MathReview Packetthfor 6 Grade MathLevel 2Decimals, Fractions, Ratios, Rates,Percent, Comparing Integers, CoordinatePlane, Perimeter, Area, Volume, EvaluatingExpressions, One-Step Equations, &Problem Solving
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Adding & Subtracting Decimals1. Write the problem vertically, lining up the decimal points.ex: 14.2 - 7.9342. Add additional zeroes at the end, if necessary, to make the numbershave the same number of decimal places.14.200- 7.9346 2663. Add/subtract as if the numbers are whole numbers4. Bring the decimal point straight downMultiplying Decimalsex: 6.94 x 7.81. Write the problem vertically with the numbers lined up to the right.The decimal points do NOT need to be lined up.6.947. 8 555248580541322. Ignore the decimals and multiply as if the numbers are wholenumbers.x3. Count the total number of decimal places in the factors and put adecimal point in the product so that it has that same number ofdecimal places.Dividing Decimals1. Write the dividend under the long division symbol and the divisor to theleft of it.4. Annex zeros in the dividend as needed until there is no remainder. Ifyour answer is a repeating decimal, write the answer using barnotation.Order of Operations3. Multiplication & Division (left to right)4. Addition & Subtraction (left to right)3 decimal places54 1328 4. 30.3 . 6322525.3 0-24 .3- 11 2- 1 9013. Divide as if the numbers are both whole numbers.2. Exponents1 decimal placeex: 25.3 0.32. Move the decimal point in the divisor after the number to turn it into awhole number and then move the decimal in the dividend the samenumber of places. Then bring it up.1. Grouping Symbols (parentheses, brackets, etc.)2 decimal places ex: 5 4(3 - 1.2)5 4(1.8)5 7.212.2
Evaluate each expression.1. 5.983 2.992. 224 - 56.733. 6.12 - 4.9234. 24.5 · 3.25. 0.23 · 76. 3.86 · 9.157. 14.8 58. 46.3 1.59. 147 2.2510. 24.33 - 2.5 · 711. 3.9 4.5212. 9.25(18.4 - 2 · 1.2)Solve each word problem, showing all work.13.Jeff had 46.18 in his wallet Monday morning.He gave half of his money to his brother. Hethen bought two donuts for 0.75 each and acup of coffee for 2.99. How much money didJeff have left?14.Five friends split a 65.20 bill at a restaurant.They also each left 2.75 for the tip. Howmuch money did each person pay in all?
Adding Fractions & Mixed Numbers1. Find a common denominator for the two fractions.31ex: 3 4 2 22. Add the two numerators and keep the denominator the same.333 3441222 24 3. Add the whole numbers.4. Simplify the answer and/or change improper fraction answers tomixed numbers.551 644Subtracting Fractions & Mixed Numbers1. Find a common denominator for the two fractions.2. Subtract the two numerators and keep the denominators the same.If the top numerator is smaller than the bottom numerator, borrowfrom the whole number and rename the top fraction.12ex: 5 4 1 313155 5 12 4 1242881 1 12 1 123-3. Subtract the whole numbers.34. Simplify the answer.712Multiplying Fractions & Mixed Numbers1. Turn any mixed numbers and whole numbers into improper fractions.14ex: 2 6 72. Cross-simplify if possible.3. Multiply the numerators and then multiply the denominators213 4265 1212136 74. Simplify the answer and/or change improper fraction answers tomixed numbers.Dividing Fractions & Mixed Numbers1. Turn any mixed numbers and whole numbers into improper fractions.2. Keep the first fraction the same, change the division to multiplication,and flip the second fraction to its reciprocal.3ex: 7 1 477 143. Multiply the fractions.4. Simplify the answer and/or change improper fraction answers tomixed numbers.171 44 471 1
Evaluate each expression.4315. 5 4318. 6 811917. 8 12 9 183120. 4 6 9119. 8 5 2 341522. 2 4 87225. 5 1021. 25 1624. 9 35216. 4 7 2 14538123. 6 8 3 224526. 5 3 2 6Solve each word problem, showing all work.127. Jaimie ran 3 2 miles on Monday. She ran halfas far on Tuesday as she did on Monday. Howfar did Jaimie run in all on Monday andTuesday?28.12A 5 2 quart pot is filled of the way with water.3How many more quarts of water can the pothold?
Ratios are comparisons of two quantities.There are 3 different ways to write ratios:A- FractionB- Colon A:BRatiosex: write the ratio of triangles to circlesin 3 ways:- Word Form A to B42 , 2:1, 2 to 121Ratios can be simplified just like fractions.Rates & Unit RatesRates are ratios that compare quantities measured in different units.A unit rate is a rate with a denominator of 1.ex: express as a unit rate:125 miles in 4 hoursTo convert a rate to a unit rate:1. Divide the numerator by the denominator125 mi4 hr2. Either write your answer as a fraction with a label for the both thenumerator and denominator OR as one number labeled with the firstunit “per” the second unit31.25 mior 31.25 miles per hr1 hrTo convert a:125 4 31.25Fractions, Decimals, & Percent- Decimal to Percent: move the decimal point 2 places to the rightex: 0.345 34.5%- Percent to Decimal: move the decimal point 2 places to the leftex: 7% 0.07- Decimal to Fraction: write the decimal over the place value of the lastdigit and then simplifyex: 0.008 - Fraction to Decimal: divide the numerator by the denominatorex:81 1000 1250.21 5 1.05459ex: 45% 100 20- Percent to Fraction: write the percent over 100 and then simplify- Fraction to Percent: convert the fraction to a decimal and thenconvert the decimal to a percentex:3 0.3 30%10Percent of a Number1. Turn the percent to a fraction or decimal.2. Multiply the fraction/decimal by the number.ex: Find 18% of 400.18 · 40 7.2
Write each ratio in 3 ways.29. A bank contains 15 pennies and 12 nickels. Write30. A bowl contains 6 apples and some bananas. Ifthe ratio of nickels to pennies.there are a total of 10 pieces of fruit, find theratio of apples to bananas.Convert each rate to a unit rate.31. 4.25 for 64 fluid ounces32. 297 miles on 11 gallons of gas33. 124 feet in 10 secondsComplete the chart by converting each number to a percent, fraction, and/or .38.0.13200Find each percent of a number.39. 30% of 9040. 15% of 3841. 50% of 8642. 75% of 16043. 24% of 3544. 2% of 74
Comparing IntegersIntegers are numbers without fractional parts. They canbe positive, negative, or zero. The further right a numberis on the number line, the greater it is.ex: compare with , , or 9 The absolute value-7of -9 9-7The absolute value of a number is the distance thenumber is from zero. 9The Coordinate Planey-axisQuadrant IIQuadrant Ix-axisoriginQuadrant IIIQuadrant IVOrdered Pair: (x, y)To graph a point on thecoordinate plane, start atthe origin. The firstnumber in the ordered pair(the x-coordinate) tells youhow far left (if negative) orright (if positive) to move.The second number (the ycoordinate) tells you howfar up (if positive) or down(if negative) to move.ex: Graph the point (-3, 2)and state the quadrantin which it is located.Start at the origin, and moveLEFT 3 and UP 2Quadrant IIPerimeter, Area and Volume-Perimeter of Any Polygon: add all side lengthsex: Find the perimeter & area:8 mm-Area of a Rectangle: A lw-Area of Parallelogram: A bh-Area of Triangle: A 1 bh2Area of Trapezoid: A 1 h(b1 b2)2--Volume of Rectangular Prism: V lwh14 mmPerimeter: P 5 8 5 14 32 mmArea: This is a trapezoid, so use the area of a trapezoid1formula: A h (b1 b2 )2The bases are the sides that are parallel, and theheight is perpendicular to the bases. A 1 (4)(8 14) 44 mm22
Compare the integers with , , or .45. -4-550. 7-646. 2-247. 5548. -7649. -1351. -17-1452. 3 253. 0-654. 4-9Graph and label each of the ordered pairs in the coordinate plane. Then state the quadrantor axis in/on which the point is located.55. A(2, 4)56. B(0, -3)57. C(1, -1)58. D(3, 3)59. E(-4, 1)60. F(2, 0)61. G(-3, -2)62. H(-2, 3)63. I(0, 2)64. J(-1, -4)Find the perimeter, area, and/or volume of the given figure.65. Find the perimeter & area:66. Find the perimeter & area:67. Find the perimeter & area:5 cm3.5 in12 cm8 in68. Find the perimeter & area:69. Find the area of a square321 in70. Find the volume:3.5 ft4 ft7 ft281 mmwith a perimeter of 45 cm63 mm46
Evaluating Algebraic Expressions1. Substitute the given numbers for the variablesex: evaluate x 4y forx 4&y 62. Evaluate the expression using the order of operations4 4(6)4 24 28One-Step Addition & Subtraction Equations- Addition Equations: Subtract the number being added to thevariable from both sides of the equationex: 4 x 18- Subtraction Equations: Add the number being subtracted fromthe variable to both sides of theequationex: 20 a - 5-4-4x 14 5 525 a a 25One-Step Multiplication & Division Equations- Multiplication Equations: Divide both sides of the equation bythe number next to the variable- Division Equations: Multiply both sides of the equation bythe number under the variableex: 7b 2877b 4nex: 5 · 10 · 55n 50Problem Solving1. Read the problem. Identify the question that is being asked and the key information inthe problem.2. Plan how you are going to solve the problem and estimate the answer.3. Solve the problem using the strategy of your choice.4. Check your answer. Make sure your answer is reasonable and compare it to yourestimate. Label your answer with appropriate units.
Evaluate each expression for a 5, b 12, c 10, & d 2.71. 2b a74.4ab 4d72. d(ab – c)73. 3 75. 2a2 – c76. b – c dbdSolve each one-step equation.77. g 3 1778. r – 6 779. 6b 1880. 9 381. 5 f – 882. 48 12b83. a 24 8384. 17 x 2386. 86.5 f – 7.6387. 6 11m85. 10 5nh388. 4 h 12
Solve each word problem using the method of your choice.89. A fencing company charges 22 per foot to installa wood fence. How much will it cost to install awood fence around a rectangular pool area that is20 feet wide and 38 feet long?90. A 6 inch-tall plant grew ¾ of an inch one weekand twice as much the following week. How tall isthe plant now?91. Jack can read 45 pages of his book in one and ahalf hours. At that rate, how long will it take him toread the entire 300-page book?92. Brian ordered 3 large cheese pizzas and a salad.The salad cost 4.95. If he spent a total of 47.60 including the 5 tip, how much did eachpizza cost? (Assume there is no tax).193. A cookie recipe calls for 34 cups of flour. Therecipe makes 3 dozen cookies. How much four isneeded to make 144 cookies?194. Ella has a box of chocolate candies. She gives 3of the candies to her sister, 4 to her brother, andshe eats the remaining 12 candies. How manychocolate candies were in the box originally?
Solve each word problem using the method of your choice.95. 20% of the 520 students in Wendover MiddleSchool were involved in school sports. Of thosestudents, 12.5% were on the wrestling team. Howmany students were on the wrestling team?96. A piggy bank contains some dimes and nickels.There are 8 more dimes than nickels in the bank.There is a total of 1.40. How many of each typeof coin are in the bank?97. An elevator in a tall building goes up 7 floors, thendown 9 floors, down 4 floors, up 8 floors, anddown 2 floors. Now it is on floor 14. On whatfloor did the elevator start?98. Jenna danced for 3 hours on Sunday, 2 hours onMonday and Tuesday, 1 hour on Thursday, 1.5hours on Friday, and 2 hours on Saturday. Shedid not dance at all on Wednesday. What is theaverage number of hours she danced each day?Round your answer to the nearest tenth of anhour.99. Jackie makes 15.25/hour babysitting. Georgemakes 18.50/hour mowing the lawn. If Jackiebabysits for 4 hours and George mows lawns for3 hours, who makes more money? How muchmore does he/she make?100. A box of 8 crayons costs 0.96. How much doeseach crayon cost? At that unit price, how muchwould a box of 30 crayons cost?
Answer KeyEvaluate each expression.1. 5.983 2.998.9734. 24.5 · 3.278.42. 224 - 56.73167.276. 3.86 · 9.151.618. 46.3 1.52.9630.86ത6.831.1975. 0.23 · 77. 14.8 510. 24.33 - 2.5 · 73. 6.12 - 4.92335.3199. 147 2.2565.3ത11. 3.9 4.5212. 9.25(18.4 - 2 · 1.2)14824.15Solve each word problem, showing all work.13.Jeff had 46.18 in his wallet Monday morning.He gave half of his money to his brother. Hethen bought two donuts for 0.75 each and acup of coffee for 2.99. How much money didJeff have left? 18.6014.Five friends split a 65.20 bill at a restaurant.They also each left 2.75 for the tip. Howmuch money did each person pay in all? 15.79
Answer KeyEvaluate each expression.4315. 5 42111 2034718 3615224. 9 3120. 4 6 946 1553 1853123. 6 8 3 222. 2 4 8323 162224526. 5 3 2 625. 5 102251 61813207136 1419. 8 5 2 35 5821. 25 16517. 8 12 9 18318. 6 811916. 4 7 2 142Solve each word problem, showing all work.127. Jaimie ran 3 2 miles on Monday. She ran halfas far on Tuesday as she did on Monday. Howfar did Jaimie run in all on Monday andTuesday?5 41 miles28.12A 5 2 quart pot is filled of the way with water.3How many more quarts of water can the pothold?1 56 quarts
Answer KeyWrite each ratio in 3 ways.29. A bank contains 15 pennies and 12 nickels. Write30. A bowl contains 6 apples and some bananas. Ifthe ratio of nickels to pennies.4:5, 4 to 5,there are a total of 10 pieces of fruit, find theratio of apples to bananas.45323:2, 3 to 2,Convert each rate to a unit rate.31. 4.25 for 64 fluid ounces32. 297 miles on 11 gallons of gas 0.07 per floz27 m
Math Review Packet for 6th Grade Math Decimals, Fractions, Ratios, Rates, Percent, Comparing Integers, Coordinate Plane, Perimeter, Area, Volume, Evaluating Expressions, One-Step Equations, & Problem Solving Level 2. Thank you for downloading this resource from Math in the Middle! This purchase grants you (the purchaser) the right to print and copy the resource for your own students. If