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.
Name Perid Date Operatins with DecimalsReview Wrksheet Find each sum r difference. t. 36.t2 + 5.793 2. 8.9 + 2.14 + 7.1 3. 3.6 + 5.27 + 8.93 4. 42.75-26.36 5. 53.85-16.47 5. 56.89-48.91 7. 5.002-4.3 8. 15.26 + 13.29 + 38.96 9.46.21. + 53.942 Find each prduct r qutient. 10. O.9L c 2.7 11. 4.6(3.e) 12. 17.3 X L5.23 13. 2.112.6 L4. 36.78 + 2.4 15.
. Name Perid Date 16. 2.33(3.s51 L7. 12.1s X 19 18. 8.7 X 0.4s le. 0.78J0.16614 z. 7s.4+s.s 21. 0.85F: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 517.84. Hw much was each persn' share? 24. Pstage stamps cst SO.SZ each. Hw much des a bk f 50 stamps cst?
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 t2 4.63 -zl= 5s t.,!: 4+: 6. 8g - s?: 108 7. q?xr1 : 35 8. n! xll : 53 g. t9 x s!: 89 l. n! -ll : 48 ll. r? 3 + 41: 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, -8 15. 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,
Cnverting Fractins & Decimals (C) Instructins: Fill in the blanks f each rw. Fractin Decimal Percent (V) Rati 7 8 7:8 0.625 62.5 8 9 0.888 60 3:5 T:4 20 0.5 9 10 0.s55 3:4 MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH
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. 2. -14: 3. -10 : 4. 30: 6. 89: 7. -56: 8. -165: adding r subtracting with integers, it is imprtant t pay attentin t the signs. -4+3: 10. 5*9: r1. 8 + (-10): t2. -1,5-7 : 12 + 1-t1 : 14. 3 + 1-8;: 1s. c10) + (-14) : 2 + (-11): 17. 6-(-181: 18. 7 + 1-3;: 19.6*8: e + (-13) : 2r. (-14)*5: 22. 9+1-8;: 23. -4 + 9: what yu knw abut integers, slve the fllwing by filling in the missing number. -4+ -3 25. - (8) : -18 26. -15+ :-11 28. 20 + (-7): 29. 16 + - : 12
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) : 11. 6 (-2): 13. (4) (-s) :_ 14. 4 (6): - ls. e (-121: 4. (-2) +: 8. e (-8): t2. rr (-2) 16. 15 (-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: 17. 56 + (-8) : 18. (a5) + (-5) : 19. (-14) + 2: 20. (-2r) + 3 : 2t. -49+-7: 22. 40 + (-8) : 23. (-32)+8: 24. 60 + (-s) : 25. 72 + (-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?
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 37 5. a number divided by 6 8. 3 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 11. 7 mre than the prduct f 6 and a number 12. 30 increased by 3 times the square f a number =. @ 6- = -= 3. 6' = t : P 6' lr Evaluate each expressin. 13. 52 L6.L22 L4.33 17. 83 15. 104 18. 28 Chapter 1 Glence Algebra 1
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. 7 + 2' 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. : 6 + 32 Multiply left t :38 right. Add 6 and 32 a. 3[2 + (12 + 3[2 + (12 +, 3+23 n.ffi Evaluate each expressin. 3)21 3+23 3+8 -F.s : Vz-4 11 :- 42.3 3)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. 11 16.3 Evaluate pwer in denminatr \' I:E.-N 11 48 Multiply. ]E :(, = i F 6 F Evaluate each expressin. 1.(8-4).2 2.(L2 + 4).6 3.10+2.3 :E.: = I,3 4.10 + 8. 1 7.12(20-t7)-3.6 5.15-L2+4 8.24+3.2-32 15+60 ^ ' T4 9.82+ (2.$+2 _9 0 'tr lo.82+b*22.7_20+e,t tq2 11.ffi 9,(9\ - L L2.:+:-.-; 6:+ d 13.250 + [5(3'7 + 4)] t+' 2. 42-8+2 1sJ 21.2 4.32-3.2 15. 3.5.- 4(52) - 4'g L'z@.s+D trz-a tz.7ffi c2 - q.2 ts',rffi Glence Algebra 1
'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 - 1 4.L29-109+1 5. -2x - 12 6.4x2*3x*7 7.20a+l%a-8 8.3x2 + 2x2 9. -6r + 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 @ E
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, 4 16. three times the sum f r and y increased by twice the sum f * and y Chapter 1 Glence AlgebraI @
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+1:15 2. -2+4x:13 3. 8x + (-4): 12 + 4x-- 45 5. 8x-(2+31:11 6. 7x+2-3x:18 12+3x-9x:-18 8. (6x + 2) + 7x: 4l 9. (10x)(2x): 40 (8x+3)+( 4x+2):17 11. 14x+3:-4x-6 13. 42: -l4p 14. 75:-5(a+5) 63:9(2-a) 16. -54 :3 (2 + 5m) 17. 17 (x - 2) : -34 -x-15:-15 19. 18 + 4.5p: 6p + 12 20. -3k+19:ft+2 BrideePublishing ReprductinPrhibited.
Math 7 NO CALCULATORS Name Add, Subtract, Multiply, Divide Ratinal Numbers @ 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) 7.-6.6 6) -10.-9._1 t) -t.6.-8 8) -3.2.-6, -: -i *,-i : Find each qutient. ll) 7 +-1 tz\ 6+3 13) -6+6 14) -45 +9 -?5 ts) +i 7 rct -z! +f 55 d
@ 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 ZT @)b - 2); use m = 5, and. p - -5 2S) '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