Contents Introduction... 5 The Language of Algebra Order of Operations... Expressions... Equations... Writing Expressions and Equations... Properties of The Four Operations... Distributive Property... Inequalities... Word Problems... Integers Integers... Opposites and Absolute Value... Add Integers 1... Add Integers 2... Explore Subtraction... Subtract Integers... Add/Subtract Roundup... Dividing a Sum or a Difference... Zero and One... Multiply Integers... Divide Integers... Integer Problems... Powers With Negative Base... Integers Reminder Sheet 1... Integers Reminder Sheet 2... 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 2 24 25 26 27 28 Solving One-Step Equations Solving Linear Equations 1... Solving Linear Equations 2... Addition and Subtraction Equations... Multiplication and Division Equations... More Practice... Equations Situations... 29 0 1 2 4 Factors and Fractions Powers and Exponents... Multiply and Divide Powers... Divisibility and Factors... 5 6 7
Factors and Fractions, cont. Prime Factorization... More on Primes... GCF and Simplifying Fractions... LCM and Equivalent Fractions... LCM and Comparing Fractions... 8 9 40 41 42 Rational Numbers Rational Numbers... Fractions and Decimals... Add and Subtract Decimals... Decimal Problems... Multiply Decimals... Divide Decimals... Scientific Notation and Powers of Ten... Equations With Decimals... Percents and Decimals... What Part and Percent... 4 44 45 46 47 48 49 51 52 Add and Subtract Fractions... 5 Multiply Fractions... 54 Divide Fractions... 55 Equations and Inequalities Addition and Subtraction Equations... 56 Multiplication and Division Equations... 57 Sequences... 58 Two-step Equations... 59 Variables on Both Sides... Using Distributive Property... Word Problems... Solving Inequalities 1... Solving Inequalities 2... Two-Step Inequalities... Coordinate Grid... Plotting Lines... Equations With Two-Variables... Slope... Intercept... Systems of Two Equations... Time and Distance Problems... Celsius and Fahrenheit... Two Speeds... Comparing Phone Services... Prices per Pound... 60 61 62 6 64 65 66 67 68 69 70 71 72 7 74 75 76 More from Math Mammoth... 77 4
Introduction Math Mammoth Grade 7-A Worksheet Collection contains worksheets covering about half of typical 7th and 8th grade mathematics topics (pre-algebra). These worksheets have problems only. In other words, this is a worksheet collection without textbook explanations. I have created the worksheets with teachers' needs in mind: each one is exactly one page, concentrating on one topic (with the exception of some review worksheets); therefore is easy to assign for students. The worksheets are very variable, with numerous word problems and problems that emphasize understanding. They are not made by a script, but hand-crafted one by one. The first part of this pre-algebra collection contains worksheets for beginning algebra topics such as expressions, linear equations, and basic properties of the four operations. There is also an extensive section on integers. Fraction and decimal topics are still present, but not anymore with such detail as on previous grades. The fraction section contains a few worksheets that touch on the concept of percent; however most of the percent related worksheets are in the 7-B collection. The section on liner equations and inequalities contains the basics of solving linear equations, and as such can easily be used on 8th grade or as part of an algebra course as well. This section also contains various sheets about example practical applications of linear equations. The 7-B collection covers the rest of the 7th grade topics: proportion and percent, statistics and graphs, probability, geometry, right triangles - and little bit on polynomials (though this last topic could be left for 8th grade or for algebra). I wish you success with math teaching! Maria Miller, the author 5
Order of Operations 1. Let's start with a mini-review of exponents. Evaluate. a. 7 2 b. 4 c. 10 4 d. 5 e. 0.1 2 f. 12.1 2 g. 1 10 2. Write these expressions using exponents. Find their values. a. 2 2 2 2 2 b. 7 7 7 c. 4 4 4 4 + 2 2 2 2 d. (20 20) (2 2 2 2) e. 7 10 10 10 10 10 10 4 10 10 10 10. Fill in the chart. 4. Find the value of these expressions. Order of operations 1) Solve first anything within. 2) Solve exponents and square roots. ) Solve and from left to right. 4) Solve and from left to right. a. 120 2 9 (2 + 9) b. 8 10 2 c. (8 10) 2 d. 1 7 5 2 e. 2 5 2 7 f. 10 4 (2,000 + 400) 10 5. Place the symbols (+,,, ) and possibly parentheses into the equations so they are true. Find different possibilities (*How many different ways are there?) a. = 0 b. = 6 c. = = 0 = 6 = 6. Find the value of these expressions. Use a calculator. Round your answer to 2 decimals. a. (0.4 + 2.22) 2 b. (0.4 + 2.22) 4 c. (2.5 + 0.45) 2 (100 4.5) 2 d. x 7 2 7 7 e. 1. 10.45 4 0.9 f. 0.4 2 0.5 + 0.52 0.4 7. Find the value of the expression x 2 x + 2 when x is a) 2 b) 4 c) 10. 6
Expressions 1. Evaluate these expressions if a = 4, b = 2, and c = 5. a. 10(c + b) b. a + c c. a b 2 2b d. 5a 2 + 2bc Variable Value of expression 2. Find the value of the expression 8 y when the variable gets the values y = 2, 4, 6, 8, and 10. Record your results in a table that lists both the values of the variable and of the expression.. Write an expression for the areas of these rectangles and squares. 5 a x a. b. b 6 and y x 7 c. 4. Write an expression for the perimeters of these geometrical shapes, and solve the problems. a. p = b. p = a. c. p = d. In figure a), if p = 21 and s =.5, what is b? e. In figure c), if x = 15.5 cm and y = 11.2 cm, what is the perimeter? f. In figure b), if the perimeter is 5 ft, what is t? b. c. 5. a. If x + 5 = 15, what is x? b. If 2y 1 has the value 11, what is y? 6. Fill in the table the missing values of the variable and the missing values of the expression. y 2y + 4 1 10 4 46 7