Algebra Readiness Properties of Numbers

1) Which one of the following is the correct answer for 3(x+2)

3x+2

3x+6

X+6

3

The given expression is 3(x+2). To simplify this expression, we distribute the 3 to both terms inside the parentheses. This gives us 3x + 6. Therefore, the correct answer is 3x+6.

Explanation

The given expression is 3(x+2). To simplify this expression, we distribute the 3 to both terms inside the parentheses. This gives us 3x + 6. Therefore, the correct answer is 3x+6.

2) Which property does the following expression represent? (4+7)+3=4+(7+3)

Distributive Property

Associative Property of Multiplication

Associative Property of Addition

Commutative Property of Addition

The given expression represents the Associative Property of Addition. This property states that when adding three or more numbers, the grouping of the numbers does not affect the sum. In the expression, the numbers 4, 7, and 3 are grouped differently on both sides of the equation, but the sum remains the same. This demonstrates the Associative Property of Addition.

Explanation

The given expression represents the Associative Property of Addition. This property states that when adding three or more numbers, the grouping of the numbers does not affect the sum. In the expression, the numbers 4, 7, and 3 are grouped differently on both sides of the equation, but the sum remains the same. This demonstrates the Associative Property of Addition.

3) Which property does the following expression represent? 8 * 1 = 8

Distributive Property

Identity Property of Multiplication

Commutative Property of Multiplication

Identity Property of Addition

The given expression represents the Identity Property of Multiplication. According to this property, when a number is multiplied by 1, the product is equal to the original number. In the given expression, 8 is multiplied by 1, resulting in the product of 8, which is equal to the original number.

Explanation

The given expression represents the Identity Property of Multiplication. According to this property, when a number is multiplied by 1, the product is equal to the original number. In the given expression, 8 is multiplied by 1, resulting in the product of 8, which is equal to the original number.

4) The following expression represents the Identity Property of Multiplication. 3 * 0 = 0

True

False

The given expression, 3 * 0 = 0, does not represent the Identity Property of Multiplication. According to the Identity Property of Multiplication, any number multiplied by 1 will give the same number as the product. In this case, 3 multiplied by 0 does not give the same number as the product, which is 0. Therefore, the statement is false.

Explanation

The given expression, 3 * 0 = 0, does not represent the Identity Property of Multiplication. According to the Identity Property of Multiplication, any number multiplied by 1 will give the same number as the product. In this case, 3 multiplied by 0 does not give the same number as the product, which is 0. Therefore, the statement is false.

5) Find the perimiter of the rectangle shown on the following picture.

4x

12x

6x

8x

The perimeter of a rectangle is found by adding up all the sides. In this case, the rectangle has two sides with length 4x and two sides with length 6x. Adding these lengths together gives us 4x + 4x + 6x + 6x = 12x. Therefore, the perimeter of the rectangle is 12x.

Explanation

The perimeter of a rectangle is found by adding up all the sides. In this case, the rectangle has two sides with length 4x and two sides with length 6x. Adding these lengths together gives us 4x + 4x + 6x + 6x = 12x. Therefore, the perimeter of the rectangle is 12x.

6) Which one of the following are properties of addition?

3 + 0 = 3

3 * 1 = 3

3 + 7 = 7 + 3

All of the above

None of the above

The properties of addition include the commutative property, which states that changing the order of the numbers being added does not change the sum. This is demonstrated by the equation 3 + 7 = 7 + 3. The other equations, 3 + 0 = 3 and 3 * 1 = 3, are not properties of addition.

Explanation

The properties of addition include the commutative property, which states that changing the order of the numbers being added does not change the sum. This is demonstrated by the equation 3 + 7 = 7 + 3. The other equations, 3 + 0 = 3 and 3 * 1 = 3, are not properties of addition.

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7) Watch the following video on distributive property, and evaluate the problem for x=3.

6

3

18

12

The video explains the distributive property, which states that when you multiply a number by a sum or difference, you can multiply each term separately and then add or subtract the results. In this problem, we have the expression 6(3 + x). Since x is given as 3, we can substitute it into the expression to get 6(3 + 3). Simplifying this, we have 6(6), which equals 36. Therefore, the answer is 36.

Explanation

The video explains the distributive property, which states that when you multiply a number by a sum or difference, you can multiply each term separately and then add or subtract the results. In this problem, we have the expression 6(3 + x). Since x is given as 3, we can substitute it into the expression to get 6(3 + 3). Simplifying this, we have 6(6), which equals 36. Therefore, the answer is 36.

Algebra Readiness Properties Of Numbers