Page 61 - ArithBook5thEd ~ BCC

2.4.1 Exercises

Perform the subtractions.

1. Subtract 31 from 7

2. 98 − 100

3. 65 − (−640)

4. Subtract 55 from 24
5. Subtract −53 from 68.6

6. −888 − (−111)

7. Subtract 22 from 5

8. −87 − 23

9. −87 − (−23)

10. A snowball at −5 Cis heated until it melts and then boils. If water boils at 100 C,by how much
◦
◦
did the temperature of the snowball rise?
11. A sunken car is salvaged from the bottom of a lake. The elevation of the lake bottom is −66 feet.
The car is lifted by a crane to a height 79 feet above lake level. Through what vertical distance
was the car lifted?

2.5 Multiplying Signed Numbers

Multiplication of positive numbers was defined in terms of repeated addition. For example,

3 × 4= 4 + 4 + 4 = 12.

There is no problem extending this definition to the product of a negative number by a positive number.

3 × (−4) = (−4) + (−4) + (−4) = −12.

Products such as
(−2) × 5
pose no problem if, for consistency, we define signed number multiplication to be commutative (we do):

(−2) × 5= 5 × (−2) = (−2) + (−2) + (−2) + (−2) + (−2) = −10.

The general rule is:

The product of two numbers with opposite signs is the negative of the product of their
absolute values.

Example 58. Find the products (a) 7 × (−11) and (b) (−12) × 5.

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