Preparing For 7th Grade Math (Enriched)

Preparing for 7th Grade Math(Enriched)William Allen Middle SchoolMoorestown, New JerseyStudent’s NameRemember this packet will be graded for accuracy!!0

Preparing for Math 7 EnrichedSHOW ALL WORK – No CalculatorThe purpose of the packet is to help you review and reinforce concepts/topics that arenecessary for seventh grade math.Instructions:Complete all sections of this packet. You MUST show all work (use additional paper ifnecessary). You will return this completed packet to your math teacher during the firstweek of school.This packet will be collected the Friday after Labor Day andGRADED FOR ACCURACY. All work must be shown and finalsolutions should be circled.You will be tested on the concepts covered in this packet duringthe 2nd week of schoolIt may be necessary to seek assistance on some questions/concepts that is fine!Websites that may be of assistance:www.mathforum.org/dr.math Use this web site if you have a math questions that youneed answered.www.allmath.com This website will provide you with links to games, reference, generalmath help and resources.www.mathforum.com This online community includes teachers, students, researchers,parents and educators who have an interest in math and math education. The siteincludes Ask Dr. Math, Problems of the Week, discussion groups and much more.www.AAAmath.com. Customized by grade level and topic, AAA Math featuresexplanations of various mathematical topics, practice problems and fun, challenginggames.www.coolmath.com This fully interactive site and allows the user to sharpen basic mathskills, play games and explore new math concepts.www.figurethis.org Created by the National Council of Teachers of Mathematics, thissite helps families enjoy mathematics outside school through a series of fun andengaging challenges.Remember this packet will be graded for accuracy!!1

Rounding DecimalsRound1.2.3.24.625 to the nearest tenthFind and underline the place value to which you want to round.Circle the digit to the right of the underlined place value.If the circled number is 5 or above, add one to the underlined place-value. If thecircle number is 4 or below, leave the underlined place value alone.4. Drop all digits to the right of the underlined digit after rounding.24.625 24.6 2 5 2 is less than 5 so LEAVE IT ALONE! 24.61. Write the name of the underlined place value position2. Round each number to that place value.1. 46.1242. 8.07693. 0.8964. 0.3345. 99.1056. 0.94567Remember this packet will be graded for accuracy!!2

Adding and Subtracting DecimalsTo add or subtract decimals:1. Line up decimal points to line up correct place-value positions.2. Insert necessary zeroes.3. For subtraction, borrow if necessary.4. Add or subtract.5. Bring decimal point straight down into answer.Add or subtract1. 0.48 2.9012. 0.125 0.783. 16.354 – 0.274. 100.211 8.995. 75 – 0.246. 37.8 – 29.8467. 84.98 0.129 – 47.68. 138.56 – 49 28.6Remember this packet will be graded for accuracy!!3

Multiplying DecimalsTo multiply decimals:1. Line up digits, NOT decimal points.2. Multiply as with whole numbers.3. Count the number of decimal places in each factor.4. The number of decimal places in the product of two decimals is the sum of thenumber of decimal places in the factors.Multiply1. 2 x 0.32. 0.4 x 3.83. 200 x 0.0044. 38.3 x 29.15. 0.44 x 0.5126. 34.2 x 80.17. 42 x 0.178. 722.86 x 0.024Remember this packet will be graded for accuracy!!4

Dividing Decimals1.2.3.4.Change the divisor to a whole number by moving the decimal point to the right.Move the decimal point in the dividend the same number of places to the right.Divide as with whole numbers. (Divide, Multiply, Subtract, Check, Bring Down)Place the decimal point in the quotient by moving it straight up from the dividend.Divide. Show All Work!1. 0.540 0.62. 129 0.33. 600.16 0.624. 0.0092 85. 0.004 0.00026. 10.5754 0.23Remember this packet will be graded for accuracy!!5

Simplifying Fractions and RatiosA fraction is in simplest form when the greatest common factor (GCF) of the numeratorand the denominator is 1.Express 28:63 in simplest formFactors of 28: 1, 2, 4, 7, 14, 28Factors of 63: 1, 3, 7, 9, 21, 63The GCF of 28 and 63 is 7.To write in simplest form, divide the numerator and denominator by the GCF.28 28 7 4 or 4:963 63 7 9Express each fraction or ratio in simplest form.1.25352. 36:803.54664. 49:72Write two different fractions that can be expressed in simplest form as each of thefollowing.5.356.17Remember this packet will be graded for accuracy!!6

Adding and Subtracting FractionsTo add and subtract fractions, rename the fractions with a common denominator asnecessary. Then add or subtract the numerators and simplify.To find a common denominator, find the least common multiple of the denominators bylisting or prime factorization.Add or subtract. Write each sum or difference in simplest form.1.11 3 15 52.2 12 5 133.53 744.82 1596.84–1195.41–58Remember this packet will be graded for accuracy!!7

Adding/Subtracting Mixed NumbersTo add or subtract mixed numbers: Add or subtract the fraction. Rename if necessary. Add or subtract the whole numbers. Simplify.Add or subtract. Write each sum or difference in simplest form.1.343 112272.318 5483.953 51244.125.533–486.273 510421 129Remember this packet will be graded for accuracy!!8

Multiplying Fractions and Mixed Numbers To multiply fractions: Cross-simplify if possible. Multiply the numerators. Thenmultiply the denominators. Simplify. You do not have to find a commondenominator.To multiply mixed numbers: Rename each mixed number as an improper fraction.Multiply like fractions and simplify.Multiply. Write each product in simplest form.1.13 7 21 132.4 35 5 143.28 3 17 44.232 15 75.12 6.541 29738Remember this packet will be graded for accuracy!!9

Dividing Fractions and Mixed NumbersTo divide fractions and mixed numbers:1. Write any mixed numbers as improper fractions.2. Find the reciprocal of the divisor (Flip the second number over).3. Cross-simplify.4. Multiply numerator-by-numerator and denominator-by-denominator.5. Simplify.Divide. Write in simplest form.1.7 1 8 42.2 5 5 83.8 144.24 15.2 131 17 146.71215 226Remember this packet will be graded for accuracy!!10

Evaluating ExpressionsAn expression is a math statement that contains variables, numbers, andoperations. To evaluate an expression, first substitute the variables with numbersand then solve according to order of operations.The order of operations are: 1) Grouping (Parentheses). 2) Exponents. 3)Multiplication/Division (From Left to Right). 4) Addition/Subtraction (L to R)Evaluate 11x – 7 if x 8. 11(8) – 7. 88 – 7. 81Evaluate each expression if r 5, s 2, x 7, and u 9.1. 6 3u2. 4r – 10s3. 24.5.– 18 86. 97 – (1/2s x) 5uRemember this packet will be graded for accuracy!!11

Graphing on the Coordinate Plane The coordinate plane is used to locate points.The coordinate plane is formed by the intersection of two number lines (x and y axis)that meet at the origin (0,0).An ordered pair (x,y) is used to locate any point on the coordinate plane.The first number is called the x-coordinate, and the second number is called the ycoordinate.Graph each ordered pair on the coordinate plane to the right.1. A(4,7)2. B(-3, -2)3. C(0, 5)4. D(-4, 8)5. E(-8,0)6. F(0,0)Refer to the coordinate plane to the right. Write the ordered pair for each point.7. A8. B9. C10. D11. E12. FRemember this packet will be graded for accuracy!!12

Comparing and Ordering Rational NumbersComparing Rational Numbers: When comparing rational numbers use the followinginequality symbols: is less than is less than orequal to is greater than is greater than orequal toExample: 10 8 (10 is greater than 8)Compare the following using an inequality symbol.I1. -5 -92. 16 16.5lII4Plotting points on a number line: Draw a number line and then put a point at thelocation of that number.Example: -4, 5, 1.5, -2, 0 I -5-4-3-2-1I 012 345Plot the following on the number line given.3. {3, -1, 4.5, -3} I-5III-4-3-24. {-5, 2, -3.5, 4}I III023-1I4 II -55III-4-3-2I I-10II23I4I 5Ordering Rational Numbers: To order, convert all numbers to decimals. Then line up thenumbers on the decimal point, use trailing zeros to fill out each number to the samenumber of decimal digits, and then compare.!lExample: {-1.5, 4, -3, }4-3 -1.5 ,!l4 4Put the following rational numbers in order from least to greatest.5. 2, 0, -6, 1, -36., -2, -2.5, 1,Remember this packet will be graded for accuracy!13

2D GeometryTo find the area of a 2 dimensional figure, you must know the formulas. A few things toremember:1. The base and height are perpendicular (they form a right angle).2. In a trapezoid, the two bases are parallel (they do not intersect).3. Base is any flat side. Use the one that has the height drawn to it.4. For π use 3.14 or 227Write the area formula for each shape.1. Rectangle2. Parallelogram3. Triangle4. TrapezoidFind the area of each figure.5.6.12.6 cm5cm6.4 cm8cmRemember this packet will be graded for accuracy!14

8.7.2.5cvL6cm15 cm9.10.IIIIIlOm1II12 In.i] - - L - - - - - 14m11.Gem12.1051011Remember this packet will be graded for accuracy!15

Adding IntegersAdding Integers with the Same Signs: Add the number together andkeep the sign.-7 -6 -13Adding Integers with Different Signs: Subtract the numbers and use thesign of the number with the greater absolute value.-7 6 -17 (-6) 1Find each sum. No Calculator.1.5 (-8)2.-6 63.-4 (-9)4.-7 135.-9 (-9)6.14 (-27)7.15 (-10)8.19 (-10)9.-12 (-18)10.-14 (-12)11.-12 (-8)12.-28 1613.-8 (-10) 1514.15 (-8) 715.-10 (-10) 5Remember this packet will be graded for accuracy!!16

Subtracting IntegersChange each subtraction problem into an addition problem, byadding the opposite number, and then use the rules for addingintegers.-10 – 15-10 – (-15)-10 (-15) -25-10 ( 15) 5Rewrite each subtraction problem as an addition problem and thenfind each sum. No Calculator.1.6 – (-8)2.-2 - 33.-8 – (-10)4.9 – 145.36 – (-12)6.5 – 127.15 – (-8)8.-16 – 69.-4 – 910.-17 – 1311.-12 – (-9)12.14 – (-22)13.5 – (-25)14.-19 – (-50)15.12 – (-52)Remember this packet will be graded for accuracy!!17

Multiplying IntegersMultiply the numbers together and use the following rules negative negative positivenegative positive negativeRemember multiplication is commutative, so order doesn’t matter.-7(-6) 427(-6) -42Find each product. No member this packet will be graded for accuracy!!18

Dividing IntegersDivide the numbers together and use the following rules negative negative positivenegative positive negativeOnce again in deciding whether the answer is negative or positive, orderdoesn’t matter.42 (-6) -7-42 (-6) 7Find each quotient. No Calculator.1.-16 (-4)2.-100 103.-28 74.52 (-4)5.-125 (-25)6.-32 (-16)7.-120 (-12)8.45 (-9)9.33 (-3)10.-36 1211.-200 (-25)12.-88 1113.14.15.Remember this packet will be graded for accuracy!!19

Solve EquationsWork backwards through the order of operations and show eachinverse operation as you isolate the variable. Use a separate pieceof paper if needed. No Calculator.4x 3 11-3 -34x 844x 21.a – 5 112.11b 1213.a 17 244.b 935.5a – 6 246.3a 12 127.9 16b - 518.x–8 57Remember this packet will be graded for accuracy!!20

Page 2 – Rounding DecimalsAnswer KeyPage 3 – Adding and Subtracting Decimals1. Ones - 462.3. Hundredths - .904.5. Tens - 1006.Page 4 – Multiplying Decimals1. 0.62.3. 0.84.5. 0.225286.7. 7.148.Page 6 – Simplifying Fractions and Ratios1. 0.92.3. 9684.5. 206.Page 7 – Adding and Subtracting Fractions1. 1 1/32.3. 1 13/284.5. 27/406.1. 5/72.3. 9/114.5. 9/15, 15/256.Page 8 – Adding and Subtracting Mixed #s1. 4 4/92.3. 3 2/34.5. 4 5/86.1. 3.3812.3. 16.0844.5. 74.766.7. 37.5098.Page 5 – Dividing DecimalsPage 9 – Multiplying Fractions & Mixed #s1. 1/32.3. 1 4/174.5. 4 ½6.Remember this packet will be graded for accuracy!!21