Eisenhower Middle School. Mathematics Summer Packet. Entering 7th Grade Algebra. Name:

Transcription

1 Name: Eisenhwer Middle Schl Mathematics Summer Packet Entering 7th Grade Algebra The fllwing is a review f imprtant tpics in 6tr grade that will be needed fr 7th grade Algebra. D nt use a calculatr. It is very imprtant that yu have mastered wrking with decimals, fractins, integers, expressins and equatins fr next year. Mastery in these areas will set yu up fr success next year. A lt f learning is lst in the summer, and every prblem des nt need t be cmpleted. Make sure yu can d a few n each page.these tpics will cme up again and again next year. Cmpletin f the packet is ptinal, and the packet will nt be cllected by yur teacher next vear.

2 Name Perid Date Operatins with DecimalsReview Wrksheet Find each sum r difference. t. 36.t Find each prduct r qutient. 10. O.9L c (3.e) X L L

3 . Name Perid Date (3.s51 L s X X 0.4s le. 0.78J z. 7s.4+s.s F:0tr 22. Alicia paid 51.32fr a bag f pint beans. The beans cst S.SS per lb. Hw much did the bag f pint beans weigh? 23. Nina and 3 friends ate lunch at a cafe. They decided t split the bill evenly. The ttal bill was Hw much was each persn' share? 24. Pstage stamps cst SO.SZ each. Hw much des a bk f 50 stamps cst?

4 edding, Subtracting, Multiplyin& and Dividing with Mixed Numbers.) Whenwrkingwithmixed numbers it is ften necessar5rt change the mixednumbert m imprper frastin. Then yu can g thrugh the rsual prcess accrdingt the peratin yu ar ding. Always check yur answer t be sure it is in simplest frm.,,+*,?r: z.f+11 : E7 3. zl+si-: l0 t zl= 5s t.,!: 4+: 6. 8g - s?: q?xr1 : n! xll : 53 g. t9 x s!: 89 l. n! -ll : 48 ll. r? : 7 t2. 5Z* 1! : 83 Slve the fllwing prblems accrding t the way mixed numbers are cnputed. 13. Ifarestaranttras z! cherrvies, +l- alplepies,and tabhreberrypie remainingafter 4 dinnerne night, hwmanypies are left? 14. If Lisa has? f her hmewrk p.ages dne and Jennifer has nly I f that amunt dne, Denise has r] shares t place with ap'hne cmpany. She wants t apply it equally 3- amng 4 f the cmpanies she has read abut. If she des this, hw many shares will she have with each cmpany? g ffi$effi i,

5 Cnverting Fractins & Decimals (C) Instructins: Fill in the blanks f each rw. Fractin Decimal Percent (V) Rati 7 8 7: :5 T: s55 3:4 MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH

6 and Negative Numbers and negative numbers are als called integers. They are equidistant apart n the line. Fr every psitive number there is an ppsite, a negative number. These carry a sign. This is the negative sign O and a psitive sign (+). When a number with n sign, it is cnsidered t be psitive. Smetimes using a number line is helpful wrking with integers. the ppsite term : : 4. 30: 6. 89: : : adding r subtracting with integers, it is imprtant t pay attentin t the signs. -4+3: 10. 5*9: r (-10): t2. -1,5-7 : t1 : ;: 1s. c10) + (-14) : 2 + (-11): (-181: ;: 19.6*8: e + (-13) : 2r. (-14)*5: ;: : what yu knw abut integers, slve the fllwing by filling in the missing number (8) : : (-7): : 12

7 Muttiplying and Dividing Psitive and Negative Numbers Multiplicatin: Multiplying a negative number with a psitive number gives a negative prduct. Multiplying a psitive number with a psitive number gives a psitive prduct. Multiplying a negative number with a negative number gives a psitive number. Slve: 1. (-8)(e): _ 5. (e) G4) : _ e. G3) (8): _ 2. 5 (-01: 6. (-7) (7): 10. (5) G5) : 3. (-r+) z: 7. (-7) (-10) : (-2): 13. (4) (-s) :_ (6): - ls. e (-121: 4. (-2) +: 8. e (-8): t2. rr (-2) (-2): Divisin: A psitive number divided by a negative number gives a negative qutient. A negative number divided by a psitive number gives a negative qutient. A piitive number divided by a psitive number gives a psitive qutient. Slve: (-8) : 18. (a5) + (-5) : 19. (-14) + 2: 20. (-2r) + 3 : 2t : (-8) : 23. (-32)+8: (-s) : (-8): 26. If Jhn gets n the elevatr n the seventh flr and ges tw flrs up, then ges three; flrs dwn, and then rides tw flrs up again, what flr is he at nw? ii If Mary gets n the elevatr in the basement and then ges three flrs up, and tw dwn, at which flr is she nw?

8 DATE Study Guide and lnterventin Variables and ExPressins PERIOD Write Mathematical Expressihs In thg algebraic expressin, (w,the letters { and ur are called Ii algebra, a variable is-used t represent unspecified numbers ;;ri"*. Any letter ""ri"uu".utr U" used Is a variable. The letters 4 and w are used abve because tft"y tf." h6t f"itltr ftfr" wrds length a\d width. In the expressin (w, ( and w are called "r" factrs, and the result is called the prduct' write an algebraic expressin fr each verbal expressin. a. fur mre than a number z The wrds mre tltan imply additin' fur mre than a number n 4*n The algebraic expressin is 4 * n' b. the difference f a number squared and 8 The expres sin dffirence f implies subtractin' the difference f a number squared and 8 n2-8 The algebraic expressin is n2-8. a.3a 3a:3'3 :81 Evaluate each expressin. 3' 3 Use3asafactr4times. MultiPlY. b. five cubed Cubed means raised t the third pwer' 53 : 5' 5' 5 Use5asafactr3times' Multiply. : L25 write an algebraic expressin fr each verbal expressin. 2. a number divided by 8 1. a number decreased by 8 3. a number squared 4. fur times a number 6. a number multiplied by a number divided by less than 5 times a number 7. the sum f 9 and a number 1"0. ne-half the square f b 9. twice the sum f 1-5 and a number mre than the prduct f 6 and a number increased by 3 times the square f a number 6- = -= 3. 6' = t : P 6' lr Evaluate each expressin L6.L22 L Chapter 1 Glence Algebra 1

9 DATE_ Study Guide and lnterventin Order f Operatins PERIOD EvalUate RatiOnal ExpfeSSiOIlS Numerical expressins ften cntain mre than ne, peratin. T evaluate them, use the rules fr rder f peratins shwn belw. Step 1 Evaluatexpressins inside gruping symbls. Order f I Step 2 Evaluate all pwers- Operatins I Step 3 D all multiplicatin and/r divisin frm left t right. Step 4 D all additin and/r subtractin frm left t right. a.7*2'4'4 Evaluate each expressin ' 4-4 =rr;: ; ^ Hi,:'nT:. :11 Subtract 4 trm 15. b. 3(2) + 4(2 + 6) 3(2) + 4(2 + 6) : 3(2) + 4(8) Add 2 and 6. : Multiply left t :38 right. Add 6 and 32 a. 3[2 + (12 + 3[2 + (12 +, 3+23 n.ffi Evaluate each expressin. 3) F.s : Vz-4 11 : )21 : B(2 + 42) 'iute 12 by 3. : 3(2 + 16) Find 4 squared. : 3(18) Add 2 and 16. : 54 Multiply 3 and 18. Evaluate pwer in numeratr. Add 3 and 8 in the numeratr Evaluate pwer in denminatr \' I:E.-N Multiply. ]E :(, = i F 6 F Evaluate each expressin. 1.(8-4).2 2.(L2 + 4) :E.: = I, (20-t7) L ^ ' T (2.$+2 _9 0 'tr lo.82+b*22.7_20+e,t tq2 11.ffi 9,(9\ - L L2.:+:-.-; 6:+ d [5(3'7 + 4)] t+' sJ (52) - 4'g L'z@.s+D trz-a tz.7ffi c2 - q.2 ts',rffi Glence Algebra 1

10 'l Glence Algebra 1 PERIOD Study Guide and lnterventin ftntinued) The Distributive PrPertY Simplify EXpfeSSiOnS A term is a number, a variable, 1 a prduct r_q_utient f.r*betr-and variables. Like terms are terms that cntain the same variables, with crrespnding variables having the same pwers. The Distributive Prpert_y. and prp.erties f equaliti", iut be used t simplify expressing:-h expressin is in simplest frm if it is repliced by an equivalent expressin with n like terms r parentheses. 4(a2 + 'ab) Simplify 4(a2 + 8,,b\ ' ab. - - =iy,iii;r -,:i: : ::;[** :;:il 4a2 + LLab Substitutin Simplify L.tAa - a each expressin. If nt pssible, write simplified. 2.3x * 6x 3.3r L x x2*3x*7 7.20a+l%a-8 8.3x2 + 2x r + 3x2 + l0x2 L.2p * in 11.10ry-4(xy+xy) I.2.2lc + 18c + 31b - 3b L3;3r-2x-2Y+2Y L6.4x + f,ox - 20y) L4.xy Zxy - L7.2 -! - 6x * x2 L5.t2a-LZb+t2c L8. hc2 + 3x2 + 2x E

11 NAME DATE- PERIOD Study Guide and lnterventin pntinued) Cmmutative and Assciative Prperties S!rypllfy Expressihs The Cmmutative and Assciative Prperties can be used alng with ther prperties when evaluating and simplifying expressins. 80+2x)+7y Simplifu 8(y + 2x\ + 7y. : 8y + LGx + 7y Distributive Prperty : 8y * 7y + 16x Cmmutative (+) : (8 + 7)y+ L6x Distriburive prperty : Lly l- LGx Substitutin The simplified expressin is 15y * 16*. Simplify each expressin. 1.4x*3v*r 2.3a*4b+a 3.8rs*2rs2+7rs 4.3a2+4b+Laz 5.6(x + y) + 2(2x + y) 6.6n * 2(4n + 5) 7.6(a+b)+a+3b 8.5(2x+3y)+6(y+r) 9.5(0.3*+0.1y)+0.2x t.3*+@*rr*f!!. z2 +.9x2 * t"' * **' L2.6(2x + 4y) + 2(x + 9) \[rite an algebraic expressin fr each verbal expressin. Then simplify. 13. twice the sum f y and z is increased by y 14. fur times the prduct f r andy decreased by 2xy 15. the prduct f five and the square f a, increased by the sum f eight, a2, and, three times the sum f r and y increased by twice the sum f * and y Chapter 1 Glence

12 Equatins in is an algebraic algrithm that is used t slve fr an unknwn value r variable. an equals (:) sign in an equatin. There is nt ne in an expressin; therefre, may be slved, nt just simplified. Answers culd be whle numbers, negative r ratinal numbers. fllwing equatins. x+1: x: x + (-4): x x-(2+31: x+2-3x: x-9x: (6x + 2) + 7x: 4l 9. (10x)(2x): 40 (8x+3)+( 4x+2): x+3:-4x : -l4p :-5(a+5) 63:9(2-a) :3 (2 + 5m) (x - 2) : -34 -x-15: p: 6p k+19:ft+2 BrideePublishing ReprductinPrhibited.

13 Math 7 NO CALCULATORS Name Add, Subtract, Multiply, Divide Ratinal 2012 Kuta Sftware LLC. All rights reserved. Evaluate each expressin. 1) (-7) + (-q) + t D (4)+s-(-z) Date Perid 3) (-r)- (-+)- (-:) 4) (-1) -4+6 Find each prduct. s) ) _1 t) -t ) , -: -i *,-i : Find each qutient. ll) tz\ ) ) ?5 ts) +i 7 rct -z! +f 55 d

14 @ Evaluate each expressin. rd (-6.3) - (-t.qe) 18) (-3.4)- l.s le); (+) zr (-r +). i 21) (-30-10) +-4+-s-z 22) s.8+2-(-0--s) Evaluate each using the values given. 23) n-(**r); use m=2,and,n=-3 24) abz;use d= -3,and.b--4 zsl 4:used=3"and ' b=-4 6' 26) (c)(a-d);use a=4,b=2,and'c=-z - 2); use m = 5, and. p S) '4+-h; use h=-6,and, j=-4 29) (-6)(m-r,);s" *=-1,and,n=-+ 30) x +x+y;use-tr=-l,und y=+ 46