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Working with the Properties of Mathematics
1) Which property is used in the following?
A. Commutative Property
C. None of the above
$7 \times(3+4)=7 \times 3+7 \times 4$
B. Associative Property
D. Distributive Property
2) Which equation shows the Commutative Property of Multiplication ?
A. $7 \times 3=7+7+7$
B. $4 \times 8-2 \times 8=(4-2) \times 7$
C. $9 \times 5=5 \times 9$
D. $6 \times 1=6$
3) Which of the following does not show the Commutative Property ?
A. $9+y=y+9$
B. $x+y=y+x$
C. $\mathrm{yx}=\mathrm{xy}$
D. $x y-4=x y$
4) Which equation shows the Identity Property of Multiplication ?
A. $\mathrm{a} \times 1$
B. $(a+b)+6=a+(6+b)$
C. $a+a+a=3 \times a$
D. $a(b+c)=a b+a c$
5) Which is an example of Associative Property of Addition?
A. $5+0=5$
B. $7+(-7)=0$
C. $8+4=4+8$
D. $(4+2)+3=4+(2+3)$
6 ) Which property would you use to simplify the following expression ? $3(y+5)$
A. Associative Property
B. Distributive Property
C
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Answer from Sia

Posted about 2 months ago

Solution by Steps

step 1

The equation $7 \times (3 + 4) = 7 \times 3 + 7 \times 4$ demonstrates the Distributive Property, as it shows how multiplication distributes over addition

step 2

The equation $9 \times 5 = 5 \times 9$ illustrates the Commutative Property of Multiplication, which states that changing the order of the factors does not change the product

step 3

The equation $x y - 4 = x y$ does not demonstrate the Commutative Property, as it involves subtraction and does not change the order of addition or multiplication

step 4

The equation $a \times 1$ shows the Identity Property of Multiplication, which states that any number multiplied by 1 remains unchanged

step 5

The equation $(4 + 2) + 3 = 4 + (2 + 3)$ is an example of the Associative Property of Addition, which states that the way in which numbers are grouped does not change their sum

step 6

To simplify the expression $3(y + 5)$, we would use the Distributive Property, which allows us to multiply a single term by each term inside the parentheses

[1] Answer

D

[2] Answer

C

[3] Answer

D

[4] Answer

A

[5] Answer

D

[6] Answer

B

Key Concept

Understanding Mathematical Properties

Explanation

Mathematical properties such as Commutative, Associative, Distributive, and Identity help in simplifying and solving expressions and equations.

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