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Students use the distributive property to rewrite and solve multiplication problems. Then they apply addition and multiplication properties to simplify numerical expressions.Key ConceptsThe distributive property is stated in terms of addition: a(b + c) = ab + ac, for all numbers a, b, and c. However, it can be extended to subtraction as well: a(b − c) = ab − ac, for all numbers a, b, and c. Here is a proof. (We have combined some steps.)a(b − c)Original expression= a(b + (−c))Subtracting is adding the opposite.= a(b) + a(−c)Apply the distributive property.= ab + a(−1 ⋅ c)Apply the property of multiplication by −1.= ab + −1(ac)Apply the associative and commutative properties of multiplication.= ab + −(ac)Apply the property of multiplication by −1.= ab − acAdd the opposite is subtracting.We can use the distributive property to make some multiplication problems easier to solve. For example, by rewriting $1.85 as $2.00 − $0.15 and applying the distributive property, we can change 6($1.85) to a problem that is easy to solve mentally.6($1.85)=6($2−$0.15)=6($2) − 6($0.15)=$12 − $0.90=$11.10One common error students make when simplifying expressions is to simply remove the parentheses when a sum or difference is subtracted. For example, students may rewrite 10 − (6 + 9) as 10 − 6 + 9. In fact, 10 − (6 + 9) = 10 − 6 − 9. To see why, remember that that subtraction is equivalent to adding the opposite, 10 − (6 + 9) = 10 + [−(6 + 9)]. Applying the property of multiplication by −1, this is 10 + (−1)(6 + 9). Using the distributive property, we get 10 + (−6) + (−9) = 10 − 6 − 9.Goals and Learning ObjectivesApply addition and multiplication properties to simplify numerical expressions.
Subject:
Numbers and Operations
Level:
Middle School
Grades:
Grade 7
Material Type:
Lesson Plan
Provider:
Pearson
Date Added:
09/21/2015
License:
Creative Commons Attribution Non-Commercial Creative Commons Attribution Non-Commercial
Language:
English
Media Format:
Text/HTML

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