Preparing for 7 th Grade Math (On-Level)

Preparing for 7 th Grade Math (On-Level) William Allen Middle School Moorestown, New Jersey Student s Name Remember this packet will be graded for accuracy! 0

Preparing for Math 7 On-Level SHOW ALL WORK No Calculator The purpose of the packet is to help you review and reinforce concepts/topics that are necessary for seventh grade math. Instructions: Complete all sections of this packet. You MUST show all work (use additional paper if necessary). You will return this completed packet to your math teacher during the first week of school. This packet will be collected the Friday after Labor Day and GRADED FOR ACCURACY. All work must be shown and final solutions should be circled. You will be tested on the concepts covered in this packet during the 2 nd week of school It 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 you need answered. www.allmath.com This website will provide you with links to games, reference, general math 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 site includes Ask Dr. Math, Problems of the Week, discussion groups and much more. www.aaamath.com. Customized by grade level and topic, AAA Math features explanations of various mathematical topics, practice problems and fun, challenging games. www.coolmath.com This fully interactive site and allows the user to sharpen basic math skills, play games and explore new math concepts. www.figurethis.org Created by the National Council of Teachers of Mathematics, this site helps families enjoy mathematics outside school through a series of fun and engaging challenges. Remember this packet will be graded for accuracy! 1

Rounding Decimals Round 2625 to the nearest tenth 1. Find and underline the place value to which you want to round. Circle the digit to the right of the underlined place value. 3. If the circled number is 5 or above, add one to the underlined place-value. If the circle number is 4 or below, leave the underlined place value alone. Drop all digits to the right of the underlined digit after rounding. 2625 26 2 5 2 is less than 5 so LEAVE IT ALONE! 26 1. Write the name of the underlined place value position Round each number to that place value. 1. 4124 8.0769 3. 0.896 0.334 5. 99.105 0.94567 Remember this packet will be graded for accuracy! 2

Adding and Subtracting Decimals To add or subtract decimals: 1. Line up decimal points to line up correct place-value positions. Insert necessary zeroes. 3. For subtraction, borrow if necessary. Add or subtract. 5. Bring decimal point straight down into answer. Add or subtract 1. 0.48 + 901 0.125 + 0.78 3. 1354 0.27 100.211 + 8.99 5. 75 0.24 37.8 29.846 7. 898 + 0.129 47.6 8. 138.56 49 + 28.6 Remember this packet will be graded for accuracy! 3

Multiplying Decimals To multiply decimals: 1. Line up digits, NOT decimal points. Multiply as with whole numbers. 3. Count the number of decimal places in each factor. The number of decimal places in the product of two decimals is the sum of the number of decimal places in the factors. Multiply 1. 2 x 0.3 0.4 x 3.8 3. 200 x 0.004 38.3 x 29.1 5. 0.44 x 0.512 32 x 80.1 7. 42 x 0.17 8. 7286 x 0.024 Remember this packet will be graded for accuracy! 4

Dividing Decimals 1. 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. 3. 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 0.6 129 0.3 3. 600.16 0.62 0.0092 8 5. 0.004 0.0002 10.5754 0.23 Remember this packet will be graded for accuracy! 5

Simplifying Fractions and Ratios A fraction is in simplest form when the greatest common factor (GCF) of the numerator and the denominator is 1. Express 28:63 in simplest form Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 63: 1, 3, 7, 9, 21, 63 The GCF of 28 and 63 is 7. To write in simplest form, divide the numerator and denominator by the GCF. 28 63 28 7 4 63 7 9 or 4:9 Express each fraction or ratio in simplest form. 25 36:80 1. 35 54 49:72 3. 66 Write two different fractions that can be expressed in simplest form as each of the following. 3 1 5. 5 7 Remember this packet will be graded for accuracy! 6

Adding and Subtracting Fractions To add and subtract fractions, rename the fractions with a common denominator as necessary. Then add or subtract the numerators and simplify. To find a common denominator, find the least common multiple of the denominators by listing or prime factorization. Add or subtract. Write each sum or difference in simplest form. 1. 11 3 2 12 15 5 5 13 3. 7 5 + 4 3 15 8 + 9 2 5. 5 4 8 1 8 11 4 9 Remember this packet will be graded for accuracy! 7

Adding/Subtracting Mixed Numbers To 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. 4 3 3 1 12 27 3 8 4 1 5 8 3. 5 3 9 5 12 4 7 3 12 5 10 4 5. 3 3 5 8 4 1 2 2 + 1 2 9 Remember this packet will be graded for accuracy! 8

Multiplying Fractions and Mixed Numbers To multiply fractions: Cross-simplify if possible. Multiply the numerators. Then multiply the denominators. Simplify. You do not have to find a common denominator. 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 4 35 21 13 5 14 3. 28 3 2 3 2 1 17 4 5 7 5. 3 12 8 5 1 2 9 4 7 Remember this packet will be graded for accuracy! 9

Dividing Fractions and Mixed Numbers To divide fractions and mixed numbers: 1. Write any mixed numbers as improper fractions. Find the reciprocal of the divisor (Flip the second number over). 3. Cross-simplify. Multiply numerator-by-numerator and denominator-by-denominator. 5. Simplify. Divide. Write in simplest form. 1. 7 1 2 5 8 4 5 8 3. 1 8 4 1 24 1 2 5. 2 13 1 1 7 14 1 5 7 2 2 6 Remember this packet will be graded for accuracy! 10

Ratios and Unit Rates A ratio is a comparison of two numbers by division. To simplify ratios first convert them to the same unit of measurement, then simplify by using the GCF. Express 4 feet : 10 inches as a ratio in simplest form. Since 1 ft = 12 inches, 4 ft = 48 inches. The ratio would be 48 inches : 10 inches before simplifying. Since the GCF of 48 and 10 is 2, the ratio is written as 24 to 5, 24/5, or 24:5 A unit rate is a rate expressed as a quantity of 1 (the denominator is 1 unit). Express 550 miles in 11 hours as a unit rate in miles per hour. Since miles per hour means in 1 hour, change the denominator to 1 unit (550/11 = x/1). To get to 1 hour, divide both the numerator and denominator by 11. 550 divided by 11 is 50. The unit rate is 50 miles per hour. Write each a ratio in simplest form. 1. 5 pounds to 15 ounces 4 cm : 5 m 3. 3 yards : 8 inches 5 seconds to 2 minutes Convert each to a unit rate 5. Mrs. Longmuir s car can travel 120 miles on 5 gallons of gas. What is the fuel efficiency in miles per gallon? Ashley spent 20 minutes typing a 3,000 word essay. What is her speed in words per minute? 7. Randall recorded 8 songs on his most recent CD. The total length of the CD is 49 minutes. Find a unit rate to represent the average length per song on the CD. 8. A 12 ounce container of yogurt contains 175 calories. Calculate the unit rate as calories per ounce. Round to the tenth. Remember this packet will be graded for accuracy! 11

Evaluating Expressions An expression is a math statement that contains variables, numbers, and operations. To evaluate an expression, first substitute the variables with numbers and 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. 81 Evaluate each expression if r = 5, s = 2, x = 7, and u = 9. 1. 6 + 3u 4r 10s 3. 2 18 + 8 5. 97 (1/2s + x) + 5u Remember this packet will be graded for accuracy! 12

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 y- coordinate. Graph each ordered pair on the coordinate plane to the right. 1. A(4,7) B(-3, -2) 3. C(0, 5) D(-4, 8) 5. E(-8,0) F(0,0) Refer to the coordinate plane to the right. Write the ordered pair for each point. 7. A 8. B 9. C 10. D 11. E 1 F Remember this packet will be graded for accuracy! 13

Comparing and Ordering Rational Numbers Comparing Rational Numbers: When comparing rational numbers use the following inequality symbols: < is less than < is less than or equal to > is greater than > is greater than or equal to Example: 10 > 8 (10 is greater than 8) Compare the following using an inequality symbol. 1. -5-9 16 15 Plotting points on a number line: Draw a number line and then put a point at the location of that number. Example: -4, 5, 1.5, -2, 0 Plot the following on the number line given. 3. {3, -1, 5, -3} {-5, 2, -3.5, 4} Ordering Rational Numbers: To order, convert all numbers to decimals. Then line up the numbers on the decimal point, use trailing zeros to fill out each number to the same number of decimal digits, and then compare. Example: {-1.5, 4, -3, } -3 < -1.5 <, < 4 Put the following rational numbers in order from least to greatest. 5. 2, 0, -6, 1, -3, -2, -5, 1, Remember this packet will be graded for accuracy! 14

2D Geometry To find the area of a 2 dimensional figure, you must know the formulas. A few things to remember: 1. The base and height are perpendicular (they form a right angle). 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. For π use 3.14 or 22 7 Write the area formula for each shape. 1. Rectangle Parallelogram 3. Triangle Trapezoid Find the area of each figure. 5. Remember this packet will be graded for accuracy! 15

7. 8. 9. 10. 11. 1 Remember this packet will be graded for accuracy! 16

Solve Equations Work backwards through the order of operations and show each inverse operation as you isolate the variable. Use a separate piece of paper if needed. No Calculator. x + 3 = 11-3 -3 x = 8 1. a 5 = 11 11b = 121 3. a + 17 = 24 b = 9 3 5. b a + 7 = 29 = 20 4 7. 13b = 143 8. y 17 = 8 Remember this packet will be graded for accuracy! 17

Page 2 Rounding Decimals 1. Ones - 46 3. Hundredths -.90 5. Tens - 100 Page 4 Multiplying Decimals Answer Key Page 3 Adding and Subtracting Decimals 1. 3.381 3. 1084 5. 776 7. 37.509 8. Page 5 Dividing Decimals 1. 0.6 3. 0.8 5. 0.22528 7. 7.14 8. Page 6 Simplifying Fractions and Ratios 1. 5/7 3. 9/11 5. 9/15, 15/25 Page 8 Adding and Subtracting Mixed #s 1. 4 4/9 3. 3 2/3 5. 4 5/8 1. 0.9 3. 968 5. 20 Page 7 Adding and Subtracting Fractions 1. 1 1/3 3. 1 13/28 5. 27/40 Page 9 Multiplying Fractions & Mixed #s 1. 1/3 3. 1 4/17 5. 4 ½ Remember this packet will be graded for accuracy! 18

Page 10 Dividing Fractions & Mixed #s 1. 3 1/2 3. 32 5. 2/3 Page 12 Evaluating Expressions 1. 33 3. 80 5. 18 Answer Key Page 11 Ratio & Unit Rate 1. 16/3 3. 27/2 5. 24 miles/1 gallon 7. 125 min/1 song 8. Page 13 Graphing on the Coordinate Plane 1. Right 4, Up 7 3. Up 5 5. Left 8 7. (2,7) 8. 9. (-6,0) 10. 11. (0,2) 1 Page 14 Comparing & Ordering 1. > 3. -3, -1, 3, 5 5. -6, -3, 0, 1, 2 Page 15 & 16 2D Geometry 1. A = lw 3. A = 1/2bh 5. 40 cm 2 7. 65 cm 2 8. 9. 48 in 2 10. 11. 130 cm 2 1 Page 17 Solving Equations 1. a= 16 3. a = 7 5. b = 80 7. b = 11 8. Remember this packet will be graded for accuracy! 19