Alg1 - 0.4 Distributive Property

Concept:

Imagine you have a quantity (let's say cookies) and you want to share them amongst a group (represented by parentheses). The distributive property allows you to distribute the cookies (multiplication) to each person (individual terms within the parentheses) separately, instead of giving the entire group the cookies all at once and then dividing them up (which can be cumbersome).

Steps to Use the Distributive Property:

1. Identify the expression: Look for multiplication where one number is outside parentheses containing an addition (or subtraction) problem. For example: 3 x (2 + 5).

2. Distribute the multiplier: Multiply the number outside the parentheses by each term inside the parentheses. In our example, 3 multiplies both 2 and 5.

3. Rewrite the expression: Expand the parentheses by writing out each product of the multiplication you just performed. Our example becomes: 3 x 2 + 3 x 5.

4. Simplify: Solve the individual multiplications and then add (or subtract) the terms as usual. In our case: 6 + 15 = 21.

Examples:

• Example 1: 4 x (3 + 1) = (4 x 3) + (4 x 1) = 12 + 4 = 16

• Example 2: -2 x (7 - 4) = (-2 x 7) + (-2 x -4) = -14 + 8 = -6 (remember, subtracting a negative number is the same as adding a positive)

Additional Tips:

• The distributive property works for subtraction as well. Just remember to distribute the minus sign along with the number outside the parentheses.

• You can also distribute variables following the same principle. For example, a(x + y) becomes ax + ay.

• Encourage students to draw squares or rectangles to visualize distributing the quantity (like cookies in our example) amongst multiple terms.

0.4 HW Distributive Property.pdf

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0.4 NOTES Distributive Property.pdf

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