Grade 6 Math Worksheet: 60 Questions on Number System, Shapes, Angles & Fractions for 11-Year-Olds

Section A: Place Value & Number System

1. What is the place value of the digit 7 in the number 9,754,321?
2. What is the digit value of the underlined digit in 4,568,192?
3. Write the number 3,000,000 + 400,000 + 5,000 + 20 + 9 in standard form.
4. In the number 2,848,150, what is the difference between the value of the digit 8 in the hundred thousands place and the value of the digit 8 in the thousands place?
5. Write the largest 7-digit number you can make using the digits 5, 1, 9, 0, 3, 2, 8 without repeating any digit.
6. Which number is the smallest?
   a) 506,789
   b) 560,789
   c) 506,879
   d) 506,798
7. The number 45,762 rounded to the nearest thousand is:
   a) 45,000
   b) 46,000
   c) 45,700
   d) 50,000
8. What is "Six million, forty-two thousand, and eleven" in standard form?
   a) 6,420,011
   b) 6,042,011
   c) 6,004,211
   d) 6,402,110
9. What is the expanded form of 205,803?
   a) 200,000 + 5,000 + 800 + 3
   b) 20,000 + 500 + 80 + 3
   c) 200,000 + 50,000 + 800 + 3
   d) 200,000 + 5,000 + 80 + 3
10. The predecessor of 10,000,000 is:
    a) 9,999,999
    b) 10,000,001
    c) 9,000,000
    d) 9,999,990

Section B: 2D and 3D Shapes

11. A polygon with 5 sides is called a __________________.
12. A quadrilateral with four equal sides and four right angles is a __________________.
13. How many vertices does a heptagon have?
14. An isosceles triangle has ___________ equal sides.
15. What is the name of a polygon with 10 sides?
16. A cube has ___________ faces, ___________ edges, and ___________ vertices.
17. A rectangular prism (cuboid) has ___________ faces, ___________ edges, and ___________ vertices.
18. A square-based pyramid has ___________ faces, ___________ edges, and ___________ vertices.
19. A triangular prism has ___________ faces, ___________ edges, and ___________ vertices.
20. A shape with 4 triangular faces, 6 edges and 4 vertices is called a __________________.

Section C: Angles

21. An angle that measures less than 90° is called a(n) __________________ angle.
22. An angle that measures exactly 180° is called a(n) __________________ angle.
23. An angle that measures more than 180° but less than 360° is called a(n) __________________ angle.
24. Look at the angle below. What type of angle is it (acute, right, obtuse, or straight)?
    
25. An angle measures 90°. What type of angle is it?
26. Find the value of angle 'x'.
    
27. Find the value of angle 'y'.
    
28. Find the value of angle 'z'.
    
29. Two angles in a triangle are 65° and 45°. What is the measure of the third angle?
30. What is the sum of all angles around a point?

Section D: Area and Perimeter

31. Find the perimeter of a square with a side length of 8 cm.
32. A rectangle has a length of 12 m and a width of 5 m. What is its perimeter?
33. The perimeter of a regular pentagon is 40 cm. What is the length of one side?
34. A rectangular garden is 20 feet long. Its perimeter is 60 feet. What is its width?
35. Find the perimeter of a rectangle with a length of 15 cm and a width of 9 cm.
36. Find the area of a square with a side length of 9 cm.
37. A rectangle has a length of 10 m and a width of 7 m. What is its area?
38. The area of a rectangle is 48 sq. inches. If its length is 8 inches, what is its width?
39. A square photo has a perimeter of 24 cm. What is its area?
40. A room is 5 meters long and 4 meters wide. What is the area of the floor?

Section E: Calculations with Fractions

41. Solve:   1/5 + 3/5 = ?
42. Solve:   2/7 + 4/7 = ?
43. Solve:   1/3 + 1/2 = ?
44. Solve:   3/4 + 2/5 = ?
45. Solve:   1 1/2 + 2 1/4 = ?
46. Solve:   7/8 - 3/8 = ?
47. Solve:   9/10 - 2/10 = ?
48. Solve:   5/6 - 1/3 = ?
49. Solve:   4/5 - 1/2 = ?
50. Solve:   3 3/4 - 1 1/2 = ?
51. Solve:   1/2 × 3/4 = ?
52. Solve:   5/6 × 2/3 = ?
53. Solve:   7 × 1/4 = ?
54. Solve:   3/5 × 10 = ?
55. Solve:   1 1/3 × 2 1/2 = ?
56. Solve:   1/2 ÷ 1/4 = ?
57. Solve:   3/5 ÷ 6/7 = ?
58. Solve:   4 ÷ 1/3 = ?
59. Solve:   5/8 ÷ 2 = ?
60. Solve:   2 1/4 ÷ 1/2 = ?