 _____ times.Ali has 8 balls. He wanis to put them in 2 boxes with equal balls. ss 8s There are 4 balls in each box. We say that 8 divided by 2 is equal to 4 There are 12 oranges in a box. We want to divide tham equally in 3 boxes. eeece ves-' [eeee 12 divided by 3 ts equal to 4. ee ee There are 4 oranges in each box. : Write the correct answers. 9+3=C |Sara's mother bought 15 buttons. She wants to put them in 3 boxes. How many buttons will she put in each box? Let's find out 15 +3 5 times 3 is equal to 15. So, 15 divided by 3 is equal te 5. bF3=5 Sara's mother can put 5 buttons in each box. Divide these numbers. CCCan you put 26 marbles in 2 groups? Let's divide 26 by 2. Write the division sum. We will start dividing from the highest place value. 1 Step | =“ “oO You can see that we put | in the tens column. Which means 10 times 2 is 20, Let’s bring the next digit down. There is nothing left. So, 264 2 = 13. Solve. 3Ahmad has 13 balls. He wants to put them in 2 boxes with equal bolls. He can put 6 balls each in 2 boxes and he will still be left with I ball, 1 is the remainder. So, 13 is not completely divisible by 2. et's find out 23 + 4. ‘call the table of 4. 4x5 =20 “times 4 is 20 and we will be left with 3 as a remainder. Ve can also write it as 23 + 4=6 Remainder 3 ‘member, remainder is alwoys smaller than divisor.Here, 3 < 4. Recall your tables ond divide these numbers, 21¢2=(_)Remeinder(_) 18 + 3 =(_) Remainder (_} 115 =(_)Remainder() 28 + 7 =(__) Remainder (_) 3048=()Remainder(_) 84 + 9=(__) Remainder (_} eeDivide 47 by 3. Write the division sum and start dividing from the highest place value. Step 1 1 3] @’ 1s Step 2 3J 47 Al es 15 2 We keep dividing until the remainder is less than the divisor, 2 < 9. 47 +3 = 15 Remainder 2.Can you divide 96 by 6? 96> 6=? Write the division sum and start dividing from the highest place value. Step 1 a ' wo pet o oa 16 6) 96 a aw ao Remainder is 0. So, 96 is completely divisiblaby 6. 96 +6 =16. Divide these numbers. 7 eFExercise 3.4 Recall your tables and complete the following: o) 1624 =([_] b) 3626 =([_] o) 2+7=(_] 4) 56+8 =([_] 2) +9 =([_] 9 zwe9=C) a) 15+ 2 =(_) Remainder (_) h) 25+ 6 =(_) Remainder (_} ) 20+3=(_) Remainder (_) ) 2848 =(__] Remainder (_) Find the quotient in each of the following: a) 4 S44 b) 2S 92 6) e44) 5) 64 3) 67 net a9 3. Work out the outputs in each of the following. @® a Q=A—O O O Q=A—O O3.5 More about division Let's divide 189 by 9. Write the division sum and start dividing from the highest place value. 11s smaller than 9. We cannot divide 1 by 9. So, we will take one more place value and divide 18 by 9. Qo You con see that we put 2 in the tena column, Which means 20 times 9 is 180, Let's bring the next digit down, 21 9 J 189 Step 2 vp E> o> - 9 == 21Zara wants to put 335 books In two shelves. How many books will she put in each shelf if she wants equal numbers of books in each shelf? 335+2 =? Write the division sum and start dividing from the aighest place value of the dividend. 167 27335 18 -—— Remainder There will be 167 books on both shelves. And 1 book will be left. i's divide 18348 by 4. Write the division sum and start dividing from the highest place value. We will keep divding untill the remainder is leas than the divisor. Remainder is 0. We can see that 18 348 is completely divisible by 4. 18348 + 4 =4587 Solve the following: 4 Jeee4 6J365 VJ3Tt7Let's divide 196 by 13. 195 +13 =? Division by 2-digit numbers is similar to division by 1-digit numbers. Write the division sum ond start dividing from the left side of the dividend. We cannot divide | by 13. So, we will take one more place value and divide 19 by 13.Exercise 3.5 1. Solve the following: a) 4Je48 ») 5 Ja585 3) 7J798 4) 3.J9856 e)2Ji458 f) 6 J936 gigyeor hiver7i 2. Find the remainder in each of the following: a) 6J848 ») 5/1654 2) aJeoe «dpa Jeo73.6 Division problems in daily life a) Sara has 32 toffees and she wants to share them equally among her 4 friends. How many toffees will each friend get? To know that, we will divide 32 by 4 $2.4 437 ERERERER 3 TEESE ~o ERERERER Each friend will get 8 toffees. { SERERER b) Re. 360 is distributed equally among 6 people. How much money will 4 rr} each person get? c) Ali's uncle makes a glass of mange juice using 5 mangoes. If he hos 36 mangoes how many glasses of mango juice can he make? d) Miss Amna brought 320 balloons and distributed them among 8 students. How many balloons did each of them get?CHAPTER 4: FACTORS AND MULTIPLES 4.1 Divisibility rules Awhole number is divisible by a: the last digit is O or divisibia by 2 (even). For example, 54, 98, 22 and 20 If the sum of ite digits Is divisible by 3, For example, 291 (2+9+1=12) re if the last digit is O or 5. For example 590, 6815 Let's check Ts 81 divisible by 37 Yes, because 8+ 1 =9 and 9 is divisible by 3. Recall 3 X 3=9, Is 250 divisible by 57 Yes, because the last digit is 0. Circle the numbers divisible by 2. (24) 32 61 761 882 1000 Circle the numbers divisible by 3. 24) 33 81 100 1101 1211 Ts 341 divisible by 2? Is 2555 divisible by 57A whole number is divisible by if the number formed from the last two digits Is divisible by 't. For oxample, 112, 1308, 2520 Ba If the number is divisible by both 2 and 3. For example, 12, 24, 114, 3312 oH © if the last digit Ie O, For example, 110, 28900 Let's check Is 1124 divisible by 4? Yes, because the number formed from the lost two digits is divisible by 4. Recall 4 X 6 =24. Is 1550 divisible by 107 Yes, because the last digit is 0. Circle the numbers divieible by 4. @2) 36 344 748 4112 Cirele the numbers divisible by 6. (2) 33 312 902 3il4 Is 2516 divisible by 4? Is 33 divisible by 67 Is 10005 divisible by 107Exercise 4.1 1. Which of the following numbers are divisible by both 2 and 37 2. Look at the following numbers: Which of the above numbers are 2) dwwbleby2? LTE IE] » awabietys?[ TL EsE._s«déE; | 2) divisible by 47 [| a | 4) dweibleby8?[ Js] *) dwoiblobye? [| I dL_| ) dwableby107 [J Ld 9) dwisible byborh2end47[ Ls] h) divisible by 2, 5 ond 10? oS4.2 Prime and composite numbers Think about number 3. Tt can only be divided by 1 and 3, without leaving a ramainder. 3 is a prime number. Some other prime numbers are 2, 5, 7, 11 and 13 etc. Think about number 4. It con be divided by 1, 2.and 4 without leaving a remainder. 44 is. a composite number. Some other composite numbers are 6, 8,9, 10 and 12 ete. Exercise 't.2 Identify prime and composite numbers and put them in correct boxes given below. 1 2 3 4 § 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20 21 22 2300¢«O24 25 26 27 28 29 «30 .4.3 Multiples Let's find multiples of 3 using o number line. +3 +3 . +3 tH o 12@4 5 @7 8 @ w Start from O and count on in 3 equal steps. You will find multiples of 3. Below we have first three multiples of 3 biscuits. 3x1=3 3x2=6 ox3=9 i} 3,6, 9, 12, 15, 18, 21, 24, 27 and 30 are first ten multiples of 3.Let's find multiples of 4 o123@5 67@2 wou @& Recall the multiplication table of 4 4x1 4x 2 4* 3 Hom OH: 4x5 4,8, 12, 16, 20, 24, 28, 32, 36 and 40 are 4x 6 the first tan multiples of 4 4x7 axe 4x9 10x 1= 10 nae 10 X 2 = 20 Let's find multiples of 10. 10 x 3 = 30 19 x 4 =-40 10, 20, 30, 40, 50, 60, 70, 80, 90 10. X06 and 100 are the first ten multiples of 10. “| 10 x 6 10x 7 Is 75 a multiple of 107 10 xX 8 76 is not a multiple of 10 becouse it Is not divisible 10x 9 10 x 10 =100 by 10. Recall divisibility rule of 10. Complete the following: a) multiples of 2 [2 | HOODOO CO b) multiples of 6 [e] le LJExercise 4.3 1. List first 10 multiples of the following numbers: a) 2 b) 3 cc) a ef . e) 6 FY FN g 8. h) 9 2. Circle the multiples of the numbers shown on the card.4.4 Factors Let's arrange 8 balls in equal groups. There is more than one way to do this. i group with & balls in it. 1x 8=8 (9009 (6000) 1999) 2groups with 4 balls in 2x48 each group. (a ror a {groups with 2 balls in | ee each group. 8X 1=8 The number 8 can be divided by 1, 2, 4 and 8 without leaving a remainder. 1,2, 4 and 8 are called factors of 8. List the factors of 40. Start with the smallest number and find all the numbers that divide 40 completely without leaving a remainder. Stop listing when numbers start to repeat. The factors of 40 are 1, 2,4, 5, 8, 10, 20 and 40.Is 3.a factor of 257 26 connot be exactly divided by 4 It leaves I as a remainder, So, 3 is not o foctor of 25, Exercise 4.4 1. Write factors for each of the following numbers: a) 12 The factorsof I2are_ 1, =, __, es. ond 12. b) 20 —*_. @@ SSS SSSSSSESSSEDEES The factors of 20 are teenie eed, err and2. Fillin the missing factors below, a) @=2t24C ).C) b) 18 =1,3, (_), C) ce) 189=1.2(0C),C).C).18 d) 392=1,(__).4.(_). 16. 32 «) 60=1,2,C_).(_),(_),50 3. Write all the factors for the numbers given below, a) 3 b) 9 es ou d) 2t e) 2 f) 28 9) 36 hy) 42 + . Answer the following questions: a) Is 5 a factor of 35? Explain. b) Is 8 a factor of 41? Explain.4.5 Prime Factorization We con express a number as a product of its prime factors, Factor Tree Method Find prime factors of 27 Start with the smallest prime number that is a factor of 27. 27 is not divisible by 2. Iris divisible by 3. So, we divide 27 by 3. Recall 3X9 =27. Write 3 and 9 as two branches of 27, 3 Is a prime number. So, we have one prime factor, 9 is not a prime number. So, we further foctorize it. Recall 3 X 3=9. Write 3 and 3 as two branches of 9. We get two more factors as 3X 3 3x3x%3=27 So, 27=3X3 x3. Find the prime factors of the following numbers.Division Method We can also find prime factors using division method Find prime factors of 18. Start with the smallest prime number that divides 16 completely. 2 ie the smallest prime number thot divides 18 without leaving o remainder. Recall 18 +2 =9 So, we write 2 on the left side of 18 separating them with a line, 2 is. a prime factor of 18. 2) 18 9 is not a prime number. 3 : 2xgxd=18 So, we divide It agoin with the smallest prime number that divides it completely. Recall 9 + 9=3. 3 Ie a prime number. Wekeep dividing untill we get all prime numbers So, prime factors of 18 =2X3X3 Find prime factors of the following numbers using division method. 3a.| (27 48 |_99 9 4 3x__x__=27 xx =99Exercise 4.5 1. Find the prime factors of the following numbers using the factor tree method, Shak 2. Find the prime factors of the following numbers using division method, a) b) s) 20 60 32 a MH 20: —*__x*__x__=60 — hk ke, =324.6 Common multiples and Least Common Multiple (LCM) Can you find common multiples of 2 and 3? Let's write firat ten multiples of 2, 2 4 6 8 10 «12014 16 18 20 Let's write first ten multiples of 3, 3.6 9 #12 #16 #118 21 24 27 30 You can see that seme numbers are multiples af bath 2 and 3. We call them common multiples. Let's circle common multiples of 2.and 3. Muliplesof 22 2 4 @ 8 10 @ 14 16 @® 20 Multiples of 3: «899 @ 9 @ 16 @ 21 24 27 30 Common multiples of 2 and 3 are 6, 12 and 18. 6 Is the smallest number which Is a common multiple of both 2 and 3. It Is called the lowest (6r least) common multiple (LCM) To find LCM, we follow the following steps. Find the firet two common multiples of 4 and 5. Identify the LCM vonole oh QOO00000000 wirelee ots OODDOOOOOOO First two common multiples of and Sare[ond[_]. The LCM of and 6 is[_]. “—sExercise 4.6 1. Write the multiples for each number given below. Circle the common multiples and find the least common multiple (LCM) for each pair of numbers. 1B Multiples of 2 Multiples of 6 LCM — (8) Multiples of 5 Maltiples of 7 LCM Multiples of 2 Multiples of 8 LCM Multiples of 4 Multiples of 6 LCM — 1@O@® Multiples of 6 Multiples of 8 LeM = ‘OO Multiples of 3 Multiples of 9 LCM —4.7 Finding LCM using prime factorization We can also find LCM using prime factorization method. Let's find LCM of 6 and 8 using prime factorization method. Write prime factors of both numbers. Prime factors of 6 =(2) x 3 [ &) (8) Prime factors of 8 =(2) xX 2 x 2 e Cx) x) Find the common factors. 2) 2)€2) Common factors = 2 Wire te foto which are not common. Remaining factors = 3, 2,2 9 Werte octr frm sop 2 ond sep 31 in LO LM=2x39x2 x2 =24 Find LCM of 18 and 27. Let's follow the steps we have learnt. Prime factors of 18 = 2 x(@) x1 Prime factors of 27 = (3) x(3) x Common factors = 3, 3 (Write all occurances) Remaining factors = 2,3 LOM=3x3x2x 3 =54Exercise 4.7 1, Find Leost Common Multiple (LCM) of the following pair of numbers using prime factorization method "@@ LOM »@@ LCM, "@®@ LCM "@@ LCM »@®@ LCM 1@®@ LCM4.8 Common factors and Highest Common Factor (HCF) Can you find common factors of 12 and 187 Let's write factors of 12. 1 2 3 4 6 12 Let's write factors of 18. 1 2 3 6 9 18 You can see that some numbers are factors of both 12 and 18. We call them common factors. Let's cirele commen factors of 12 and 18. Factors of 12: ®@O © + © 2 Factors of 18: Oo @® © © 9 18 Common factors =1, 2, 3, 6. 6 is the greatest number which Is the common factor of both 12 and 18. It is called the highest common factor (HCF) To find HCF, we follow the =_—— steps. =, Find the common factors of 32 and 40. Identify the HCF Factors of fC] Factors of 40:{_ |[_ |] Common factors ore{ | [~][ Jona[_] The HCF of $2 and 40is[]Exercise 4.8 1. Write the factors for each number given below. Circle the common factors and find highest common factor (HCF) for each pair of numbers, a FIC) Factors of 3 Factors of 9 HCF ot " Factors of 1§ ———H_ Factors of $6 ——____ HCF — » CO Factors of 6 Factors of 24 HCF fae 4) &) Factors of 1é| —————___ Factors of 28 HCF — Factors of 33). Factors of 27 HCF os a le) Factors of 11 Factors of 22 HCF —_—4.9 Finding HCF using prime factorization We can also find HCF using prime factorization method, Let's find HCF of 6 and 24 using prime factorization method. * Find prime factors of both numbers. Prime factors of & (2) X @) Prime factors of 24 ©) x @)x 2. x2 = BR Common factors are 2 and 3 e Multiply the common factors to find HCF. ooo HCF =2 x 3 =6 Find HCF of 30 and 45. ascent, S08 Prime factors of 30 = 2 x 3)x G) Prime foctors of 45 = 3 x (8)x 6) Common factors =3, 5 HCF=3x5 =15