Natural number set exercises

O set of natural numbers is formed by the numbers we use to count. The smallest natural number is zero; the greatest it is not possible to determine, as the set is infinite.

The set of natural numbers is represented by the letter $\dpi{120} \mathbb{N}$ and can be written as follows:

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$\dpi{120} \mathbb{N} \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...\}$

See how the basic operations between natural numbers and their main properties are done.

Operations with natural numbers:

Addition: a + b = c → a and b are the parts and c is the sum or total.
Subtraction: a – b = c (a $\geq$ b) → a is the minuend, b is the subtrahend and c is the remainder or difference.
Multiplication: a. b = c → a and b are the factors and c is the product.
Division: a ÷ b = c (b $\nq$ 0) → a is the dividend, b is the divisor, and c is the quotient.

Properties of natural numbers:

Commutative: addition → a + b = b + a; multiplication → a.b = b.a
Associative: addition → (a + b) + c = a + (b + c); multiplication → (a.b).c = a.(b.c)

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Distributive: multiplication → (a + b).c = a.c + b.c; division → (a + b)÷c = a÷c + b÷c

To learn more about this subject, check out, below, a set of natural numbers exercise list. All exercises are solved, step by step!

List of exercises for the set of natural numbers

Question 1. Using the symbols < or >, rewrite each of the sentences below:

a) 2 is less than 8.
b) 13 is greater than 7.
c) 19 is less than 20.

Question 2. Which of the numbers below belong to the set of natural numbers?

a) 0
b) – 4
c) 1
d) 0.5
e) 1,000,000,000
f) $\dpi{120} \frac{2}{3}$

Question 3. Complete with the missing value and write your name in each of the operations:

a) 1432 + _____ = 2800
b) _____ – 1040 = 5390
c) 141. _____ = 846
d) 12000 ÷ _____ = 800

Question 4. Determine the unknown value in each of the operations:

a) 8 + ____ – 10 = 6
b) 3. (7 + ____) = 27
c) (26 – ____) ÷ 4 = 5
d) 30+3. ____ = 54

Question 5. Solve operations in two different ways:

a) 5. 9 + 5. 11 =
b) 8. 19 + 3. 19 =
c) (21 + 35) ÷ 7 =

Question 6. Write as a single power:

The) $\dpi{120} 2^3 \cdot 2^6\cdot 2$

B) $\dpi{120} 7^{19} \div 7^8$

w) $\dpi{120} (10^5)^8$

d) $\dpi{120} [(3^2)^4]^2$

Question 7. Determine the result of $\dpi{120} (3 -2)^2 + 3\cdot {\sqrt{25}} - 30 \div 2$ .

Question 8. Calculate the result of $\dpi{120} 8\cdot 4 + \{4[6 + 3\cdot (2\cdot 9 - 7)] - 5\cdot (60 -35)\}$ .

Resolution of question 1

a) 2 < 8.
b) 13 > 7.
c) 19 < 20.

Resolution of question 2

ah yes.
b) No.
c) Yes.
d) No.
and yes.
f) No.

Resolution of question 3

a) 1432 + _____ = 2800

2800 – 1432 = 1368 ⇒ 1432 + 1368 = 2800

1368 is called a plot.

b) _____ – 1040 = 5390

5390 + 1040 = 6430 ⇒ 6430 – 1040 = 5390

6430 is called a minuend.

c) 141. _____ = 846

846 ÷ 141 = 6 ⇒ 141. 6 = 846

6 is called a factor.

d) 12000 ÷ _____ = 800

12000 ÷ 800 = 15 ⇒ 12000 ÷ 15 = 800

15 is called a divisor.

Resolution of question 4

a) 8 + ____ – 10 = 6

⇒ 8 + ____ = 6 + 10
⇒ 8 + ____ = 16
⇒ 8 + 8 = 16

b) 3. (7 + ____) = 27

⇒ 7 + ____ = 27 ÷ 3
⇒ 7 + ____ = 9
⇒ 7 + 2 = 9

c) (26 – ____) ÷ 4 = 5

⇒ 26 – ____ = 5. 4
⇒ 26 – ____ = 20
⇒ 26 – 6 = 20

d) 30+3. ____ = 54

⇒ 3. ____ = 54 – 30
⇒ 3. ____ = 24
⇒ 3. 8 = 24

Resolution of question 5

a) 5. 9 + 5. 11 =

1st form) 5. 9 + 5. 11 = 45 + 55 = 100

2nd form) 5. 9 + 5. 11 = 5.(9 + 11) = 5. 20 = 100

b) 8. 19 + 3. 19 =

1st form) 8. 19 + 3. 19 = 152 + 57 = 209

2nd form) 8. 19 + 3. 19 = (8 + 3). 19 = 11. 19 = 209

c) (21 + 35) ÷ 7 =

1st form) (21 + 35) ÷ 7 = 56 ÷ 7 = 8

2nd form) (21 + 35) ÷ 7 = (21 ÷ 7) + (35 ÷ 7) = 3 + 5 = 8

Resolution of question 6

The) $\dpi{120} 2^3 \cdot 2^6\cdot 2 2^{3 + 6 + 1} 2^{10}$

B) $\dpi{120} 7^{19} \div 7^8 7 ^{19 - 8} 7^{11}$

w) $\dpi{120} (10^5)^8 10^{5\cdot 8} 10^{40}$

d) $\dpi{120} [(3^2)^4]^2 3^{2\cdot 4\cdot 2} 3^{16}$

Resolution of question 7

$\dpi{120} (3 -2)^2 + 3\cdot {\sqrt{25}} - 30 \div 2$

$\dpi{120} 1^2 + 3\cdot {\sqrt{25}} - 30 \div 2$

$\dpi{120} 1 + 3\cdot 5 - 30 \div 2$

$\dpi{120} 1 + 15 - 15$

$\dpi{120} 1$

Resolution of question 8

$\dpi{120} 8\cdot 4 + \{4[6 + 3\cdot (2\cdot 9 - 7)] - 5\cdot (60 -35)\}$

$\dpi{120} 32 + \{4[6 + 3\cdot (18 - 7)] - 5\cdot (60 -35)\}$

$\dpi{120} 32 + \{4[6 + 3\cdot (11)] - 5\cdot (25)\}$

$\dpi{120} 32 + \{4[6 + 33] - 125\}$

$\dpi{120} 32 + \{4\cdot [39] - 125\}$

$\dpi{120} 32 + \{156 - 125\}$

$\dpi{120} 32 +31$

$\dpi{120} 63$

You may also be interested:

Prime numbers
Cardinal numbers
Decimal numbers
negative numbers
mixed numbers
Complex numbers
Numerical sets