PRIMARY _—, MATHEMATICS 4A TEXTBOOKWhole Numbers 1 Numbers to 100,000 2 Rounding Off Numbers PRACTICE 1A Factors & 4 Multiples & PRACTICE 1B GB w Multiplication and Division of Whole Numbers 1 Multiplication by a 1-digit Number, Division by a 1-digit Number and by 10 PRACTICE 2A 2 Multiplication by a 2-digit Number PRACTICE 2B REVIEW A Fractions 1 Adding Fractions 2 Subtracting Fractions PRACTICE 3A PRACTICE 3B 3 Mixed Numbers 4 Improper Fractions 5 Fraction of a Set PRACTICE 3C REVIEW B 12 18 19 23 27 28 35 36 40 41 42 46 50 51 52 54 58 65 66woo SG Tables and Graphs i] Presenting Data Angles 1 Measuring Angles Perpendicular and Parallel Lines 1 Perpendicular Lines 2 Parallel Lines + Area and Perimeter 1 Rectangles and Squares 2 Composite Figures PRACTICE 7A REVIEW C 70 74 78 81 84 87 31One dollar Ten dollars One hundred dollars One thousand dollars Ten thousand dollarsHow much money is there altogether? $20,000 $3000 Twenty thousand dollars Three thousand dollars $500 Five hundred dollars = $8 Eight dollars The total amount of money is $23,548. $23,548 Twenty-three thousand, five hundred forty-eight dollars 723,548 = 20,000 + 3000 + 500 + 40 +8 23,548 = 23,000 + 548 Twenty-three thousand, five hundred forty-eight te ° N 9 1. Read and write the following in words. (a) 2753 (b) 7919 () 4908 (d) 3056 (e) 7280 (f) 5002 (g) 27,165 (h) 18,057 () 42,605 @) 30,003 (kK) 60,109 (81,900 2. Write the following in figures. (a) Eight thousand, twelve (b) Forty-nine thousand, five hundred one (c) Seventeen thousand, four (d)_ Ninety thousand, ninety3. What are the missing numbers? 5000 | 6000 | 7000 20,000 29,500 | 29,600 | 29,700 : 30,100 ; 28,800 24,230 L 24,130 60,000 24,030 70,000 23,830 23,770 23,670 23,690) 4. Use place-value cards to make a 5-digit number like this: In 68,974, the digit 8 stands for {MJ and the digit 6 stands for @. 5. What does the digit 8 stand for in each of the following 5-digit numbers? (a) 16,814 (b) 82,114 (©) 48,050 co6. (a) Count the ten thousands, thousands, hundreds, tens and ones in this chart. (b) What number is represented by the set of number discs? (<) Which digit is in the hundreds place? (d)_ Which digit is in the ten thousands place? (e) What is the value of each digit in the number? 7. 26,345 people watched a soccer game at a stadium. (a) Use a set of number discs to represent 26,345. (b) 26,345 is il more than 26,000. (Cc) 26,345 is il more than 6345. 108. What number does each letter represent? a A B c D E 7 ' t 4 + | eee eae tet eee etee eee eee eee 5000 5500 6000 P Q R s T ) t : 4 { 4 50,000 55,000 60,000 (a) Which number is smaller, 56,700 or 75,600? 50,000 is smaller than 70,000 OS e (b) Which number is greater, 32,645 or 32,498? 600 is greater than 400 ° 2, 4 ° £7 7 [eeceenes > Find the value of (a) 6000 + 8000 (b) 27,000 + 4000 (c) 15,000 — 6000 (d) 31,000 — 5000 (e) 7000 x4 (f) 10,000 x 5 (g) 12,000 + 3 (h) 30,000 + 6 (livia9 Rounding Off Numbers Our Savings Maggie $61 | save about $60. Rosa $68 Brandy $75 3 y a Maggie 61 8 75 Peep pe pe py 50 60 70 80 90 They round off each of the numbers 61, 68 and 75 to the nearest ten, 12— pee 2 60 70 3} 61 is between 60 and 70. It is nearer to 60 than to 70. So the nearest ten is 60. 61 is 60 when rounded off to the nearest ten. aS poet 68 is between 60 and 70. Itis nearer to 70 than to 60. Lo ste nearest ten is 70. ~~ “3 75 is halfway between 70 and 80. (C vetae 80 to be the nearest ten. — 75 is 80 when rounded off to the nearest ten. B1. Round off each number to the nearest ten. (a) 29 (b) 38 () 82 (d) 95 2. Round off each number to the nearest ten. (a) 234 234 | (ep 220 230 240 250 234 is between 230 and 240. 234 is nearer to 230 than to 240. 234 is J when rounded off to the nearest ten. (b) 1458 a ra es tae pe eg oe UEC 1440 1450 1460 1470 1458 is between 1450 and 1460. 1458 is nearer to 1460 than to 1450. 1458 is JJ when rounded off to the nearest ten. (©) 2735 2735 | J 2720 2730 2740 2750 2735 is halfway between 2730 and 2740. 2735 is HJ when rounded off to the nearest ten. 3. Round off each number to the nearest ten. (a) 129 (b) 201 () 452 (d) 685 (e) 2069 (f) 4355 (g) 4805 (h) 5508 800 297 ——» 300 518 —— 500 io 4 800 — 300 + 500 = The value of 786 — 297 +518 is about 9. 11. Estimate the value of (a) 418 + 293 + 108 (b) 784 +617 +399 (Q) 814 + 208 — 587 (d) 1205 — 489 — 596 (WiserPRACTICE 1A 1. Write the following in figures. (a) Twelve thousand, eight hundred three (b) Twenty thousand, fifty (©) Seventy thousand Write the following in words. (a) 1758 (b) 5306 (© 72,903 (d) 91,120 What is the value of the digit 6 in each of the following? (a) 54,060 (b) 34620 (c) 60,143 (d) 27,006 Complete the following number patterns. (a) 5780, 5880, @%, H 6180 (b) 32,465, 33,465, Hi, HL 36,465 (©) 53,700, 63,700, 73,700, 3, Arrange the numbers in increasing order. (a) 30,601, 30,061, 30,160, 30,016 (b) 29,999, 90,000, 20,990, 29,909 Round off each number to the nearest ten. (a) 89 (b) 725 (c) 4621 (d) 9099 Round off each number to the nearest hundred. (a) 837 (b) 15,468 (c) 39,963 (d) 46,050 Round off each number to the nearest hundred and then estimate the value of (a) 576 +329 (b) 2154 + 887 (©) 3948 + 208 (d) 682 — 207 (e) 7078 — 238 (f) 5402 — 179 (g) 2590 + 109 — 484 (h) 1368 — 919 — 289® Factors & © ®@ © Ge ©S@€S 3x4=12 12 is the product of 3 and 4. 3 and 4 are factors of 12. S68 OHHH HHmhoS & Hw SAAS HHS 24 is the product of 2, 3 and 4. 2, 3 and 4 are factors of 24. 19CEA BF \.<- ae eS 2x3=6 a aif / We can write a number as a product of two factors in different ways. ) 1, 2, Hl and Gi are factors of 6, Is 4 a factor of 6? Is S a factor of 6? PESSSS SG SS PSEH SSO) 2 and 8 are factors of 16. Ay < Name other factors of 16. a Find the factors of each number. (a) 7 (b) 9 (<) 10 (d) 18 (a) Which of the following numbers have 2 as a factor? 8, 10, 15, 24 (b) Which of the following numbers have 5 as a factor? 15, 20, 2a 32 205. @ ) (a) (b) (a) (b) © (a) (b) Is 3 a factor of 22 7 3)21 21 —<—~_— 0 21 can be divided by 3 exactly. 0, So 3 is a factor of 21. ° aX) |s 3 a factor of 26? 26 cannot be divided by 3 exactly. So 3 is not a factor of 26. Is 2 a factor of 98? Is 4 a factor of 98? Is 4 a factor of 60? Is 4 a factor of 84? Is 4.a common factor of 60 and 84? ls 5 a common factor of 75 and 80? ls 8. a common factor of 72 and 96? Find the missing factors. (a) © (e) 28=7x ia (o) 40=5~x i 72=8x ml @) 81=9x 63=9x i () 56=7x 210. Find the factors of 32. The factors of 32 are 1, 2, MN, HM, Bl and gi. 11. Find the factors of 48. 48 =1x 48 48=2xHl 48=3x@ 48=4x i 48=6x The factors of 48 are 1, 2, 3, 4, 6, Mf, MM, MM, BM and 48. 12. Find the factors of 100. 13. Find the factors of each number. (a) 40 (b) 50 ( 75 (d) 80 C 22® Multiples ee ee ee eee eee ece eece eece eece 3x1=3 3x2=6 3x3=9 3x4=12 —_———_——_- 9 is a multiple of 3. 3 is a factor of 9. 12 is a multiple of 3. 3 is a factor of 12. Name other multiples of 3. 23(a) Is 3a factor of 362 (b) Is 36 a multiple of 3? w | w ols clan” aln - (a) Is 3 a factor of 23? (b) Is 23 a multiple of 3? - (a) Is 12 a multiple of 2? (b) Is 12 a multiple of 3? (c)_ Is 12 a multiple of 4? (d). Is 12 a multiple of 5? (e) Is 12 a multiple of 6? List the first four multiples of 5. oN 5x2=10 Sx3=15 List the first four multiples of 9. Find the next three numbers in each of the following number patterns. (a) 4,8, 12,16, i, (b) 6, 12, 18, 24, 247. In the table below, the multiples of 2 are circled and the multiples of S are crossed. 1|@) a1 {12} 21 22) 31 (G2) na a2) [51 (69) | 61 (62) (712) 73. “21 (@2) 83 (@4 [at EN) (a) When a number is a multiple of 2, its ones digit is 0, 2, @ Bo @. (b) When a number is a multiple of 5, its ones digit is or @. 8. Write any number that is a multiple of 3. Find the sum of the digits of the number. Is the sum a multiple of 3? 259. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 12 is a common multiple of 4 and 6. Name the next two common multiples of 4 and 6. There are more than one common 10. (a) Which of the following numbers are common factors of 36 and 63? 3] [4] [6] [9] [2 L (b) Which of the following numbers are common multiples of 6 and 9? 9} |18| |27) |36| [4s 11. Find a common multiple of 3 and 5. The multiples of 5 are 5, 10, 15, 20,... 15 is also a multiple of 3. 26PRACTICE 1B 1. Write down all the factors of 18. 000950000055005500 [600000606] (9090000 |©0900200008 200000 eS 0090000 (b) Write down the next four multiples of 5. Peed epee py py 0 5 10 15 20 af ry a A Find the missing factors. (a) 4x Mi =36 (b) 6x =54 () @xs=56 (dd) Mx9=27 Find the factors of each number. (a) 8 (b) 15 () 20 (d) 50 (e) 75 (f) 98 Find a common factor of each pair of numbers. (a) 15 and6 (b) 12 and 16 (©) 15 and 18 List the first four multiples of each number. (a) 2 (b) 6 © 8 Find a common multiple of each set of numbers. (a) 3.and4 (b) 4and5 () 4and6 27Multiplication and Division of Whole Numbers 0 Multiplication by a 1-digit Number, Division by a 1-digit Number and by 10 Sean has 1135 U.S. stamps. He has 3 times as many foreign stamps as U.S. stamps. (a) How many stamps does he have altogether? There are more foreign stamps { than U.S. stamps, U.S. Foreign | EE Hi 1135 x 4 = 4540 je has 4540 stamps altogether. = When 1135. ismu(b) If Sean puts the stamps equally into 5 packets, how many stamps are there in each packet? 4540 + 5 = 908 40 There are 908 stamps in each packet. a8 9 90 908 5)4540 5)4540 5)4540 45 45 45 Soa 7 40 0 Divide 45 Divide 4 Divide 40 hundreds by 5. tens by 5. ones by 5. When 4540 is divided by 5, the quotient is 908 and the remainder is 0. 291. 2. 3. 4. Multiply 3726 by 5. Multiply. (a) 2950x6=@) (b) 8x3245= 2950 3245 x 6 x 8 pe P| Estimate the value of 6218 x 4. _—— (0 x4 ) 6218 x 4 “ 7000 x 4 6218 is nearer to 6000 than to 7000. 6000 x 4= 8 The value of 6218 x 4 is about [. Estimate and then multiply. (a) 4076x5 (b) 4317x8 (©) 2050x9 (d) 7x 6931 (e) 9x 2173 (f) 6x 3840 [masa 30Ww . Divide 4206 by 3. . Divide. (a) 3250+5=9 (b) 4235+ 7=( oa 2m 5)3250 7)4235 . (a) 40+10= @— @) oo a (b) 400+ 10= @ =10 @ _s0, ) ; @() 440+ 10=— (d) 4440+ 10= 8. Estimate the value of 3840 + 6. a / 3840+ 6. * 4200+ 6 3840 is nearer to 3600 than to 4200. i ° 3600+ 6 = @ The value of 3840 + 6 is about fi. 9. Divide 3245 by 10. 3 32 324 10)3245 10)3245 10)3245 30 30 SOS 2 24 2. 2 2 3210. Estimate and then divide. (a) 3604+9 (b) 3580+ 7 (c) 3120+8 (d) 8128+ 10 (e) 7528 +3 (fF) 7180+ 6 41. The number of cars is 4 times the number of motorcycles in a town. (a) If there are 4356 cars, how many motorcycles are there? There are more cars than motorcycles. | Cars Motorcycles [| == 4356 + 4= 1089 There are 1089 motorcycles. (b) How many cars and motorcycles are there altogether? Method 1: 4356 + 1089 = There are @ cars and motorcycles altogether. Method 2: 1089 x 5 = There are J cars and motorcycles altogether. 3312. 13, Mr. Cohen earns $2935 a month. If he spends $1780 each month and saves the rest, how much will he save in 6 months? First, | find the amount Mr. Cohen saves each month. — fo} He saves $1155 each month. 2935 — 1780 = 1155 1155 x6 = He will save $4 in 6 months. David bought 6 cameras at $1340 each. Then he bought another 8 cameras at $1248 each. How much money did he spend altogether? _—————_——_ David spent on the first 6 cameras and the total amount he spent on { First, | find the total amount the next 8 cameras. 1340 x 6 = 8040 He spent 8040 on the first 6 cameras. 1248 x 8 = 9984 He spent 9984 on the next 8 cameras. 8040 + 9984 = He spent $f altogether. crete 34PRACTICE 2A Find the value of each of the following: YRwNe 2 10. @ (b) © 3x 2011 4x 2107 3450 x 5 6 x 4215 3917 x 7 6258 x 9 2109 + 3 4036 + 4 2510+ 5 7212 + 6 3968+ 8 8181+ 9 6431+ 7 4750 + 10 3299 + 10 A baker sold 1380 cakes last month. He sold 3 times as many cakes this month as last month. How many cakes did he sell this month? The cost of a computer is 4 times the cost of a printer. If the computer costs $2560, find the cost of the printer. Josh had 1536 rubber bands. He put them equally into 6 boxes. How many rubber bands were there in each box? James bought 3750 kg of rice. He packed the rice in bags of 10 kg each. How many bags of rice did he have? The total cost of a scooter and 2 motorcycles is $9798. The cost of each motorcycle is $3654, Find the cost of the scooter. For the last 4 months, Jake’s monthly salary was $1895. He saved $3032 during the 4 months and spent the rest. How much did he spend? a5® Multiplication by a 2-digit Number © @® , 9809 © = 90 > 9000 O66 32 x 10 = 320 320 x 2 = 640 @O @000 eo o> = 9600 = 0900 @ 66 @®@ 32x 2=64 64 x 10 = 640 @® , OOO @O = 0000 @ @@ 32 x 20 = 6401. Multiply. (a) 16x10 (b) 40x 10 () 254x 10 (d) 10x 29 (e) 10x96 (f) 10 x 380 Find the product of 14 and 30. Method 1: 14x30 = 14x 10 x3 = 140 x3 =a Method 2: 14x 30 = 14x 3x10 Method 3: 4x3 =42 14 x 30 = 420 Multiply. (a) 284x20=@ (b) 40x 309= 284 309 x 20 x 40 5680 “12,360 374. Multiply. (a) 23x30 (d) 50x36 5. Multiply 34 by 15. 34x15= (b) 68x70 (e) 90x45 CT. 34x 10 = 340 34x5 =170 34x 15 = 340 + 170 (c) 392 x 80 (f) 560 x 60 6. Multiply. (a) 64x27= x 64 27 448 1280 1728 38 —— 64x7 e— 64x2010. (b) 19x 278= 278 Cae: 2502 «— 278x9 2780 «<— 278~x 10 5282 Multiply. (a) 20x 60 (b) 50x 80 (d) 500 x 30 (e) 40x 600 Estimate the value of 32 x 68. 30 x 70 = The value of 32 x 68 is about [i Estimate the value of 48 x 315. 50 x 300 = The value of 48 x 315 is about Mi. Estimate and then multiply. (a) 49x 18 (b) 21x 72 (A) 412 x 23 (ce) 383% 58 (g) 51x 490 (h) 69 x 786 39 () 70x90 (f) 400 x 50 () 62x47 (f) 685 x 32 (i) 88x 594PRACTICE 2B Estimate and then find the value of each of the following: PWNS 10. () (b) © 2907 x 4 6032 x 5 7902 x 7 4170+ 6 5616+ 8 8019+ 9 48x11 61x 29 88 x 67 101 x 13 289 x 53 786 x 78 Miguel delivers 165 copies of a newspaper every day. How many copies of the newspaper will he deliver in 30 days? Tom bought 15 sheets of stamps. If there were 25 stamps on each sheet, how many stamps did he buy? After buying 12 chairs at $128 each, Catherine had $342 left. How much money did she have at first? 300 children are divided into two groups. There are 50 more children in the first group than in the second group. How many children are there in the second group? The difference between two numbers is 2184. If the bigger number is 3 times the smaller number, find the sum of the two numbers. Mrs. Garcia saved $2001 in two years. She saved $65 a month in the first 15 months. She saved the same amount every month in the next 9 months. How much did she save a month in the next 9 months? 40REVIEW A 1 What is the value of the digit 6 in each of the following? (a) 39,164 (b) 16,083 (c) 62,375 Write the following in figures. (a) Twenty-four thousand, thirty-eight (b) Seventy-four thousand, two Write the following in words. (a) 42,310 (b) 15,206 (c) 20,815 Bill has $2486 in his savings account. Round off this amount of money to the nearest $100. (a) Write down a common factor of 12 and 20. (b) Write down a common multiple of 8 and 12. Find the product of (a) 64 and 25 (b) 1250 and 8 Find the quotient and remainder when (a) 1026 is divided by 3 (b) 5000 is divided by 6 (©) 4984 is divided by 7 (d) 2831 is divided by 9 A shopkeeper packed 3284 pieces of soap into 6 equal packages. How many pieces of soap were there in each package? How many pieces of soap were left over? Mary had 1240 picture cards. She kept 80 cards for herself and gave the rest to a group of children. Each child received 8 cards. How many children were there in the group? 3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile? 41Fractions — 4D Adding Fractions Lila drank 2 liter of milk. Her brother drank 2 liter of milk. How much milk did they drink altogether? 1 fifth + 2 fifths = 3 fifths They drank §@ liter of milk altogether. 1. Find the sum of 2 and 2 2 3 —— 5 5 2 fifths + 3 fifths oa epi = a 2 eee 2432 Hee a 422 and z 3 8 2. (a) Add 3. Add, “ho +0 hn FID MO SIN An TID HHO MIN wlin EfSas51 1 4. Add 5 and r 2,1.8 3°6 6 a a ‘ 6, What are the missing numbers? gene 2a eee eee @O sta ©) 3t5 -3,@ -,1 gee: 9° 9 _i a [a8 448. What are the missing numbers? Bice 9. Add. 10 + Aiea © m long. OW There are 2i watermelons, The total amount of water is 33 liters. ea 3 7 15, 25 and 33 are mixed numbers. When we add a whole number and a fraction, the result is a mixed number. 521. Write a mixed number for each of the following: (b) 2 wholes 1 sixth = Mil 2. What number does each letter represent? (a) -—+ 0 3 wie Ls ro > N i 5 ieee 8 8 8 8 8 8 8 3. Find the value of @ 3+2 () +2 0) 1 2 2 2 @ 2-4 © 3-3 5-3 53© Improper Fractions What is the length of each of the following strips of paper? 1 im 1 third = 2 3 2 thirds = 2 3 3 ———*+~_____.,, Cy as 3 thirds = 3 3 4 mortim 3 3 — . EE ae 4 thirds = a 3S mori2 | a uien —_ 5 EL eee 8S thirds = 2 E irds = 3 3, ‘ and 2 are improper fractions. An improper fraction is equal to or greater than 1. improper fractions : wo, i 2 3 a 5 & 2 8 3 3 i + 3 3 es 3 Re a Spey 0 1 4 8 2 2 22 naan An improper fraction can be expressed as a whole number or a mixed number. —~— or ° 541. How many halves are there in 3h There are @ halves in 35. 2. Write an improper fraction for each of the following: i I 12 sixths = 3 553. Change the improper fractions to mixed numbers. & 5. Express each of the following as a mixed number or a whole number. @ 7 ©) 2 © 3 @ 2 6. Change the mixed numbers to improper fractions, 5610. n. 12. Change 3 1 6 =3+ - 8 6 to an improper fraction. aoe 6 + i 6 Express each of the following as an improper fraction. 5 @ 22 (@ 1% Find the missing numerator in each of the following: (a) 2i= 1 (d) 35 2 1 () 22 © 24 2_,m Oye ics | @) 45=35 © 3i=2 ) 42=3 a 4 a 4 Express each of the following as a whole number or a mixed number in its simplest form. @ 2 o) 2 © 22 @ 28 © 28 ® 32 @ 18 (ny 28 Add. Give each answer in its simplest form. OP OLE 0 fe oie oft oht Subtract. Give each answer in its simplest form. @ 3-3 (b) 2-3 @ 4-3 @ 2-% @) 2-3 ) 3-3 S7© Fraction of a Set 2 out of 5 children are girls. What fraction of the children are girls? 2 out of 5 groups of children are girls. What fraction of the children are girls? 581. What fraction of each set is shaded? ° ee | "la ala Al. "|@@@/@@@/000 " looclaoaloaelooglooolons. [eto rete 27 @@O0o0 0c @®@0O0O 0 dof 12> le 12 into fs equal groups. e group is + of 12. 3. Find the value of 2 of 20. f 12 is 4. @ @ @ ® . SF fof 20= 209 ica) = of 20= @1 1x 20 1 20 = \ 4 4 $ of 20 is the same as 3 99 = 3x20 4 4 Find the value of 2 of 18. Sy 4g = 2% 18 6 = a “aac > Find the value of 3 of 9. @@@I0 pron2e ee -@ a at [ee ie Find the value of (@ fof 12 (b) of 20 © 5 of4 @ 5 of 9 (@) 2 of 16 3) 2 of 10 607. Kelley buys 24 flowers, 2 of them are white. How many white flowers are there? Divide 24 into 3 equal parts. 24 = 3 units Method 1: 2 of 24 = 2 units tins 5 fs} Sado ——- 3 units = 24 Tunit = 3 2 units = @ of 24 is the same as There are {J white flowers. a 2x24, Method 2: ee 5x 24= There are J white flowers. 2 3 2 3 8. There are 8 coins. 6 of them are ten-cent coins. What fraction of the coins are ten-cent coins? Bie 6 out of 8 is 3 2 is a common factor of 6 and 8. 2, Divide 6 and 8 by 2: 2 Bs 1 of the coins are ten-cent coins. Resiv95.09 619. Minghua had 42 stamps. 10. 11. He lost 6 of them. What fraction of the stamps did he lose? 6 6 out of 42 is a 6 «=i Express S in its simplest form, He lost iJ of the stamps. Jenny’s handspan is 16 cm. What fraction of 1m is 16 cm? JG og 100 16 cm is H@ of 1m. [test ewes? > David spent 2 of his money on a storybook. The storybook cost $20. How much money did he have at first? T unit 5 units = $y He had $j at first. 6212. Meiling had $20. She used Z of it to buy a book. How much did she have left? Method 1: fe 2 _ 2x20° First, | find the amount of x20 = 2320 money she used. =8 — 20 She used $8. 20-8=—8 She had $/g left. Method 2: 1— : = 2 First, | find what fraction of the money is left. She had 2 of her money left. 2«20= i She had $2 left. Method 3: 5 units = $20 Tunit = Si 3 units = $M She had $2 left. 63