1. 1
Introduction to Algebra:
Integers

2. R.1 Fractions
1.6 Multiplying Integers
Objectives
Use a raised dot or parentheses to express multiplication.
Multiply integers.
Identify properties of multiplication.
Estimate answers to application problems involving multiplication.

3. Use a raised dot or parentheses to express multiplication.
Numbers being multiplied are called factors and the answer is called the product.

4. Use a raised dot or parentheses to express multiplication.
Rewrite the multiplication in three different ways. Identify the factor and the product. 10 × 7
Example
The factors are 10 and 7 and the product is 70.

5. Multiply integers.
Multiply Two Integers
If two factors have different signs, the product is negative.
For example,
If two factors have the same sign, the product is positive. For example,

6. Multiply integers.
Multiply the integers.
2 • 8
Example
The factors have different signs, so the product is negative.

7. Multiply integers.
Multiply the integers.
Example
The factors have the same sign, so the
product is positive.

8. Multiply integers. Multiply the integers. Example 3 • (4 • 5)
Multiply numbers in parentheses first.
Then multiply the resulting pair of numbers.

9. Multiply integers. Multiply the integers. Example
Multiply the first pair of numbers.
Then multiply the resulting pair of numbers.

10. Identify properties of multiplication.
Multiplication Property of 0
Multiplying any number by 0 gives a product of 0.
Some examples are shown below.
16(0) = 0 (0)(5) = 0 32,977(0) = 0

11. Identify properties of multiplication.
Multiplication Property of 1
Multiplying a number by 1 leaves the number unchanged.
Some examples are shown below.
6(1) = 6 –12(1) = –12 (1)(5876) = 5876

12. Identify properties of multiplication.

13. Identify properties of multiplication.
Show that the product is unchanged and name the property that is illustrated.
Example
Both products are 28.
Commutative property of multiplication

14. Identify properties of multiplication.
Show that the product is unchanged and name the property that is illustrated.
Example
Both products are 100.
Associative property of multiplication

15. Identify properties of multiplication.

16. Identify properties of multiplication.
Rewrite the product, using the distributive property. Show that the result is unchanged.
Example

17. Estimate answers to application problems involving multiplication.
Last year Videoland had to replace 392 defective DVDs at a cost of $19 each. How much money was lost on defective DVDs?
Example
Estimate: Use front end rounding: 392 rounds to 400 and –$19 rounds to –$20.
Exact:
Videoland lost $7448 in defective DVDs.