Exercise 82 Page 161

We want to simplify the given quotient without using a calculator.

- 8 \div (- 4)

We can recall that division is the opposite of multiplication. This operation represents the process of calculating how many times one quantity, called the divisor, is contained within another quantity, called the dividend. The result is called the quotient of the division. Let's consider an example quotient

6 \div 2 .

Let's apply this method to the quotient we are given. We can start by finding the number of groups of

- 4

that exist in

- 8 .

- 8 = 2 groups - 4 + (- 4)

There are

2

groups of

- 4

- 8 .

This means that the quotient of

- 8

and

- 4

2 .

We want to simplify the given quotient without using a calculator.

18 \div (- 3)

In this case, we want to determine how many times the divisor,

- 3,

is contained within the dividend,

18 .

We can start by finding the number of groups of

3

18 .

18 = 6 groups 3 + (3) + \dots + (3)

There are

6

groups of

3

18 .

This means that the quotient of

18

and

3

6 .

18 \div (3) = 6

We can recall that the quotient of a positive number,

18,

and a negative number,

- 3,

is negative. In this case, the quotient of

18

and

- 3

is a negative number,

- 6 .

18 \div (- 3) = - 6

We want to simplify the given quotient without using a calculator.

- 24 \div 2

We can simplify the quotient by finding how many times the divisor,

2,

is contained within the dividend,

- 24 .

First, let's determine the number of groups of

2

24 .

24 = 12 groups 2 + (2) + \dots + (2)

There are

12

groups of

2

24 .

This means that the quotient of

24

and

2

12 .

24 \div 2 = 12

In this case, the quotient of

- 24

and

2

is a negative number,

- 12 .

We want to simplify the given quotient without using a calculator.

17 \div (- 1)

Notice that we want to determine how many times the divisor,

- 1,

is contained within the dividend,

17 .

We can start by finding the number of groups of

1

17 .

17 = 17 groups 1 + (1) + \dots + (1)

There are

17

groups of

1

17 .

This means that the quotient of

17

and

1

17 .

17 \div (1) = 17

We can recall that the quotient of a positive number,

17,

and a negative number,

- 1,

is negative. In this case, the quotient of

17

and

- 1

is a negative number,

- 17 .

17 \div (- 1) = - 17

Subchapter links

3.2.1 Subtraction of Integers p.143-144

3.2.2 Connecting Addition and Subtraction p.147-148

3.2.3 Multiplication as Repeated Subtraction p.152

3.2.4 Multiplication of Decimals p.158

3.2.5 Addition, Subtraction, Multiplication, and Division of Integers p.161