Page 13 - 新思维数学学生用书7 样章

1 Integers

1.2 Multiplying and dividing integers

In this section you will … Key word

• multiply and divide with positive and negative integers. product

3 × 4 = 3 + 3 + 3 + 3 = 12 Tip
In a similar way, −3 × 4 = −3 + −3 + −3 + −3 = −12.

5 × 2 = 2 + 2 + 2 + 2 + 2 = 10 You say that ‘12
In a similar way, 5 × −2 = −2 + −2 + −2 + −2 + −2 = −10. is the product
of 3 and 4’ and

that ‘−12 is the

Worked example 1.4 product of −3
and 4’.
Work out:
a 6 × −4 b −9 × 3

Answer
a 6 × 4 = 24

So 6 × −4 = −24.
b 9 × 3 = 27

So −9 × 3 = −27.

Division is the inverse operation of multiplication.

3 × 4 = 12 So 12 ÷ 4 = 3.
This is also true when you divide a negative integer by a positive integer.
−3 × 4 = −12 So −12 ÷ 4 = −3.

The product of a positive and a negative integer is always negative.
For example, 6 × −9 = −54 and −4 × 12 = −48.
The same is true for division. When one integer is positive and the other is negative, the answer is
negative. For example, −48 ÷ 6 = −8 and 63 ÷ −7 = −9.

Worked example 1.5

Work out:
a −20 ÷ 5 b 20 ÷ −10 c 5 × (1 + −4)

12