6th grade math - EduBird

Section 1: Ratios (22 points)

Part-to-Whole Ratios

In a basket of 12 fruits, there are 5 apples. What is the ratio of apples to total fruits?
Answer: ______
A class has 18 students. If 7 are wearing glasses, what is the ratio of students wearing glasses to the whole class?
Answer: ______
Write the ratio of vowels to total letters in the word “MATHEMATICS”.
Answer: ______
In a parking lot of 30 cars, 9 are red. What is the ratio of red cars to all cars?
Answer: ______
A bag has 4 blue marbles and 6 green marbles. What is the ratio of blue marbles to the total number of marbles?
Answer: ______

Ratios with Tape Diagrams & Word Problems

The ratio of cats to dogs at a shelter is 3:5. If there are 15 cats, how many dogs are there?
Answer: ______
For every 2 adults on a bus, there are 3 children. If there are 18 children, how many adults are there?
Answer: ______
The ratio of fiction to non-fiction books on a shelf is 7:4. If there are 28 fiction books, how many non-fiction books are there?
Answer: ______

Ratios and Measurements

A map scale is 1 inch : 10 miles. How many miles are represented by 4.5 inches?
Answer: ______ miles
Convert the ratio 2 feet : 18 inches to a simplified ratio of feet to inches.
Answer: ______

Ratios in Recipes (Word Problem)

A lemonade recipe calls for 3 cups of water for every 1 cup of lemon juice. If you use 8 cups of lemon juice, how many cups of water do you need?
Answer: ______ cups

Section 2: Rates and Percentages (18 points)

Solving Unit Rate/Price Problems

If 5 pounds of apples cost $7.50, what is the cost per pound?
Answer: $______
A printer can print 120 pages in 4 minutes. What is the unit rate (pages per minute)?
Answer: ______ pages/minute

Fraction, Decimal, and Percent Converting

Convert $\frac{3}{5}$ 53 to a decimal and a percent.
Decimal: ______ Percent: ______
Convert 0.72 to a fraction (simplified) and a percent.
Fraction: ______ Percent: ______
Convert 45% to a fraction (simplified) and a decimal.
Fraction: ______ Decimal: ______

Percent of a Number

What is 30% of 80?
Answer: ______
Find 15% of 200.
Answer: ______

Finding Common Percentages

What is 100% of 47?
Answer: ______
What is 50% of 120?
Answer: ______

Section 3: Negative Numbers (30 points)

Adding and Subtracting Negative Numbers

$5 + (- 9) =$ 5+(−9)= ______
$- 7 + 3 =$ −7+3= ______
$- 4 - 6 =$ −4−6= ______
$8 - (- 5) =$ 8−(−5)= ______
$- 12 - (- 8) =$ −12−(−8)= ______
$- 3 + (- 10) =$ −3+(−10)= ______
$0 - 15 =$ 0−15= ______
$- 20 + 20 =$ −20+20= ______
$14 + (- 17) =$ 14+(−17)= ______
$- 1 - (- 1) =$ −1−(−1)= ______

Multiplying and Dividing Negative Numbers

$(- 6) \times 4 =$ (−6)×4= ______
$5 \times (- 8) =$ 5×(−8)= ______
$(- 7) \times (- 3) =$ (−7)×(−3)= ______
$(- 24) \div 6 =$ (−24)÷6= ______
$18 \div (- 2) =$ 18÷(−2)= ______
$(- 40) \div (- 5) =$ (−40)÷(−5)= ______
$(- 9) \times 0 =$ (−9)×0= ______
$(- 15) \div (- 3) =$ (−15)÷(−3)= ______

Negative Numbers in Word Problems

The temperature at noon was 5°F. By midnight, it had dropped 18 degrees. What was the temperature at midnight?
Answer: ______ °F
A submarine is 250 feet below sea level. It rises 75 feet. What is its new position relative to sea level?
Answer: ______ feet
Sam has $20 in his bank account. He withdraws $35. What is his account balance now?
Answer: $______

Negative Fractions and Decimals

$- \frac{1}{4} + \frac{1}{2} =$ −41+21= ______
$- 0.6 - 0.1 =$ −0.6−0.1= ______
$(- 0.5) \times 4 =$ (−0.5)×4= ______
$- \frac{3}{5} \div 2 =$ −53÷2= ______

Section 4: Equations and Inequalities (20 points)

Solving Equations

$x + 9 = 15$ x+9=15
$x =$ x= ______
$3 y = 27$ 3y=27
$y =$ y= ______
$m - 7 = 4$ m−7=4
$m =$ m= ______
$p \div 6 = 8$ p÷6=8
$p =$ p= ______
$2 n + 5 = 19$ 2n+5=19
$n =$ n= ______

Inequalities – Solve each inequality.

$k - 4 > 10$ k−4>10
Solution: $k$ k ______
$3 t \leq 21$ 3t≤21
Solution: $t$ t ______
$w + 8 < 5$ w+8<5
Solution: $w$ w ______

Inequalities in Word Problems – Write and solve.

Lisa needs to save at least $50 for a gift. She has saved $22. Write and solve an inequality to find how much more she needs to save.
Inequality: ________________
Solution: ______
A bus can hold at most 45 students. There are already 31 students on the bus. Write and solve an inequality to find how many more can board.
Inequality: ________________
Solution: ______

Two-Step Inequalities – Solve.

$2 x + 3 \geq 11$ 2x+3≥11
Solution: $x$ x ______
$\frac{y}{4} - 2 < 1$ 4y−2<1
Solution: $y$ y ______
$5 - 3 z > 14$ 5−3z>14
Solution: $z$ z ______

Section 5: Plane Figures (20 points)

Parallelogram Area

Find the area of a parallelogram with a base of 12 cm and a height of 7 cm.
Answer: ______ cm²
A parallelogram has an area of 54 in² and a height of 6 in. What is the length of its base?
Answer: ______ in

Areas of Triangles (Missing Height or Base)

Find the area of a triangle with a base of 10 m and a height of 5 m.
Answer: ______ m²
A triangle has an area of 36 ft² and a base of 9 ft. What is its height?
Answer: ______ ft
A triangle has an area of 20 cm² and a height of 8 cm. What is the length of its base?
Answer: ______ cm

Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)

Find the area of a trapezoid with bases of 5 in and 9 in, and a height of 4 in.
Answer: ______ in²
A trapezoid has an area of 70 mm². Its bases are 8 mm and 12 mm. What is its height?
Answer: ______ mm
Find the area of a trapezoid with bases of 6.5 cm and 9.5 cm, and a height of 3 cm.
Answer: ______ cm²

Test Complete – Please review your work.

Answer Key (For Teacher Use)

Section 1:

5:12
7:18
4:11
9:30 or 3:10
4:10 or 2:5
25
12
16
45
4:3
24

Section 2:
12. $1.50
13. 30
14. 0.6, 60%
15. 18/25, 72%
16. 9/20, 0.45
17. 24
18. 30
19. 47
20. 60

Section 3:
21. -4
22. -4
23. -10
24. 13
25. -4
26. -13
27. -15
28. 0
29. -3
30. 0
31. -24
32. -40
33. 21
34. -4
35. -9
36. 8
37. 0
38. 5
39. -13
40. -175
41. -$15
42. 1/4 or 0.25
43. -0.7
44. -2
45. -3/10 or -0.3

Section 4:
46. 6
47. 9
48. 11
49. 48
50. 7
51. $k > 14$ k>14
52. $t \leq 7$ t≤7
53. $w < - 3$ w<−3
54. $m \geq 28$ m≥28, $m =$ m= money needed
55. $s \leq 14$ s≤14, $s =$ s= students
56. $x \geq 4$ x≥4
57. $y < 12$ y<12
58. $z < - 3$ z<−3

Section 5:
59. 84
60. 9
61. 25
62. 8
63. 5
64. 28
65. 7
66. 24