Natural Numbers Worksheet

Solutions

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. Square Root

2. Square Root

3. Square Root

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. Square Root

Square Root Operations

2. Square Root

Square Root Operations

3. Square Root


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