BSD Grade 6 Study Guide

C. Accurately multiply and divide non-negative fractions.Example: Accurately i. multiply2 33 4 and ii. divide 1 24 15 3Answer:2 3 6 1 1 2 21 5 21 3 63 13i. ii. 4 1 23 4 12 2 5 3 5 3 5 5 25 25Practice Problems:6. Multiply or divide.1 3 2 1 12 = 23 11 3 5 83 3 1 11 = 6 320 4 2 321 =5D. Multiply and divide whole numbers and decimals by 1000, 100, 10, 1, 0.1, 0.01 and 0.001.Example: i. Multiply 0.01 x 435, ii. Multiply 100 x 435, iii. Divide 435 ÷ 1,000, iv. Divide 435 ÷ 0.1Answer: i. 0.01 x 435 = 4.35; ii. 100 x 435 = 43,500; iii. 435 ÷ 1,000 = 0.435 and iv. 435 ÷ 0.1 = 4,350Practice Problems:7. Mentally compute each of the following:0.001 x 2,300 = 1,000 x 2,300 = 2,300 ÷ 0.001 =0.10 x 0.342 = 100 x 0.342 = 0.342 ÷ 1,000 =2 x 0.001 = 2 x 0.1 = 2 ÷ 10 =

E. Multiply and divide non-negative decimals.Example: i. Find the product of 0.84 x 1.5 and ii. Find the quotient of 7.85÷0.32Answer:24.53i. 0.84 1.5 re-write as 0.84 ii. 7.85 0.32 re-write as 32.0 785.0x 1.5 - 64420 145840 -1281.260 170-160100-964Practice Problems:8. 0.21 x 15 = 5.32 x 130 = 1.22 x 0.14 =3.31 ÷ 0.22 = 17.28 ÷ 2.4 =

F. Solve single- and multi-step word problems involving operations with fractions and decimalsand verify the solutions.Example: Every day has 24 hours. Ali sleeps 3/8 of the day. Dawson sleeps 1/3 of the day. Maddiesleeps 7.2 hours in a day. Who sleeps the longest? By how much?Answer: Ali: 24 x (3/8) = 9 hours Dawson: 24 x (1/3) = 8 hours Maddie: 7.2 hoursAli sleeps more than Dawson by 1 hour and more than Maddie by (9-7.2) = 1.8 hours.Practice Problems: Solve each word problem and verify the solutions.9. In a recent survey of 440 people, 0.25 said that they watched television every evening, 2 5said they watch television five or six nights each week and the remainder said they watch fournights or less a week.a. How many people in the survey said they watch television every night? Show your work orexplain your answer.b. How many people in the survey said they watch television five or six nights each week?Show your work or explain your answer.c. What fraction of the people surveyed watch television four nights or less a week? Showyour work or explain your answer.d. How many people in the survey watch television four nights or less a week? Show yourwork or explain your answer.

ii. Mathematical Expressions and EquationsA. Write mathematical expression or equation with variables to represent information in a tableor given situation.Example: A t-shirt printing company charges $7 for each t-shirt it prints. Write an equation thatrepresents the total cost, c, for ordering a specific quantity, t, of these t-shirts.Answer: c = 7tPractice Problems:10. Elena has a part-time job that pays $10 per hour. Which expression shows how much moneyshe will earn next week if h stands for the number of hours she works and m stands for money?a. m=10 x (7h) b. m = 10 h c. m = 10 + 7h11. Greg started a computer club with 9 of his friends. He hopes to get 5 more people to join eachmonth. Which expression shows the future club membership? The variable m stands formonths and the variable p stands for people.a. p = 9 + 5m b. p = m x (9 + 5) c. p = 10 + 5m12. George plans to save $15 each week. Using the variables s and w, write an equation that showsthe savings (s) for any number of weeks (w).13. The dance club had 400 members, but has been losing about 10 members each month. Writean equation that shows the membership (m) for any number of months (n).

B. Draw a first-quadrant graph in the coordinate plane to represent information in a table orgiven situation.Practice Problems:14.

15.

C. Evaluate mathematical expressions when the value for each variable is given.Example: Evaluate 2s + 5t when s = 3.4 and t = 1.8Answer: 2(3.4) + 5(1.8) = 6.8 + 9 = 15.8Practice Problems:16. Substitute the given value for the variable to evaluate each expression.i. (80 ÷ g) – 5 for g = 10 ii. 2b + 15 for b = 6____________________________________iii. (4 x 0.5) + 7 – w for w = 3 iv. ( p + 30 ) ÷ (98 ÷ 14) for p = 5______________________________________D. Apply the commutative, associative, and distributive properties and use the order ofoperations to evaluate mathematical expressions.Example: i. Simplify1 16 2 3, with and without the distributive property andAnswer:ii. Evaluate 31.7 – 3(10.8 – 7)i.1 1 3 2 5 30 1 1 6 66 6 6 5 or with distributive 6 3 2 52 3 6 6 6 6 2 3 2 3ii. 31.7 – 3(10.8 – 7) = 31.7 – 3(3.8) = 31.7 – 11.4 = 20.3with distribution 31.7 – 3(10.8 – 7) = 31.7 – 32.4 + 21 = 20.3Practice Problems:17. Evaluate. Use the order of operations.i. 25 – (4 + 3) x 2 = ii. (12.2 – 5) x 2 + 1 = iii. 5 x (12 ÷ 3) – 5 =

18. Insert parentheses to make each equation true.i. 24 ÷ 8 – 2 = 4 ii. 9 – 16 ÷ 8 = 7 iii. 9 x 3 – 5 = 22 iv. 16 – 9 ÷ 3 x 4 = 5219. Simplify1 14 2 4two ways. First without using the distributive property and second with thedistributive property.20. Simplify 21.4 – 2(3.5 + 2) two ways. First without using the distributive property and secondwith the distributive property.E. Solve one-step equations and verify solutions.Example: Solve for the variable in each equation below.i.) 112 = 7a ii.) 3 = 2 + b iii.)y 745 15Answers: i.) 112 = 7(16); so a = 16 ii.) 3 = 2 + 1; so b = 1 iii.)Practice Problems:21. Solve for the variable in each equation below.i. 25 = 5c ii. 21 = 10 + a iii. 12 = 5r + 2y 7 21 ; so y = 2145 15 45iv.b 136 6v.y 320 5

iii. Ratios, Rates and PercentsA. Identify ratios as comparisons of part-to-part and part-to-whole relationships.Example: If there are 10 boys and 12 girls in a class, what is the ratio of boys to girls? What is the ratioof the number of boys to the total number of students in the class?Answer: Boys to girls: ratio 10 : 12; boys to total students: ratio 10 : 22Practice Problems:26. Jenny has a bag that contains 4 red marbles, 5 blue marbles, 8 yellow marbles and 12 whitemarbles.a. What is the ratio of blue marbles to red marbles?b. What is the ratio of yellow marbles to white marbles?c. What is the ratio of red marbles to the total number of marbles in the bag?d. What is the ratio of blue marbles to the total of red and yellow marbles combined?B. Write ratios to represent a variety of rates.Example: Julio drove his car 579 miles and used 15 gallons of gasoline. How many miles per gallon didhis car get during the trip?Answer: The ratio of miles per gallon can be written as miles : gallon or miles/gallon. So, Julio got579:15 mpg or 579/15 mpg which is equivalent to 38.6 mpg.Practice Problems:27. Represent each of the rates as a ratio. Make sure to include units.a. 12 feet per 10 seconds.b. 175 gallons per 3 hours.c. 17 meters per 20 minutes.d. 225 miles per 12 gallons.

C. Convert between the fractional, decimal and percent representations of a number.Example: Represent 13 as a decimal and as a percent.16Answer:0.812513 is the same as dividing 13 by 16 and 16 13.0160.8125 in decimal form can be written as 81.25% in percent form.Practice Problems:28. Represent 40% as a fraction and as a decimal.29. Represent 0.756 as a fraction and as a percent.30. Represent 56% as a fraction and as a decimal.31. Represent 1832as a decimal and as a percent.32. Represent 4 9as a decimal and as a percent.33. Represent 1730as a decimal and as a percent.

D. Solve single- and multi-step word problems involving ratios, rates, and percents.Example: An item is advertised as being 25% off the regular price. If the sale price is $42, what was theoriginal regular price?Answer: 25% off means that 1 – 25 or 75 % of the original price is left.To solve find 0.75 x (Original Price) = $42 or 0.75(P) = 42. Original Price = $42/0.75 = $56.Practice Problems:34. A shirt is originally priced at $35. If it is marked down 15% what will the sale price be?35. The cost to a dealership is $10,500 for a brand new car. If the manager wants to sale the carwith a 35% mark-up, meaning he wants to add an additional 35% to the cost of the vehicle, whatshould he put as a sticker price?36. An item is advertised as being 40% off the original price. If the sale price is $25, what was theoriginal regular price?37. Julie has $25 and wants to purchase a book that has a sale price of $22. She knows that there isa 9.8% sales tax that will be added to the price of the book. Will she have enough money topurchase the book? If so, how much will she get back in change? Show your work or explainyour answer.

iV. Two Dimensional Figures (Geometry)A. Determine the circumference and area of circles.Example: Determine the area and circumference of a circle with a diameter of 12 inches. Use 3.14inches for pi.Answer: Radius = 12/2 = 6 inches. Area = (pi)(radius)(radius) = 3.14(6)(6) = 113.04 inches squaredCircumference = 2(pi)(radius) = 2(3.14)(6) = 37.68 inchesPractice Problems:38. Find the area and circumference of a circle with radius of 4 feet.39. Find the area and circumference of a circle with a diameter of 13 meters.40. Find the area and circumference of a circle with a radius of 10 inches.41. Find the radius of a circle with the circumference of 43.96 inches.B. Determine the perimeter and area of a composite figure that can be divided into triangles,rectangles, and parts of circles.Practice Problems:42. Determine the area and perimeter of each of the following figures. The curved portion of FigureB is a semi-circle.Figure AFigure B235146Area: _________________Perimeter: _____________Area: _________________Perimeter: _____________