Fill in the blanks to make the following statements true.
a. (-45) x 16 = _ x (-45)
b. 79 x (0 - 60) = (_ x 0) - (79 x _)
c. -34 x 1 = 1 x _
d. -1 x (_ x 56) = (-1 x 0) x _
e. 99 x (-71) = _ x 99
Answer (2)
Let's solve each part of the question using the properties of multiplication, specifically the Commutative and Associative Properties.
a. ( − 45 ) × 16 = _ × ( − 45 ) According to the Commutative Property of Multiplication , which states that changing the order of factors does not change the product, we can conclude that the blank should be filled with 16 .
b. 79 × ( 0 − 60 ) = ( _ × 0 ) − ( 79 × _ ) This is noticeable as an application of the Distributive Property a × ( b − c ) = ( a × b ) − ( a × c ) . Therefore, the blanks should be filled with 79 and 60 .
c. − 34 × 1 = 1 × _ Using the Identity Property of Multiplication , which states that any number multiplied by 1 remains unchanged, the blank should be filled with − 34 .
d. − 1 × ( _ × 56 ) = ( − 1 × 0 ) × _ The understanding of multiplication by zero is crucial here. According to the Multiplicative Property of Zero , any number multiplied by zero is zero, and the associative property doesn't change anything here. The blanks should be filled with 0 and 56 , respectively.
e. 99 × ( − 71 ) = _ × 99 Similarly to part a, this uses the Commutative Property of Multiplication . The blank should be filled with − 71 .
These solutions make use of fundamental properties of multiplication, such as commutative, associative, distributive, identity, and zero properties, which help simplify and solve multiplication problems effectively.
To solve each statement, we utilize properties of multiplication like the Commutative and Distributive Properties. The answers are: a) 16, b) 79 and 60, c) -34, d) 0 and 56, e) -71. These properties help establish equality in multiplication expressions effectively.
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