1.Homework Folders are marked and can be picked up 1.Late for 50% hand in to Mr. Dalton 2.Map test dates are on the wiki homepage 3.Lesson: Distributive Property 4.Work on Homework (if time)

To distribute means to separate or break apart and then dispense evenly. The Distributive Property allows you to multiply each number inside a set of parenthesis by a factor outside the parenthesis and find the sum or difference of the resulting products. Sometimes it is faster and easier to break apart a multiplication problem and use the distributive property to solve or simplify the problem using mental math strategies. The distributive property is linked to factoring. In fact, it’s the opposite operation of factoring.

Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; When a number or letter is separated by parentheses and there are no other operation symbols – it means to distribute by multiplying the numbers or variables together. Find the sum (add) or difference (subtract) of the distributed products. Notice that it doesn’t matter which side of the expression the letter a is written on because of the symmetric property which states for any real numbers a and b; if a = b, then b = a. If a(b + c) = ab + ac, then ab + ac = a(b + c) Notice that it doesn’t matter which side of the expression the letter a is written on because of the symmetric property which states for any real numbers a and b; if a = b, then b = a. If a(b + c) = ab + ac, then ab + ac = a(b + c)

Or use the Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; Multiply 67  9 Break apart the number 67 into (60 + 7) – the value of this number is still the same. Multiply 67  9 Break apart the number 67 into (60 + 7) – the value of this number is still the same. Add

Or use the Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; Multiply 48  7 Break apart the number 48 into (50 - 2) – the value of this number is still the same. Multiply 48  7 Break apart the number 48 into (50 - 2) – the value of this number is still the same. Subtract

Or use the Distributive Property For any numbers a, b, c, and d a(b + c + d) = ab + ac + ad For any numbers a, b, c, and d a(b + c + d) = ab + ac + ad Multiply 6  473 Multiply 473  6 Break apart the number 473 into ( ) – the value of this number is still the same. Multiply 473  6 Break apart the number 473 into ( ) – the value of this number is still the same. Add

Use the Distributive Property For any numbers a, b, and c a(b + c ) = ab + ac For any numbers a, b, and c a(b + c ) = ab + ac Simplify 5(3n + 4) Notice the pattern: No symbol between the 5 and the parenthesis indicates a multiplication problem. Distribute by multiplication then perform the indicated operation inside the parenthesis. Notice that 15n means (15)(n) and is linked by multiplication and that the number 20 is by itself. These two terms are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem. Simplified

A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x 2

The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y 2 1 3)

Like Terms are terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x 3 y, xy 3 No, the exponents are on different variables.

Use the Distributive Property For any numbers a, b, and c a(b + c ) = ab + ac For any numbers a, b, and c a(b + c ) = ab + ac Simplify 4(7n + 2) +6 Notice the pattern: No symbol between the 4 and the parenthesis indicates a multiplication problem. Distribute by multiplication then perform the indicated operation inside the parenthesis. Notice that 28n cannot be combined with any other n terms. The constant terms 8 and 6 are linked with addition and can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem. Simplified

Use the Distributive Property For any numbers a, b, and c a(b + c ) = ab + ac For any numbers a, b, and c a(b + c ) = ab + ac Simplify 3(n + 2) + n Notice the pattern: No symbol between the 3 and the parenthesis indicates a multiplication problem. Distribute by multiplication then perform the indicated operation inside the parenthesis. Notice that n has a coefficient of 1. After applying the distributive property – you can combine like terms. 3n and 1n can be combined to form 4n. The constant term 6 cannot be combined with any other constant terms. The answer 3n + 6 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem. Simplified

Homework Page 74 # 5-12, 16, 17, 22-25, odd, 47