Ontario Grade 7 Mathematics Chapter 1 PDF

Ontario Grade7 hfathemaCics CHAPTERI -NUATBER CONCEPTS› CHAPTER1 NUMBER CONCEPTS 1.1 Rounding and Estimation 1.2 Multiples and Factors...

Ontario Grade7 hfathemaCics CHAPTERI -NUATBER CONCEPTS› CHAPTER1 NUMBER CONCEPTS 1.1 Rounding and Estimation 1.2 Multiples and Factors 1.3 Exponents and Scientific Notation 1.4 Squares and Square Roots 1.5 Fractions and Decimals 1.6 Comparing and Ordering Fractions and Decimals 1.7 Integers It is unlawful to photocopy or reproduce cc ntent without permission from Dynamic Classroom Inc. This guide is licensed to the end user forPERSONAL useonly. All rights reserved. Ontario Grade7 Mathemntics CHAPTER1 —NUMBER CONCEPTS 2 1.1 Rounding and Estimation Rounding Numbers Rounding numbers involved place value and thevalue of digits. We round up whena digit to the right of the one of interest is5 or greater and round down when it is lesa than 5. To round numt›ers, use the following procedure. 1. Oo to the column immediately to e_thright ofthedigit in the place value asked for: 2. Round ¡jp if the digit in that column is5 or greater (5 to 9) and round down ifthenumber is less than5 (0 to 4). 3. Replace the digits to the right with 0’s. If the digits are to the right of the decimal point, delete them. Example: Round 2463.71 A. tothenearest 100 Go to the tens cols It isa 6. Roundthehundreds up from4 to5. Replace the digits to the right of the hundreds The answer is 2500. B. to the nearest 10 Go totheones cohimn. It isa 3. Replace tire digits to the right of the tens with ’6. The answer is 2460. C. tothe nearestl Go to the tenths column. It isa 7. Roundtheones up from3 to4. Delete K digits to the right of the ones. The answer is 2464. D. to the nearest tenth Go to the hundredths column. It isa 1. Delete the digits to the right of the tenths The answer is 2463.7. It ia unlawful to photo.copy or reproduce content wit:I+out parmisaion from Dynamia Classroom Inc. Thls guide ie licensed to the end user forPERSONAL useonly. Alt rights reserved. Ontai lo Grade7 Mathematics CHAPTER1 —NUMBER CONfiRPTS E omtWgNombere Estimating numbers involves makinga judgpient about their approximate values, usually by using rounding. Estimation is used toquickly find the approximate value and to check ifan answer is reasonable. 1. Estimate the sum of 32 and 69. Rounding each number tothenearest 10, we get 30 and 70. An approximate value forthe sum is 100. 2. Estimate the cost of7 CDs at 514.90 Rounding 514.90, we get $15. ' Ch ’ An approximate cost is7 x 15 — $105. 3. Estimate the product of 38 and 51. Rounding tothenearest 10, we get 40 and 50. An approximate product is 40 x 50 = 2000. Exercises 1.1 1. Round 7638 to 5iolution a thenearest thousand. b. the nearest hundred. c. the nearest ten. 2. Round 2364.608 to a thenearest thousand. b. the nearest hundred. c. the nearest ten. d. the nearest one. f. the nearest hundredth It ia unlawful to photocopy or reproduce content without permission frorri Dynarr4c Classy Inc. This guida Is licensed to the end user forPERSONAL useonly. All righa reserved. Ontario Grade7 Mathematics CHAP3'kR1 —N U3tBElt CONC1iP’l“S 4 3. Estimate lhe product of f›27 and 592 to the nearest 100. 4. Estimate the product of7 20 10 and 12 to the nearest whole number. 5. Estimate the sum of 42.3, 122.9, and 12.2 to the nearest whole number. 6. E.stimate the product of 29.25, 32.1 and 49.0 to thenearest whole mrmber. 7. The school soccer team paid $1355 for19 team uniforms. Approximately how much did each uniform cost? If 18 oranges cost $5.76, approximately how much didonet range cost? 9. A concert was attended by 289 girls, 210 boys and 97 adults.Approximately how many were inattendance in total? 10. Jilly needed toknow approximately how much money was needed forhimsclf and his classmates to attenda mO vic. It tickets cost S8.75 each and there were 21 inthcclass, approximatcly how much would it cost‘? It is unlawful to photocopy or reproduce content without permission from Dynamic ClassroomI nc. This guide is licensed to the end user forPERSONAL useonly. All rights reserved. Ontario Grade7 Mathezastics CHAPTER1 — NUMBER CONCEPTS Extra forExperts 11. A number, rounded to thenearest ten, iS 2480. Ifit was rounded up,what number(s) could have been intheones column? 12.A number, rounded tothenearest hundredth, is 45.28. Ifit was rounded down, what number(s) could have been inthethousandths column? 13.Kathy had 19 files on a computer disk. If the files used up 485 kb of memory andthere were another 921 kb available, approximately how many lbofmemory were on thedisk in total? 14. Jake counted 33 lines on each page ofan essay that he had written. There areabout8 words on each line. If he handed in 11 pages, approximately how many words, in total, were inhisessay? MORE QUESTlONS w.Math-Help.c ON OUT WE 8 SITE It is unlawful to photocopy or reproduce content without permission mam Dynamic Classroom Inc. This guide is licensed to the end user forPERSONAL useonly. All rights reserved. Ontario Grede7 Mathematics CHAPTER1 -NUMBER CONCEPTS 1.2 Multiples and Factors A prime number is an integer greater than1 that has no other positive integer factors other than1 Example: 2,3,5, and 7 art prime numbers, since their only factors are1 and themselves (for example, the only factors of3 are1 and 3).6 is not prime since it has two different sets of integer factors:I and 6 or2 and 3. A factor ofa number isa divisor of that number (it divides evenly into it). Examples: 1. List all factors of 10. 1, 2, 5, and.10 are all factors of 10 since they all divide evenly into it. Of these.factors; only2 and5 areprime factors. 2. Show thefollowing numbers asproducts of nrime falters. 12 =2 x2 x3 50 =2 x 5 x 5 A multiple ofa number is the product of that number times another whole number greater than 0. Example: Multiples of5 are (5 x 1) = 5; (5x 2) = 10; (5 x 3) = IS; (5x 4) = 20; etc. A composite number is not a prime number andcanbe factored in more than one way. Allnumbers that are not prime arecomposite (with the exception of 1). Example: l5 isa composite number since it can be factored as 15x I or5 x 3. EZazapleB wttb Colntioay Solution 1. Which pfthefollowing numbers arenotprime? 1, 3, 4, 5, 7, 9, 1i, 15 1 is not prime since it is not greater than 1. 4, 9, and l5 are not prime. They are composite, Bruce they have more than one pair of factors. Por example,9 can be factored as 9 r 1 or3 x 3. It ie unlawful to photocopy or repioduce content without permission from Dynamic C4as6foom IN This guide is licensed to the end user fcir PERSONAL usaonly. All ñghts reserved. Ontario Grade7 Mathematics CHAPTER1 —NUMBER CONCEPTS 2.List all factors of 20. Factor 20 as2 x 2 x 5. The set of all factors consists of all numbers that divide evenly into 20. The numbers are1 plus all combinations of 2, 2, and 5 shown instep 1. Answer: 1, 2, 4, 5, 10, 20 3. List all multiples of7 less than 40. Multiples of7 consist of numbers that are the product of7 times 1, 3, 4,... ,etc. We want multiples of7 less than 40 7 x 1,7 x 2,7 x 3,7 x 4,7 x 5, (7 x6 is 42, which is larger than 40). Answer: 7, 14, 21, 28, 35 4.Show 90asa product of prime factors. Factor 90 until all factors are broken down into prime factors. 90 =9 x 10 =3 x 3 x 2 x5 Exercises 1.2 1. Identify whether or not each number is prime. Givea reason foryour answer. Number YES O Reason a. 22 b. 31 c. 77 d. 57 e. 43 f. 51 2. List all factors of each number. Then list the prime factors only. Number AllFactors Prime Factors Onlv b. 100 It is unlawful to photocopy or reproduce content without permission from Dynamic Classroom Inc. This guide is licensed to the end user farPERSONAL useonly. AU rights reserved. Ontario Grade7 mathematics CHAPTER1 — NIJSfBER CONCEPTS c. 75 d. ‹10 c. 135 f. 38 3. List all multiples of the lollowing nuiinbCrs that meet cach ct›ndiiioo. Number Multiples of the Number a. All multiples of 11 that are grcatcr than 40 and tess than 100 b. All multiples of’5 bet een 11 and 41 c. All multiples of9 less than 100 d. All multiples of 20 less than 200 c. All multiples of 13 less than 100 that arc add numbers 4. Write each number asa product of prime factors. Number Prt›duct of Primes Number Product of‘ Primes a. 30 f. 1000 b. 12 li. 216 1. ?6 i. 196 e. 250 j. 242 Extra torExperts 5. List all factors that are common toboth9 and 30. It is unlawful to photocopy or reproduce content without permission from Dynamic Classroom Inc. This guide islicensed to the end user forPERSONAL useonIy. All rights reserved. Ontario Crade7 htathezoatics CHAPTERi —N U$'IBER CONCEPTS 6. List all factors that are common to10,14,and70. 7. List all numbcrs less than 100 which aremultiples of both 15 and 10. 8. List all numbers less than 50 which aremultiples of both3 and 5. 9. I am a multiple of both9 and 15.I am lcss than 200 and more than 150. Who am 1? 10. I am a nirtliiple of 3, 5, and 10.I am less than 100. \V1io am I? 11.I am a multiple of 3, 5, and 7 and am betu'een 300 and 400. W'ho am 1? 12. I am a number less than 50. Ifl am a multiple of both2 and 14,who am 1'? vw.Math-H elp.ca It is unlawful to photocopy or reproduce content without permission from Dynamic ClassroomI nc. This guide is licensed to the end user forPERSONAL useonly, All rights reserved. Ontario Grade7 Mathematlcs CBAPTRRI-NUMBERCONCRPT6 10 1.3Exponents and Scientific Notation Numbers Written asa Base toa Power (orexponent) The following numbers arefactored into prime factors. 27 =3 x 3 x3 16 =2 x2 x2 x 2 In. the first example,3 appears three times asa factor, and 2 appears four time8 asa factor in the Becond example. Whena number IB lRultiplied by itself2 or more times, in can write ita ahorter way, by usinga raiaed number, called an exponent orpower. Example: 3 x3 x3 can be written aa 3' and2 x2 x2 x 2 can be written as24. Intheabove exemple, the3 and the2 are called the base. power (exponent) of4 fixample s sx5x5 ’ base of5 The5 is called the base. It is the number that we are going to multiply by itself. The 4 is called the power orexponent It tells us how manytimes we are going tomultiply the base by itself. Scientific Notation A number is written in scientific notation when it is expressed asa number that is more thanI but less than 10, multiplied by some power of 10. Example: Write each number using scientific notation. 2400 = 2.4x 1000 = 2.4x IN 48 000 = 4.8x 10 000 = 4.8x 10 392 = 3.92x 100 — 3.92x lO Scientific notation is used torepresent very large oumbeis. Example: The distance from theearth to the sun is appmximately 1y1 million kilometres. ISI 000 000 = 1.51x 10 km It ie unlawful to photocopy or reproduce.content without permission from Dynamic Classfaom Inc. ‹ suide is licensed to the and user forPERSONAL oaeonly. All right8 reeerved. Ontario trade7 Watbematics CHAPTER1 —X UMBER CONCEPTS 11 Examples with Solutions Solution 1. Write 11x 11x 11 x 11 asa base written to an exponent. 11 is multiplied by itself4 times. 11 is the base and4 is the exponent. 11x 11 x 11 x 11 = 1I 2. What is the value of the following number as a single numeral? 7 is the base and3 is the exponent. 7' 7 is multiplied by itself three times. 7 —7 x7 x 7= 343 3. Write the following number asa product ofa liumber timesa factor witha base and 275= 11x 25 exponent. = 11 x 5 x5 x5 2 = 11 2’75 4. Write the following number using scientific notation. Write thenumber asa numeral between1 and 10, timesa number that isa power of 10. 2143 2143 = 2.143x 1000 Now write the number asa product of the numeral times 10 to an exponent. 2143 = 2. 143 x 103 Exercises 1.3 1. Find thevalue of each expression. a. 112 b. 3* c.252 d.92 e. 4’ f. 10’ g.5 x 32 h. I I x 24 i. 3 x 9‘ It is unIav\rfuI to photocopy or reproduce content without permission from Dynamic Classroom Inc. This guide is licensed to the end user forPERSONAL useonly. All rights reserved. Ontario Grade7 Mathematics CHAPTER1 —NUMBER CONCEPTS J2 j. (0.5)’ x 52 k.1.3 l. (1.2) 2. Show each expression usinga powef anda base. a. 6 x 6 b. 30 x 30 x 30 c. 13 x 13 x 13 x 13 d. 3 x 3 x3 x 3 x 3 x3 e. 100 x 10()x 100 f. 5 x 5 x 5 x 5 x 5 x 5 x 5 y. (0.4)(0.4)(0.4) li. (3.7)(3.7)(3.7)(3.7) 2 2 2 2 2 3 3 3 3 3 3. Show each number asa product ot'prime factors. Then u'rite it using powers and bases. Number Product of Prirnc Factors Powers and Bases a. 25 b. 27 c. 125 d. 1000 e. 243 f. 343 g. 147 h. 405 It is unlawful to photocopy or reprc duce content without permission from Dynamic Classroom Inc. This guide is licensed ten the end user forPERSONAL useonIy, A|] rfghts reserved. Ontario Crude7 Stathematics CHAPTER1 -NUMBER CONCEPTS 13 4. Write cach number using scientific notation. a. 237 b.38 000 c. 125 400 d. 2 544 000 c. 18 OUU ()00 f. 2 505 000 5. Write each number asa single nurnera1. b. 1.05x 10' c. 3.52x 10’ d. 2.46x T 0’ e. 1.0101x 10’ f. 0.0()53x 1 O’ Exlra forExperts 6. Find eaCh unknown. a. 3 x IO" — 3000 b. ? x 10’ = 21 500 It is unlawful to photocopy or reproduce content without permission from Dynamic Classroom Inc. This guide is licensed to the end user farPERSONAL useonly. All rights reserved. Ontario tiradt7 Alaihematics CIL¥PTER1 — NUSIBER CONCEPTS 14 c. 0.615x 10* = 61 500 d.? x 10 4 = 5300 e. ? x 10’ = 106 000 f. 0.0079x ? = 7900 7. A rticket sent into space travelled ata rate of 7000 in/min. How many metres would it trav'el in1 hour? Show your answer using scientific notation. 8. Ifa projectile were totravel ata rate of 2500 m/sec. How far would it travel in one hour? Show your answer using scientific munition. w —. 4 2 10 4 To oraer fractions from smallest to largest, or from largest to smallest: 1. Rewrite each fraction asa decimal fraction. 2. Use plan value to order the 3. Rewrite thefractions in dieir original forms. It is unlawful to photocopy orreproduce content without permission from Dynamic Classroom Inc. This guide is licensed to the and ueqr forPERSONAL useonly. ” AJI rights raeeruecl. Ontario Grade7 Mathematics CTTAPTER1 — NUMBER CONCEPTS 30 Examples with Solutions 1. Compare each pair of fractions. Which is largest or smallest? AnSwer 3 3 a. ':md - 0.5 and - 0.6 : —