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QuestionIdentify the property illustrated in each case: a. (6⋅7)0=0(6 \cdot 7) 0=0 b. 3(5⋅7)=3(7⋅5)3(5 \cdot 7)=3(7 \cdot 5) c. 3(5⋅7)=(5⋅7)33(5 \cdot 7)=(5 \cdot 7) 3 d. (5+7)1=5+7(5+7) 1=5+7 e. 3(5+7)=3⋅5+3⋅73(5+7)=3 \cdot 5+3 \cdot 7 f. (3+5)(6+7)=(3+5)6+(3+5)7(3+5)(6+7)=(3+5) 6+(3+5) 7

Studdy Solution

STEP 1

Assumptions1. We need to identify the mathematical property illustrated by each given expression. . We are given the following options for each expression A. The commutative property of multiplication B. The associative property of multiplication C. The zero multiplication property D. The distributive property of multiplication over addition. The identity property of multiplication

STEP 2

Let's start with the first expression (6⋅7)0=0(6 \cdot7)0=0. This expression is showing that any number multiplied by zero equals zero. This is known as the zero multiplication property. So, the answer for this expression is C. The zero multiplication property.

STEP 3

Next, let's look at the expression 3(5⋅7)=3(7⋅5)3(5 \cdot7)=3(7 \cdot5). This expression is showing that the order in which numbers are multiplied does not change the product. This is known as the commutative property of multiplication. So, the answer for this expression is B. The commutative property of multiplication.

STEP 4

Now, let's look at the expression 3(⋅7)=(⋅7)33( \cdot7)=( \cdot7)3. This expression is showing that the order in which numbers are multiplied does not change the product. This is also an example of the commutative property of multiplication. So, the answer for this expression is D. The commutative property of multiplication.

STEP 5

Next, let's look at the expression (5+7)1=5+7(5+7)1=5+7. This expression is showing that any number multiplied by one equals the number itself. This is known as the identity property of multiplication. So, the answer for this expression is. The identity property of multiplication.

STEP 6

Now, let's look at the expression 3(5+)=3⋅5+3⋅3(5+)=3 \cdot5+3 \cdot. This expression is showing that the product of a number and the sum of two other numbers equals the sum of the products of the first number and each of the other two numbers separately. This is known as the distributive property of multiplication over addition. So, the answer for this expression is D. The distributive property of multiplication over addition.

STEP 7

Finally, let's look at the expression (3+5)(6+7)=(3+5)6+(3+5)7(3+5)(6+7)=(3+5)6+(3+5)7. This expression is also showing the distributive property of multiplication over addition. So, the answer for this expression is D. The distributive property of multiplication over addition.

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