# 8 th Grade Summer Mathematics Review Packet

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1 8 th Grade Summer Mathematics Review Packet Table of Contents Topic One: Adding and Subtracting Integers Topic Two: Multiplying and Dividing Integers Topic Three: Order of Operations Topic Four: Solving On- step Equations Topic Five: Solving Two- Step Equations Topic Six: Area and Perimeter Topic Seven: Fraction Decimal Percent Conversions Topic Eight: Operations on Fractions

3 8 th Grade Summer Mathematics Review Packet Please complete this chart as you complete the assignments. You may complete assignments in any order you like, as long as you stay on track to finish by the beginning of September. Good luck, and feel free to e- mail me with questions! Assignment Topic One: Adding and Subtracting Integers Topic Two: Multiplying and Dividing Integers. Topic Three: Order of Operations Topic Four: Solving On- step Equations Topic Five: Solving Two- Step Equations Topic Six: Area and Perimeter Topic Seven: Fraction Decimal Percent Conversions Topic Eight: Operations on Fractions Topic Nine: Proportions Topic Ten: An Assortment of Word Problems J Parent/Guardian Signature Date Completed

4 TOPIC ONE: ADDING AND SUBTRACTING INTEGERS Instructions: Find the Sum or Difference without using a calculator. Calculators will not be allowed on the quiz in the fall. If you do work on a separate sheet of paper, please staple that sheet to this worksheet (- 1)

5 (- 8) (- 5) (- ) (- 8) (- 1) (- 14)

6 TOPIC TWO: MULTIPLYING AND DIVIDING INTEGERS Review To multiply two integers, multiply their absolute values. If the signs are the same, the product is positive If the signs are different, the product is negative To divide two integers, find the quotient of their absolute values. If the signs are the same, the quotient is positive If the signs are different, the quotient is negative Instructions: Find the product or quotient without using a calculator. Calculators will not be allowed on the quiz in the fall. If you do work on a separate sheet of paper, please staple that sheet to this worksheet g 7. 6 g ( 9) g ( g 7) 10. 5g g ( 4) ( 3) 1. 3 g ( 15)

7 ( 9) 1. 7( gg 3) 15. ( g 8) (Different problem than #0) ( 7) gg ( 30) g ( 80) g ( 1)

8 TOPIC THREE: ORDER OF OPERATIONS When you have a number sentence that contains several operations, you use the order of operations to know which operation must be completed first. 1. Do all operations within parentheses first. This is called clearing parentheses.. Perform all operations that involve exponents next. 3. Do multiplication and division in the order that they appear from left to right. There is no rule that multiplication comes before division. These two are on the same level. You have to make sure you work from left to right. 4. Do addition and subtraction in the order that they appear from left to right. Again, these to are on the same level. We don t add before we subtract we do whichever of the two comes first, when reading from left to right. You have to make sure to work from left to right. ( ) Example: g : (6 17) (7 ) (0 10)

9 7. (5g 3) ( ) g (9 14) 9. 9 ( 30) (14 16) (40) (5 3) 16. 4( g 8) g ( 7 8) g g ( 1)

10 TOPIC FOUR: SOLVING ONE STEP EQUATIONS There are five types of one- step equations that we learned to solve. In all cases, the goal is to undo whatever operation has been performed on the variable in order to get it alone. To do that, we just undo whatever has been done to the variable. Addition Equations: To solve, we just subtract from both sides what was added to x. x + 7 = 1 Subtraction Equations: To solve, we just add to both sides what was subtracted from x. x 8 = 10 Multiplication Equations: To solve, we just divide both sides by what multiplied x. 5x = 5 Division Equations: To solve, we just multiply both sides by what divided x. x = 7 3 Fractional Equations: To solve, we just multiply both sides by the reciprocal of the fraction that multiples x x = Instructions: Solve each equation, but undoing what has been done to the variable. 1. b + 15 = 8 d 3. = d = 4. 4b = 76

11 5. z 0 = x = x = 14. = p = c p = w = x + 0 = x = 17. p 8= i 9 = = 1 + q = 7x h = 1 d 1. = y = 10

12 TOPIC FIVE: SOLVING TWO STEP EQUATIONS The goal of solving two- step equations is simple: get the variable alone on one side of the equal sign. To do this we first undo addition or subtraction, and then we undo multiplication or division. Solve each equation. Then check your solution. Example : 10 = 3x (Subtract 1 from both sides) 9 = 3 x (To get x alone, divide both sides by 3) 9 3x = = x To check the solution, substitute it into the original equation for x: If we are correct and x=3, then 3x + 1 must equal 3(3) + 1 = = 10 Because our original equation was 3x + 1= 10, and when we checked our answer we got 10, we know we solved correctly. Instructions: Solve each equation. Then check your solution by plugging it into the original equation in place of the variable. Because there are two steps to each problem, I have only given you 10 problems to complete. 1. = 10d g = 4. 7= + 3b n = 1

13 5. x + 8= 6 m = 9 4 h 6. 6 = 8 3 k = 4 5 c = e = +

14 TOPIC SIX: AREA AND PERIMETER The perimeter of a shape is the sum of the lengths of its sides. To find the perimeter, you simply add the lengths of the figure s sides. Remember to always write units your answer should never be just a number! The area of a shape is the amount of space it takes up. Use the formula sheet included in this review packet to help you with this activity. These formulas should be committed to memory, so that you can recall them quickly. I expect everyone will have these memorized by the beginning of the year. Instructions. 1. Draw each figure. You do not have to use a ruler, a rough sketch is fine.. Find the Perimeter of the figure. 3. Find the Area of the figure. 1. Rectangle with length 8 cm and width 6 cm.. A parallelogram with base 1 inches and height 7 inches. 3. A square with sides 14 m. 4. A triangle with base 16 cm and height 9 cm. 5. A trapezoid with one base of 3 feet, another base of 8 feet, and a height of 6 feet.

15 TOPIC SEVEN: FRACTION DECIMAL PERCENT CONVERSIONS A percent is a special fraction with a denominator of 100. We practiced going back and forth between percents, decimals, and fractions in 7 th grade. Here is a quick review % is the same as which is the same as To convert a decimal into a percent, multiply it by (100) = 64% o (100) = 105% (100) = 5% To convert a percent into a decimal, divide it by % = o 107% = % = To convert a fraction into a percent, first write it the fraction as a decimal by dividing the numerator by the denominator. Then multiply that decimal by 100 to get a percent. 1 To convert into a percent, first we write it as a decimal: 1 4 = 0.5 o 4 Next we convert the decimal into a percent (100) = 5% To covert a percent into a fraction, first write it as a decimal. Then write that decimal as a fraction. Finish by reducing the fraction % = o Now we reduce by dividing both the numerator and denomenator by a "fancy 1 = " = Write each decimal as a percent and as a fraction reduced to simplest form

16 Write each fraction as a decimal and as a percent. Use a calculator to help with division if needed. You may use a calculator on this section if you wish Write each percent as a decimal and as a fraction reduced to simplest from % % 4. 93% 4. 78%

17 TOPIC EIGHT: OPERATIONS ON FRACTIONS This is a topic I expect everyone to master by the beginning of eighth grade! Use whatever resources you have to become an expert on these operations. These will be on the high school entrance exam, and you will not be allowed to use a calculator! Please keep that in mind while completing this worksheet

18 Simplify the following fractions. This is a skill at which you should become an expert. Your goal is to get yourself to a point (by September) where these problems come naturally for you

19 TOPIC NINE: PROPORTIONS We have learned two ways of solving proportions: cross- multiplication and finding scale factor. Please try to complete these BOTH ways. Again, if you need help, check out Khan Academy or Google it! Scale factor method: Cross- multiplication method:

21 4. Maeve s family recipe for macaroni and cheese makes 4 servings of 310 calories each. Maeve decided to make 1 ½ times the amount in the recipe. How many calories are in Maeve s batch of macaroni and cheese? 5. If 1 bucket + 5 jars = 1 tub, and 3 buckets + jars = tubs, how many jars are equal to 1 tub? 6. If x J y is defined as xy + (x y), what is the value of 4 J? 7. Arlene has 1/3 as many goldfish as Isabelle. Isabelle has 5 times as many goldfish as Anaele. If Anaele has 18 goldfish, how many goldfish does Arlene have? 8. Meaghan started a baking service. During her first month in business, Meaghan spent \$380 on supplies and drove 800 miles at an average cost of \$0.30 per mile. In addition, her business phone and other expenses were \$198. That month, Meaghan completed 60 jobs, earning \$50 per job. What was Meaghan s profit during her first month in business? Show all your work!!!!

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