6th grade math

Sections: Ratios, Rates & Percentages, Negative Numbers, Equations & Inequalities, Plane Figures

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Section 1: Ratios (16 questions, 16 points)

Part-to-Whole Ratios

1. In a basket of fruit, there are 8 apples and 12 oranges. What is the ratio of apples to the total pieces of fruit? Write in simplest form.
   Answer: ______
2. A class has 15 boys and 10 girls. What is the ratio of girls to the total number of students? Write in simplest form.
   Answer: ______
3. A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. What is the ratio of blue marbles to the total marbles?
   Answer: ______
4. In a parking lot, 7 cars are silver and 13 are black. What is the ratio of silver cars to the total number of cars?
   Answer: ______
5. A box has 9 pencils and 6 pens. What is the ratio of pens to the total number of writing tools?
   Answer: ______

Ratios with Tape Diagrams & Word Problems

6. The ratio of cats to dogs at a pet shelter is 3:5. If there are 15 cats, how many dogs are there?
   Answer: ______
7. The ratio of students who ride the bus to those who walk is 7:4. If 28 students ride the bus, how many walk?
   Answer: ______
8. In a recipe, the ratio of flour to sugar is 4:1. If you use 8 cups of flour, how much sugar do you need?
   Answer: ______ cups
9. The ratio of fiction to nonfiction books in a library is 6:5. If there are 90 fiction books, how many nonfiction books are there?
   Answer: ______
10. The ratio of adults to children at a park is 2:7. If there are 18 adults, how many children are there?
    Answer: ______

Ratios and Measurements

11. A map scale is 1 inch : 10 miles. How many miles are represented by 4 inches?
    Answer: ______ miles
12. A model car is built at a scale of 1:24. If the model is 3 inches long, how long is the real car in feet?
    Answer: ______ feet
13. Convert 3 feet to inches using the ratio 12 inches : 1 foot.
    Answer: ______ inches
14. A recipe calls for 2 cups of milk for every 3 cups of flour. If you use 9 cups of flour, how many cups of milk are needed?
    Answer: ______ cups
15. If 5 pounds of apples cost $8, what is the ratio of dollars to pounds?
    Answer: ______

Ratios in Recipes (Word Problem)

16. A lemonade recipe calls for 1 cup of lemon juice for every 6 cups of water. If you want to make 28 cups of lemonade total, how many cups of lemon juice do you need?
    Answer: ______ cups

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Section 2: Rates and Percentages (20 questions, 20 points)

Solving Unit Rate/Price Problems

17. If 4 notebooks cost $12, what is the cost per notebook?
    Answer: $______
18. A car travels 240 miles in 5 hours. What is the unit rate in miles per hour?
    Answer: ______ mph
19. If 3 pounds of bananas cost $1.50, what is the price per pound?
    Answer: $______
20. A printer can print 30 pages in 2 minutes. How many pages can it print per minute?
    Answer: ______
21. You buy 6 granola bars for $4.80. What is the unit price?
    Answer: $______

Fraction, Decimal, and Percent Converting

22. Write $\frac{3}{4}$43​ as a decimal and a percent.
    Decimal: ______ Percent: ______
23. Write 0.6 as a fraction (simplified) and a percent.
    Fraction: ______ Percent: ______
24. Write 40% as a fraction (simplified) and a decimal.
    Fraction: ______ Decimal: ______
25. Write 0.05 as a fraction and a percent.
    Fraction: ______ Percent: ______
26. Write $\frac{5}{8}$85​ as a decimal and a percent.
    Decimal: ______ Percent: ______

Percent of a Number

27. What is 25% of 80?
    Answer: ______
28. Find 60% of 150.
    Answer: ______
29. What is 10% of 230?
    Answer: ______
30. Calculate 75% of 64.
    Answer: ______
31. Find 5% of 300.
    Answer: ______

Finding Common Percentages

32. A shirt costs $40 and is on sale for 20% off. What is the sale price?
    Answer: $______
33. You leave a 15% tip on a $30 meal. How much is the tip?
    Answer: $______
34. A test has 50 questions. If you got 86% correct, how many questions did you answer correctly?
    Answer: ______
35. A town’s population increased by 10% from 2,000 people. What is the new population?
    Answer: ______
36. A $90 jacket is on sale for 30% off. What is the discount amount in dollars?
    Answer: $______

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Section 3: Negative Numbers (26 questions, 26 points)

Adding and Subtracting Negative Numbers

37. $5+(-9)=$5+(−9)= ______
38. $-7+4=$−7+4= ______
39. $-3-6=$−3−6= ______
40. $8-(-2)=$8−(−2)= ______
41. $-10+(-5)=$−10+(−5)= ______
42. $-1-(-8)=$−1−(−8)= ______
43. $12+(-15)=$12+(−15)= ______
44. $-4-7=$−4−7= ______
45. $6-(-3)=$6−(−3)= ______
46. $-9+(-2)=$−9+(−2)= ______

Multiplying and Dividing Negative Numbers

47. $(-4)\times 6=$(−4)×6= ______
48. $10÷(-2)=$10÷(−2)= ______
49. $(-7)\times (-3)=$(−7)×(−3)= ______
50. $(-18)÷3=$(−18)÷3= ______
51. $(-5)\times (-4)=$(−5)×(−4)= ______
52. $24÷(-6)=$24÷(−6)= ______
53. $(-8)\times 2=$(−8)×2= ______
54. $(-15)÷(-5)=$(−15)÷(−5)= ______

Negative Numbers in Word Problems

55. The temperature at 6 a.m. was -4°F. By noon, it had risen 11 degrees. What was the temperature at noon?
    Answer: ______ °F
56. A scuba diver is at -30 feet. She ascends 12 feet. What is her new depth?
    Answer: ______ feet
57. A checking account has a balance of -$25. You deposit $60. What is the new balance?
    Answer: $______
58. The elevation of a valley is -150 feet. A nearby mountain has an elevation of 1,200 feet. What is the difference in elevation between the mountain and the valley?
    Answer: ______ feet

Negative Fractions and Decimals

59. $-\frac{1}{2}+\frac{3}{4}=$−21​+43​= ______
60. $-0.8-0.3=$−0.8−0.3= ______
61. $(-\frac{1}{4})\times 8=$(−41​)×8= ______
62. $-1.5÷0.5=$−1.5÷0.5= ______

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Section 4: Equations and Inequalities (18 questions, 36 points)

Solving Equations

63. Solve for $x$x: $x+8=15$x+8=15
    Answer: $x=$x= ______
64. Solve for $y$y: $3y=27$3y=27
    Answer: $y=$y= ______
65. Solve for $n$n: $n-12=20$n−12=20
    Answer: $n=$n= ______
66. Solve for $a$a: $\frac{a}{4}=7$4a​=7
    Answer: $a=$a= ______
67. Solve for $k$k: $5k+2=32$5k+2=32
    Answer: $k=$k= ______

Inequalities – Solve each inequality.

68. $x+3>7$x+3>7
    Solution: $x$x ______
69. $2y\le 16$2y≤16
    Solution: $y$y ______
70. $m-5<10$m−5<10
    Solution: $m$m ______
71. $\frac{p}{3}\ge 4$3p​≥4
    Solution: $p$p ______
72. $4n-1>11$4n−1>11
    Solution: $n$n ______

Inequalities in Word Problems

73. Emily has at most $50 to spend. She buys a book for $18. Write an inequality to find how much more she can spend.
    Inequality: ______
74. A number decreased by 7 is greater than 20. Write and solve an inequality.
    Inequality: ______ Solution: ______
75. To ride a roller coaster, you must be at least 48 inches tall. If $h$h represents height, write an inequality.
    Inequality: ______

Two-Step Inequalities

76. Solve: $3x+5\le 20$3x+5≤20
    Answer: $x$x ______
77. Solve: $2y-7>9$2y−7>9
    Answer: $y$y ______
78. Solve: $\frac{m}{2}+4\ge 10$2m​+4≥10
    Answer: $m$m ______
79. Solve: $5n-3<22$5n−3<22
    Answer: $n$n ______
80. Solve: $6+4k\le 30$6+4k≤30
    Answer: $k$k ______

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Section 5: Plane Figures (10 questions, 20 points)

Parallelogram Area

81. Find the area of a parallelogram with base 10 cm and height 7 cm.
    Answer: ______ cm²
82. A parallelogram has an area of 54 in² and a height of 6 in. What is the length of its base?
    Answer: ______ in

Area of Triangles (Missing Height or Base)

83. Find the area of a triangle with base 12 m and height 5 m.
    Answer: ______ m²
84. A triangle has an area of 36 ft² and a base of 9 ft. What is its height?
    Answer: ______ ft
85. Find the area of a triangle with base 8.5 cm and height 4 cm.
    Answer: ______ cm²
86. A triangle has an area of 24 in² and a height of 6 in. What is the length of its base?
    Answer: ______ in

Area of Quadrilaterals with Two Parallel Sides (Trapezoids)

87. Find the area of a trapezoid with bases 6 cm and 10 cm, and height 5 cm.
    Answer: ______ cm²
88. A trapezoid has an area of 75 yd², a height of 5 yd, and one base of 12 yd. Find the length of the other base.
    Answer: ______ yd
89. Find the area of a trapezoid with bases 9 in and 15 in, and height 7 in.
    Answer: ______ in²
90. A trapezoid has an area of 48 ft², bases of 5 ft and 7 ft. What is its height?
    Answer: ______ ft

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Test Complete – Well done! Please review your answers.

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Answer Key (For Teacher Use)

Section 1:

1. 2:5
2. 2:5
3. 5:12
4. 7:20
5. 2:5
6. 25
7. 16
8. 2
9. 75
10. 63
11. 40
12. 6
13. 36
14. 6
15. 8:5
16. 4

Section 2:
17. 3
18. 48
19. 0.50
20. 15
21. 0.80
22. 0.75, 75%
23. 3/5, 60%
24. 2/5, 0.4
25. 1/20, 5%
26. 0.625, 62.5%
27. 20
28. 90
29. 23
30. 48
31. 15
32. 32
33. 4.50
34. 43
35. 2,200
36. 27

Section 3:
37. -4
38. -3
39. -9
40. 10
41. -15
42. 7
43. -3
44. -11
45. 9
46. -11
47. -24
48. -5
49. 21
50. -6
51. 20
52. -4
53. -16
54. 3
55. 7
56. -18
57. 35
58. 1,350
59. 1/4
60. -1.1
61. -2
62. -3

Section 4:
63. 7
64. 9
65. 32
66. 28
67. 6
68. $x>4$x>4
69. $y\le 8$y≤8
70. $m<15$m<15
71. $p\ge 12$p≥12
72. $n>3$n>3
73. $x\le 32$x≤32
74. $n-7>20,n>27$n−7>20,n>27
75. $h\ge 48$h≥48
76. $x\le 5$x≤5
77. $y>8$y>8
78. $m\ge 12$m≥12
79. $n<5$n<5
80. $k\le 6$k≤6

Section 5:
81. 70
82. 9
83. 30
84. 8
85. 17
86. 8
87. 40
88. 18
89. 84
90. 8