Grade 7 Please show all work. Do not use a calculator! Please refer to reference section and examples.

Transcription

1 Grade 7 Please show all work. Do not use a calculator! Please refer to reference section and examples. Name Date due: Tuesday September 4, 2018

2 June 2018 Dear Middle School Parents, After the positive feedback we received from last year's summer math program, we decided to continue with it this year. Practicing math skills will tremendously help students in throughout the year. t is important that the students do not experience loss over the summer. Please also, have your child continue to practice basis math facts as needed. The math packets are to be completed over the summer. The packets are designed as review of previously learned topics. t is highly recommended that your child complete a portion of the packet each week, so they do not feel overwhelmed. (1 hour each week, suggested time 3 days for 20 minutes) The packet will be due September 4, 2018 and will be the first test grade in your child's math class. There will be a penalty for late work. Students need to show all work and should not use a calculator! We strive to help our students meet high academic success. Sincerely, Mrs. Doucette Mrs. Reid Cc: Mrs. Sullivan My child has completed their Summer Math Packet. Parent Signature

3 Summer Math Students entering Grade 7 Find the sum, difference,. product, or quotient~ : s: X : x You are buying T-shirts for the school store to sell. The T-shirts come in boxes of 48 each; You buy 11 boxes. Estimate the number of T-shirts you buy. Find the value of the power cubed squared Evaluate the expression :- 2 15~ 25 x Evaluate the expression when x = 3 and y = Sx 17. 6x -:- 2 + y 18. y2-2x Choose an appropriate customary unit and metric unit for the length. 19. thickness of a textbook 20. distance of a marathon Find the perimeter and area of the. rectangle or square. 21. a square that is 7 in. by 7 in. 22. a rectangle that is 12 ft by 9 ft 23. Make a bar graph of the number of students with a bii:thday.' in each season.. Season Winter Spring Summer Fall Number of students

4 Graph the points on the same coordinate grid. 24. (2, 5) 25. (4, 0) 26. (-3, 1) 27. (1, -2) y s > <---t ~--r ~~--< l ~ , l l , - --1' i ~ x i 2 "t---t t--+, i J 4 --T s -- -t :--- r--- Find the mean, median, mode(s), and range of the data. 28. Number of pieces of mail: 4, 8, 6, 2, 0, 3, 7, 5, 8, Average inches of r~nfall e~ch month: 3,~3,~3,4, 3,4,5,4,4,4 Write the number as a decimal. 30. eighty-nine ten thousandths 31. twenty-six and fourteen hu~dredths Write the decimal n words. 32~ Complete the statement with <, >, or = _J_ _J_ Round the decimal as specified (nearest tenth) (nearest thousandth) Find the sum or difference Find the product. 43~ 3 x x x 11

5 Use the distributive p~operty to find the product ( ) 47. 6(43) 48. 5(7.2) Find the product or quotient x ; x ;- 1.2 _Find the product or quotient using mental math x x ; , Tell_ whether the number is prime, composite~ or neither. _ Find the GCF of the numbers , , , 81 Write two fractions that are equivalent to the given fraction '. 72.., Tell wh~ther the fraction is in simplest form. f not, simplify it _} _2_ 14

6 Find the LCM of the numbers , , , 6, 12 Rewrite the number as an improper fraction or mixed number ~ so '. Write the decimal as a fraction or. mixed number in simplest form Find the sum or difference. Write yo~r answer in simplest form. 85. ~ +! ±_ + ~ _!_ ' You went shopping with a group of friends from 11 :45 A.M. until 3:20 P.M. How long were you shopping? Find the product.or quotient~ Write your answer in simplest form. 9 2 ~xl ~ x 41_ A recipe calls for 2t cups of flour. You already measured 1 }-cups. How much more flour do you need? 97. You bought 9 feet of elastic to make hair ties. Each hair tie needs.3f.inches of elastic. How many hair ties can you make? Complete the statement qt 2 pt = _?_ pt in. = _?_ yd _?_ ft ~ in. Find the sum or difference ft: 8 in. + 7 ft 6 in lb 4 oz - 2 lb 11 oz

7 Write the unit rate. 161 miles 432 words gallons 6 minutes Solve the pr,oportion. a = = ' b 8 48.yards seconds 6 c = Write the percent as a decimal and a fraction % % % Write the fraction or decimal as.a percent ~ ~ 8 w Find the percent of the number % of % of % of A bank account pays 3 % annual interest. How much simple interest will $4500 earn in 5 years? n Exercises 118~120, use the diagram shown Name a pair of complementary angles Find the measure of LDAE Find the measure of LFAE. B E Find the area of the figure described Parallelogram: base= 1_4 in., height= 32 ill Triangle: base = 8 cm, height = 5 cm Find the circ.umference and area of the circle described r = 16 ft 124. d = 350 mm

8 Find the sum or difference (-25) Find the product or quotient~ (-12) ;- (-9) ~ (-6) (-4) ;- (-14) Write the sentence as an equation The product of 6 and a. number n is The sum of a number x and 4 is 13. Solve the equation p = = 9n 139. x - 8 = 9 z = 6 Make an input-i>utput table using the function rule and the input values x = 0, 1, 2, 3, and 4. Graph the function y = x y = ~x - 2.._.,..._~s-Y 'l l----l-~l> ~7f l i 6.f-' ~-+--~ 5 ' ~ '----~---~ !. > <-+-3~ ~ ~~~,~-+--~2r -t ~! i 1r-r 1-5 -A x J..._ _J J_:.. J J L i L._J l. y B 10...,...9 ;! 1 ---T] 1---l f--... s _L_. 7 i e-- --: ' !' >-+--l-~-t ~ j

9 : 6>< ANSWER SHEET Grade "" >< rjl ~ is ~ 79.~ 80 '

10 ANSWER SHEET Grade >< -~ ~

11 --- Division-with No Remainder 1.igoes into si time. --. Multiply 5 s j 620 j s 2 o x 1 and -5 subtract 1 from 6. Division-with a Remainder 6j Divide as usual. Finding Greatest Common Factor Resource Pages 2. Bring down the 2. 5 goes into twelve times. 7 2 R5 6f ' 5f6?0-5 t Since 6 is too -4 2 large to go into 1 7 fi, this is the -1 2 / remainder Bring down the 0. 5 goes into twenty 4 times. 1 2 l 5l6?Q k -~ t : 1 2 : -1 0 t Q 0 To find the Greatest Common Factor (GCF), list all of the factors of the numbers. The factors that are the same between the numbers are the common factors. The number that is the highest among the common factors is the greatest common factor. Example: Find the GCF for the numbers 15 and 30. Factors of 15-1, 3, 5,@. } 1, 3, 5, and 15 are the common factors between Factors of 30-1, 2, 3, 5, 6, 10,@,30 15 and is the greatest common factor. Finding Least Common Denominator The least common denominator (LCD) is the lowest number that 2 or more different denominators can be divided into. Example: Find the LCD among the denominators of the fractions i, ~'and 1. Multiples of 2-2, 4, 6, 8, } Multiples of 3-3, 6, 9,@ Multiples of 4-4, 8,@ Fractions-Changing Fractions to Simplest Form Change 1520 to 1. Divide 15 and 20 by 12 is th~ least common denominator among the fractions. t f f 1&: b _ 3 th. 4 1s e s1mp 1 es orm or 2o ecause 3 simplest form. their greatest and 4 have no factors in common common factor, 5. other than 1 _ Fractions-Changing Fractions t~ Mixed Numbers Change ~ to A fraction can be c~a.nged to a m.ixed number ~hen it names a number a mixed number. greater than 1. This 1s called an improper fraction. 1. Divide 10 by 7. 7Rt83... z 3 2. Since 7 goes into 10 once, the whole number will be 1. Since there is a remainder of 3, it becomes the numerator and goes above the denominator of 7. Therefore, the mixed number for~ is 1 ~. Carson-Dellosa CD-3748 ii

12 Fractions-Changing Mixed Numbers to mproper Fractions Change 31 to 1. Multiply the whole 2. Add the numerator, an improper number, 3, by the 1, to 12. fraction. denominator, 4. 3 x 4 = = 13 Fractions-Making Fractions Equivalent is now the new numerator. The denominator, 4, remains the same. Therefore, the improper fraction for 3! is ~. Find a fraction To find an equivalent for a fraction, equal to 1. multipl~ the numerator and the denommator by the same number Fractions-Multiplying Fractions 2x3 3 5 To multiply fractions, multiply the numerators. and the denominators. 1 x 4 = 4 Therefore,~ is equal to i. 2x4=8. 2x3= = 3 x 5 = 15 Therefore, 3x 5=15 =5 Fractions-Multiplying Whole Numbers and Fractions 3x Rename the whole 2. Multiply the fractions. number as a fraction. 3=3 3x1=3 1 1x4=4 Fractions- Mu.ltiplying Mixed Numbers and Whole Numbers 1. Rename both the whole number and 2. Multiply the the mixed number as fractions. fractions. Fractions-Adding Fractions with the Same Denominators 16 x4_ 64 5 x Add the numerators, while keeping 2. Change to simplest form the denominators the same. when possible. 3+Z _10 -a-~a 10_11 a- 4 Fractions-Adding Fractions with Different Denominators 3. Change to simplest form ~ Rename the fractions so each 2. Add the fractions that 3. Change to has the same denominator. have been renamed. simplest form ~ = 1~ and ~ = 1 ~ 1~ + 1~ = ~ ~ ~ ~ = 1 1 ~ Fractions-Adding Mixed Numbers with Different Denominators Rename each mixed number 2. Rewrite the problem 3. Change to so that the fractions have the and solve. simplest form same denominator. when possible _ _ 10 and = = 7 10 Carson-Dellosa CD-3748 iii

13 Fractions-Subtracting Fractions with the Same Denominators 1. Subtract the numerators and 2. Change to simplest form keep the denominators the when possible. same = 6 Fractions-Subtracting Fractions from Whole Numbers 8-~ 5 1. Rename the whole 2. Rename the fractions number so it is a so they have the same fraction. denominator. ~ Subtract the fractions and change to simplest form. 8=~ ~-~ = ~0-~ 40 _ ~ Fractions-Subtracting Mixed Numbers with the Same Denominators 1. Rename 7 so you 2. Use the renamed fraction 3. can subtra~t 3 ~ from it. to rewrite the problem. 7 ~ - 3 ~ 7 ~ = ~ = 6 ~ Subtract the whole numbers, then subtract the fractions. s 1 J-3~=3~ Fractions-Subtracting Fractions with Different Denominators 1. Rename the fractions so they 2. Subtract the renamed fractions. both have the same denominator. Fractions-Subtracting Mixed Numbers with Different Denominators Rename the fractions so they 2. Rewrite the problem with the renamed both have the same denominator. mixed numbers and subtract =; 3 6 Fractions-Dividing Fractions 1. 1 ~Dividend 2 7 = 2 14 The multiplicative reciprocal of a number is 1 divided by 4 -:- 2.._Divisor the number. For example, the reciprocal of a is ~ Decimals-Adding Decimals = 1. Line up the decimals and add as usual Multiply the dividend 2. Simplify the by the reciprocal of fraction when the divisor. possible. 1 x g = 4 4 =2 8 x =T 214 = 24 Carson-Dellosa CD-3748 iv

14 Decimals-Subtracting Decimals = 1. Line up the decimals and subtract as usual ,16 Decimals-Multiplying Decimals Multiply as usual. x x Count the number of digits to the right of the decimal point..212~ 3 digits are to the right of the decimal point. 3. Place the decimal point in the answer to the left as many spaces as you counted Decimals-Dividing Decimals 1. Count the number of digits to the right of the decimal point in.06j5.412 the divisor (.06)..06 _.. 2 digits are to the right of the decimal. 3. Divide as usual s ls Changing Decimals to Fractions 2. Move the decimal point in the dividend (5.412) to the right as many spaces as you counted in the divisor. jsg>4 t2 ~--J 4. Bring up the decimal point f To change a decimal to a fraction, use the decimal as a numerator over a denominator of either the number 10, 100, 1,000, etc., depending on the number of digits after the decimal point. Change to simplest form. Study the chart below. Examples: Number of digits after decimal point Denominator ,000 Changing Fractions to Decimals To change a fraction to a decimal, divide the denominator into the numerator in the following manner. 1. f the numerator has one digit, place a decimal point just after the numerator as a dividend. 2. f the numerator has two digits, place a decimal point just after the second number of the numerator as a dividend. Carson-Dellosa CD-3748 v Example: 4 5 = 5f4F =.8 Example: ~~ - 1 = 125 j25.00 =.20

15 Changing Fractions to Percentages To change a fraction to a percentage, first change the fraction to a decimal, then multiply the decimal times 100. Changing Percentages to Fractions To change a percentage to a fraction, multiply the percentage number times rao and reduce to simplest form. Examples: ~ = 5fl0 =.8.8 x 100 = 80% 21 = 25 p.oo = x 100 = 4% Examples: 75% = 75 x ~ = ~ = ~ 25% = 25 X _L = A = Changing Percentages to Decimals To change a percentage to a decimal, Examples: multiply the percentage times.01. 7% x.01 =.07 17% x.01 = % x.01 =.125 Finding Percentages 20%of 80= Change the percentage number to a decimal and multiply times the whole number. 20% of 80 = x 80 = 16 Rewrite the problem in the form of is _% of = ~ an equation and solve = n% x ,900 = 95n 19 is % of n =100 x. n = 20 Rewrite the problem in the form of is 60% of_ _ 4. 2,400 = 60n an equation and solve = 1~ x n 5. n = is 60% of = 1 ~ Rewrite the problem in the form of 1. is 40% of n = 12 an equation and solve. 2. n = 1 ~ x 30 is 40% of n = ~ '., Geometry-Lines and Line Segments A line has no end points and is denoted in the following way: ~...,. To name a line, name any two points on the line. Line AB or Line BA A line segment has two end points and is denoted in the following way: C To name a line segment, name the end points. Line Segment CD or Line Segment DC A ray has one end point and is denoted in the following way: To name a ray, name the end point and the point nearest it. Carson-Dellosa CD-3748 vi A B E F... Ray EF 0

16 Geometry-Angles side G Angle EFG, denoted by L EFG, has two sides and a vertex. To name an angle, use the vertex as the middle letter..5 inl...,,.5 in.5 in..., 1.5 in = 4 in 1.5 x.5 =.75 square in or.75 in 2 Finding the Area of Triangles Find the area of a triangle. 3ft 1. Use the following formula: 2. Solve the equation. Area= 1/2 x (base x height) Area = 1 /2 x 12 = 6 tt 2 Area = 1 /2 x ( 4 x 3) or six square feet 4ft Finding Volume Find the volume of a rectangular solid. 1. Use the following formula~ 2. Solve the equation. Volume = length x width x height Volume= 15 x 4 Volume = 5 x 3 x 4 Volume = 60 m 3 or sixty cubic meters Finding Circumference Find the circumference 1. Use one of the following formulas: Circumference = 3.14 x 2 x radius or Circumference = 3.14 x diameter Circumference = 3.14 x 2 x 6 2. Solve the equation. Circumference = 3.14 x 12 Circumference = cm Carson-Dellosa CD-3748 vii