Basic Math Practice Assignments
Mixed Practice Exercise:
Simplify the following:
Answer Mixed Practice:
Answer Explanations:
Other basic math practice:
Please solve the following without any calculator:
Practice 1:
Simplify the following expressions:
1. 39 – (25 – 17)
2. 3 (4 – 2) ÷ 2
3. 15 × 3 ÷ 9
4. (9 – 5) – (4 – 2)
5. 14 – 3 (4 – 6)
6. –5 × 1 ÷ 5
7. (4) (–3) (2) (–1)
8. 5 – (4 – (3 – (2 – 1)))
9. –4 (5) – 12 ÷ (2 + 4)
10. 17(6) + 3(6)
Practice 2:
Evaluate the following expressions while taking common, if possible. Otherwise simplify it:
11. –12 × 2 ÷ (–3) + 5
12. 32 ÷ (4 + 6×2)
13. –10 – (–3)2
14. –52 =
15. –23 ÷ 2
16. 53 – 52
17. 5(2+1) + 25
18. (–2)3 – 52 + (–4)3
19. 5(1)+ 5(2)+ 5(3)+ 5(4)
20. 3 × 99 – 2 × 99 – 1 × 99
Practice 3:
Combine as many like terms as possible:
21. nr2 – (2nr + nr2)
22. 1 + 2√4 + 2√2
23. 12xy2 – 6(xy)2 + (2xy)2
24. 3π + xπ -2π
25. √2 + x√2 – 2√2
26. 12xy – (6x+ 2y)
27. 3x – (3x + 5 – (2x – 3))
28. π2r2 – πr+ 2πr2 + π (r2) + (πr)2 + 2πr
29. 2x2 – (2x)2 – 22 – x2
30. 4x2 + 2x – (2√x)2
Practice 4:
Distribute the following expressions. Simplify as necessary:
31. 3(5–y)
32. –(a – b)
33. (2x + y)z
34. √3 (√2 + √3)
35. 5.2r(2t – 10s)
36. (–3.7x + 6.3)102
37. 6k2l(k – 2l)
38. –√3 (–n√12 + √27)
39. d(d2 – 2d + 1)
40. xy2z(x2z+ yz2 – xy2)
Practice 5:
Simplify the following expressions by combining like terms. If the base is a number, leave the answer in exponential form (i.e. 23, rather than 8):
41. x5 × x3
42. 76 × 79
43. 55 ÷ 53
44. (a3)2
45. 4(–2) × 45
46. (–3)a ÷ (–3)2
47. (32)(–3)
48. 114 ÷ 11x
49. x2 × x3 × x5
50. (52)x
Practice 6:
Solve the following equations:
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
Answers & Explanation:
Practice 1:
1. 39 – (25 – 17)
= 39 – 8
= 31 (Answer)
2. 3 (4 – 2) ÷ 2
= 3 (2) ÷ 2
By applying left to right rule
= 6 ÷ 2
= 3 (Answer)
3. 15 × 3 ÷ 9
By applying left to right rule
= 45 ÷ 9
= 5 (Answer)
4. (9 – 5) – (4 – 2)
= 4 – 2
= 2 (Answer)
5. 14 – 3 (4 – 6)
= 14 – 3 (–2)
= 14 – (3) (–2)
= 14 – (–6)
= 14 + 6 {As (–ve) × (–ve) = +ve}
= 20 (Answer)
6. –5 × 1 ÷ 5
{As we know, × and ÷ come together, followed left to right}
= –5 ÷ 5
= (–5) ÷ 5
= –1 (Answer)
7. (4) (–3) (2) (–1)
As all numbers are multiplying, so we rearrange;
= (4) (2) (–3) (–1)
{As, for all numbers a, b, c and d: a × b × c × d = a × c × b × d}
= (8) (3)
= 24 (Answer)
8. 5 – (4 – (3 – (2 – 1)))
= 5 – (4 – (3 – 1))
= 5 – (4 – 2)
= 5 – 2
= 3 (Answer)
9. – 4 (5) – 12 ÷ (2 + 4)
= – 4 (5) – 12 ÷ 6
= –20 – 2
= –22 (Answer)
10. 17(6) + 3(6)
= (10 + 7)(6) + 3 (6)
= (60 + 42) + 18
= 102 + 18
= 120 (Answer)
Practice 2:
11. –12 × 2 ÷ (–3) + 5
= –24 ÷ (–3) + 5
= 8 + 5
= 13 (Answer)
12. 32 ÷ (4 + 6×2)
= 32 ÷ (4 + 12)
= 32 ÷ 16
= 2 (Answer)
13. –10 – (–3)2
= –10 – (–3). (–3)
= –10 – (9)
= –10 – 9
= –19 (Answer)
14. –52
= – (5).(5)
= –25 (Answer)
15. – 23 ÷ 2
= – 8 ÷ 2
= –4 (Answer)
16. 53 – 52
= 5 × 5 × 5 – 52
= 25 × 5 – 25
= 125 – 25
= 100 (Answer)
17. 5(2+1) + 25
= 5 × 5 × 5 + 25
= 25 × 5 + 25
= 125 + 25
= 150 (Answer)
18. (–2)3 – 52 + (–4)3
= –8 – 25 + (–64)
= –8 – 25 – 64
= –96 (Answer)
19. 5(1) + 5(2) + 5(3) + 5(4)
By taking 5 common,
= 5 (1 + 2 + 3 + 4)
= 5 (10)
= 50 (Answer)
20. 3 × 99 – 2 × 99 – 1 × 99
By taking 99 common,
= 99 (3 – 2 – 1)
= 99 (0)
= 0 (Answer)
Practice 3:
21. nr2 – (2nr + nr2)
By opening brackets, –ve sign multiplies with each number inside bracket
= nr2 – 2nr – nr2
= –2nr (Answer)
22. 1 + 2 √4 + 2√2
= 1 + 2(2) + 2√2
= 1 + 4 + 2√2
= 5 + 2√2 (Answer)
23. 12xy2 – 6(xy)2 + (2xy)2
= 12xy2 – 6x2y2 + 2x2y2
= 12xy2 – 4x2y2
= 4xy2 (3 – x) (Answer)
24. 3π + xπ –2π
By taking π common,
= π (3 + x –2)
= π (1 + x) (Answer)
25. √2 + x√2 – 2√2
By taking √2 common,
= √2 (1 + x – 2)
= √2 (x – 1) (Answer)
26. 12xy – (6x+ 2y)
= 12xy – 6x –2y
By taking 2 common,
= 2 (6xy – 3x – y) (Answer)
27. 3x – (3x + 5 – (2x – 3))
= 3x – (3x + 5 – 2x + 3)
(As multiplication with –ve sign changes all signs inside bracket)
= 3x – 3x – 5 + 2x – 3
= 0 + 2x – 8
= 2x – 8 (Answer)
28. π2r2 – πr + 2πr2 + π (r2) + (πr)2 + 2πr
By taking πr common,
= πr (πr – 1 + 2r + r + πr + 2)
= πr (2πr + 3r + 1) (Answer)
29. 2x2 – (2x)2 – 22 – x2
= 2x2 – 4x2 – 4 – x2
= –3x2 – 4 (Answer)
30. 4x2 + 2x – (2√x)2
= 4x2 + 2x – 4(√x)2
= 4x2 + 2x – 4x
= 4x2 – 2x (Answer)
Practice 4:
31. 3(5 – y)
By multiplying 3 inside the bracket, it’ll multiply each number having relationship of +ve or –ve
= 3×5 – 3×y
= 15 – 3y (Answer)
32. – (a–b)
= –a + b (Answer) or = b – a (Answer)
33. (2x + y)z
= 2xz + yz (Answer)
34. √3 (√2 + √3)
= √3 . √2 + √3 . √3
= √(3×2) + (√3)2 (As, √a × √b = √ab )
= √6 + 3 (Answer)
35. 5.2r(2t – 10s)
= 10.4rt – 52rs (Answer)
36. (–3.7x + 6.3)102
= (–3.7x + 6.3) 100
= –370x + 630 (Answer) or = 630 – 370x (Answer)
37. 6k2l(k – 2l)
= 6k3l – 12k2 l2 (Answer)
38. –√3 (–n√12 + √27)
= n√36 + √27)
= n(√6)2 + √9 × √3
= 6n + 3√3 (Answer)
39. d(d2 – 2d +1)
= d3 – 2d2 + d (Answer)
40. xy2z(x2z+ yz2 – xy2)
= x3y2z2 + xy3z3 – x2y4z (Answer)
Practice 5:
41. x5 × x3
= x(5+3)
= x8 (Answer)
42. 76 × 79
= 7(6+9)
= 715 (Answer)
43. 55 ÷ 53
= 5(5 – 3)
= 52 or = 25(Answer)
44. (a3 )2
= a(3×2)
= a6 (Answer)
45. 4–2 × 45
= 4(5 – 2)
= 43 or = 64 (Answer)
46. (-3)a ÷ (-3)2
= (-3)(a-2) (Answer)
47. (32)–3
= (3)2 × (–3)
= 3(–6)
= 1/36 (Answer)
48. 114 ÷ 11x
= 11(4-x) (Answer)
49. x2 × x3 × x5
= x2+3+5
= x10 (Answer)
50. (52)x
= 52x (Answer)
Practice 6:
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.