1. Tell what property allows you to compute [tex]\frac{1}{3} \times (6 \times \frac{4}{3}) = (\frac{1}{3} \times 6) \times \frac{4}{3}[/tex]
a) Associative property of addition
b) Associative property of multiplication
c) Commutative property of multiplication
d) Commutative property of addition
2. [tex]42(4 + 2) = (42 \times 4) + (42 \times 2)[/tex] is an example of
a) commutative property
b) distributive property
c) associative property
d) closure property
3. Solve: [tex]3m = 5m - \frac{8}{5}[/tex]
a) 4
b) 5
c) [tex]\frac{3}{5}[/tex]
d) [tex]\frac{4}{5}[/tex]
Answer (1)
To compute 3 1 × ( 6 × 3 4 ) = ( 3 1 × 6 ) × 3 4 , the property that allows this rearrangement is the Associative Property of Multiplication . The associative property states that the way in which numbers are grouped does not affect the product when multiplying. For example, ( a × b ) × c = a × ( b × c ) . So, the correct answer is (b) Associative property of multiplication .
The equation 42 ( 4 + 2 ) = ( 42 × 4 ) + ( 42 × 2 ) is an example of the Distributive Property . The distributive property involves the distribution of multiplication over addition or subtraction, and it is expressed as a ( b + c ) = ab + a c . Here, 42 is distributed over the addition of 4 and 2. Thus, the correct answer is (b) Distributive property .
To solve the equation 3 m = 5 m − 5 8 , let's follow these steps:
Subtract 5 m from both sides to get: 3 m − 5 m = − 5 8 .
This simplifies to − 2 m = − 5 8 .
Divide both sides by − 2 to solve for m :
m = − 2 − 5 8 .
Multiply inside out to simplify: m = 10 8 = 5 4 .
Thus, the solution to the equation is m = 5 4 , so the correct answer is (d) 5 4 .
