This document discusses multiplying real numbers. It states that if the signs of two numbers being multiplied are the same, the sign of the answer is positive, but if the signs are different, the sign of the answer is negative. It then lists several properties of multiplication, including that the order of factors can change (commutative property) and that multiplying a number by zero equals zero. Finally, it provides examples of multiplying real numbers like -10*-4=40 and using the commutative property and properties of zero in justifications.

1. 2.4 Multiply Real Numbers

2. Multiplying integers
If the signs are the same, the sign of the
answer is positive.
If the signs are different, the sign of the
answer is negative.
negative x negative = positive
negative x positive = negative
positive x positive = positive

3. Properties
• Commutative property • Identity property
– order changes – product of a number and
– product stays the same one is the number
– 5(4) = 4(5) – 5(1) = 5
• Associative property • Property of zero
– grouping changes – product of a number and
– product and order stay the zero is zero
same – 6(0) = 0
– (6 * 2) * 3 = 6 *(2 * 3) • Property of negative one
– Product of a number and
negative one is the
opposite of the number
– 77 (-1) = - 77

4. Example 1 Multiply real numbers
Find the product.
a. 2 (–5 ) ( – 4) = ( –10) (–4 ) Multiply 2 and – 5.
= 40 Same signs; product is positive.
1 1
b. – (– 4) (–3) = 2 (–3) Multiply – and – 4.
2 2
= –6 Different signs; product is negative.

5. Guided Practice for Example 2
2. Which property is used in the equation
5• ( – 6 ) = – 6 • 5?
ANSWER commutative property of multiplication

6. Example 3 Use properties of multiplication
Find the product ( –4x) • 0.25. Justify your steps.
( –4x ) • 0.25 = 0.25 • ( –4x )
= [0.25 • ( –4 )] x
= –1 • x
= –x

7. Guided Practice for Examples 3 and 4
Find the product. Justify your steps.
3
( 5y)
10