Natural Numbers Worksheet

1. Look for the term unknown and indicate its name in the following operations:

1. 327 + ....... = 1,208

2. ....... – 4,121 = 626

3. 321 · ....... = 32,100

4. 28,035 : ....... = 623

2. Look for the term unknown in the following operations:

1. 4 · (5 + ...) = 36

2. (30 – ...) : 5 + 4 = 8

3. 18 · ... + 4 · ... = 56

4. 30 - ... : 8 = 25

3. Calculate two different ways of completing the following operations:

1. 17 · 38 + 17 · 12 =

2. 6 · 59 + 4 · 59 =

3. (6 + 12) : 3

4. Remove the common factor:

1. 7 · 5 - 3 · 5 + 16 · 5 - 5 · 4 =

2. 6 · 4 - 4 · 3 + 4 · 9 - 5 · 4 =

3. 8 · 34 + 8 · 46 + 8 · 20 =

5. Express the follwing numbers in powers:

1. 50,000

2. 3,200

3. 3,000,000

6. Calculate:

1. 3³ · 3⁴ · 3 =

2. 5⁷ : 5³ =

3. (5³)⁴ =

4. (5 · 2 · 3)⁴ =

5. (3⁴)⁴ =

6. [(5³)⁴ ]² =

7. (8²)³

8. (9³)²

9. 2⁵ · 2⁴ · 2 =

10. 2⁷ : 2⁶ =

11. (2²)⁴ =

12. (4 · 2 · 3)⁴ =

13.(2⁵)⁴ =

14. [(2³ )⁴]⁰=

15. (27²)⁵=

16. (4³)² =

7. Using powers, carry out the polynomial decomposition of these numbers:

1. 3,257

2. 10,256

3. 125,368

8. Calculate the square roots:

1.

2.

3.

9. Calculate:

1. 27 + 3 · 5 – 16 =

2. 27 + 3 – 45 : 5 + 16 =

3. (2 · 4 + 12) (6 − 4) =

4. 3 · 9 + (6 + 5 – 3) – 12 : 4 =

5. 2 + 5 · (2 · 3)³ =

6. 440 − [30 + 6 (19 − 12)] =

7. 2{4 [7 + 4 (5 · 3 − 9)] − 3 (40 − 8)} =

8. 7 · 3 + [6 + 2 · (2³ : 4 + 3 · 2) – 7 · ] + 9 : 3 =

1

Look for the unknown term and indicate its name in the following operations:

1. 327 + ....... = 1,208

addend.

1,208 − 327 = 881

2. ....... – 4,121 = 626

Minuend.

4,121 + 626 = 4,747

3. 321 · ....... = 32 100

Factor.

32,100 : 321 = 100

4. 28,035: ....... = 623

Divisor .

28,035 : 623 = 45

2

Look for the unknown term in the following operations:

1. 4 · (5 + ...) = 36

4

2. (30 – ...) : 5 + 4 = 8

10

3. 18 · ... + 4 · ... = 56

2 and 5

4. 30 - ... : 8 = 25

40

3

Calculate two different ways of completing the following operations:

1. 17 · 38 + 17 · 12 =

1. 17 · 38 + 17 · 12 = 646 + 204 = 850

2. 17 · 38 + 17 · 12 = 17 (38 + 12) = 17 · 50 = 850

2. 6 · 59 + 4 · 59 =

1. 6 · 59 + 4 · 59 = 354 + 236 = 590

2. 6 · 59 + 4 · 59 = 59 (6 + 4) = 59 · 10 = 590

3. (6 + 12) : 3

1.(6 + 12) : 3 = 18 : 3 = 6

2.(6 + 12) : 3 = (6 : 3) + (12 : 3) = 2 + 4 = 6

4

Remove the common factor:

1. 7 · 5 - 3 · 5 + 16 · 5 - 5 · 4 =

7 · 5 - 3 · 5 + 16 · 5 - 5 · 4 = 5 (7 − 3 + 16 − 4)

2. 6 · 4 - 4 · 3 + 4 · 9 - 5 · 4 =

6 · 4 - 4 · 3 + 4 · 9 - 5 · 4 = 4 (6 − 3 + 9 − 5)

3. 8 · 34 + 8 · 46 + 8 · 20 =

8 · (34 + 46 + 20)

5

Express the following numbers in powers:

1. 50,000 = 5 · 10 ⁴

2. 3,200 = 32 · 10 ²

3. 3,000,000 = 3 · 10 ⁶

6

Calculate:

1. 3³ · 3⁴ · 3 = 3⁸

2. 5⁷ : 5³ = 5⁴

3. (5³)⁴ = 5¹²

4. (5 · 2 · 3) ⁴ = 30⁴

5.(3⁴)⁴ = 3¹⁶

6. [(5³)⁴]² = (5¹²)² = 5²⁴

7. (8²)³ =[( 2³)²]³ = (2⁶)³ = 2¹⁸

8. (9³)² = [(3²)³]² = (3⁶)² = 3¹²

9. 2⁵ · 2⁴ · 2 = 2¹⁰

10. 2⁷ : 2⁶ = 2

11. (2²)⁴ = 2⁸

12. (4 · 2 · 3)⁴ = 24⁴

13.(2⁵)⁴ = 2²⁰

14. [(2³ )⁴]⁰ = (2¹²)⁰ = 2⁰ = 1

15. (27²)⁵ =[(3³)²]⁵ = (3⁶)⁵ = 3³⁰

16. (4³)² = [(2²)³]² = (2⁶)² = 2¹²

7

Using powers, carry out the polynomial decomposition of these numbers:

1. 3,257

3,257 = 3 · 10³ + 2 · 10² + 5 · 10 + 7

2. 10,256

10,256 = 1 · 10⁴ + 0 · 10³ + 2 · 10² + 5 · 10 + 6

3. 125,368

125,368 = 1 · 10⁵ + 2 · 10⁴ +5 · 10³ + 3 · 10² + 6 · 10 + 8

8

Calculate the square roots:

1.

2.

3.

9

Calculate:

1. 27 + 3 · 5 – 16 =

= 27 + 15 − 16 = 26

2. 27 + 3 – 45 : 5 + 16=

27 + 3 – 9 + 16 = 37

3. (2 · 4 + 12) (6 − 4) =

= (8 + 12) (2) = 20 · 2 = 40

4. 3 · 9 + (6 + 5 – 3) – 12 : 4 =

= 27 + 8 – 3 = 32

5. 2 + 5 · (2 ·3)³ =

= 2 + 5 · (6)³ = 2 + 5 · 216 = 2 + 1080 = 1082

6. 440 − [30 + 6 (19 − 12)] =

= 440 − (30 + 6 · 7)] = 440 − (30 + 42) =

= 440 − (72) = 368

7. 2{4[7 + 4 (5 · 3 − 9)] − 3 (40 − 8)} =

= 2[4 (7 + 4 · 6) − 3 (32)] = 2[4 (7 + 24) − 3 (32)]=

2[4 (31) − 3 (32)]= 2 (124 − 96)= 2 (28)= 56

8.7 · 3 + [6 + 2 · (2³ : 4 + 3 · 2) – 7 · ] + 9 : 3 =

= 21 + [ 6 + 2 · (2+ 6) – 14] +3 =

= 21 + ( 6 + 2 · 8 – 14) +3 =

= 21 + ( 6 + 16 – 14) + 3 =

= 21 + 8 + 3 = 32