The Distributive Property Quiz Part 2
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Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the expression (7+5)+4⋅13−2
.
(1 point)
To simplify the expression (7+5)+4⋅13−2, we need to follow the order of operations.
First, we perform the addition inside the parentheses:
(7+5) = 12
The expression now becomes:
12 + 4⋅13−2
Next, we perform the multiplication:
4â‹…13 = 52
The expression now becomes:
12 + 52 - 2
Finally, we perform the addition and subtraction in order from left to right:
12 + 52 = 64
64 - 2 = 62
So the simplified expression is 62.
To simplify the expression (7+5)+4⋅13−2, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Step 1: Calculate the value inside the parentheses.
(7 + 5) = 12
Step 2: Perform multiplication.
12 + 4 * 13 - 2 = 12 + 52 - 2
Step 3: Perform addition and subtraction from left to right.
12 + 52 = 64
64 - 2 = 62
Therefore, the simplified expression is 62.
To simplify the given expression, follow the order of operations (also known as PEMDAS or BODMAS) which determines the sequence in which mathematical operations are performed:
P: Parentheses (simplify expressions within parentheses)
E: Exponents (perform any calculations involving exponents)
MD: Multiplication and Division (perform multiplication and division from left to right)
AS: Addition and Subtraction (perform addition and subtraction from left to right)
In this case, we have the expression (7+5)+4⋅13−2. Let's simplify it step by step:
Step 1: Add the numbers within the parentheses:
(7+5) = 12
Step 2: Replace the parentheses with the simplified result:
12+4⋅13−2
Step 3: Perform the multiplication:
4â‹…13 = 52
Step 4: Replace the multiplication with the simplified result:
12+52−2
Step 5: Perform the addition:
12+52 = 64
Step 6: Replace the addition with the simplified result:
64−2
Step 7: Perform the subtraction:
64−2 = 62
Therefore, the simplified expression is 62.
The Distributive Property Quiz Part 1
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Question
Multiple Choice
Use the Distributive Property to simplify the expression.
(–1)(4 – c)
(1 point)
Responses
4 – c
4 – c
–4 + c
–4 + c
4 + c
4 + c
–4 – c
To simplify the expression (–1)(4 – c) using the Distributive Property, we need to distribute the –1 to each term inside the parentheses.
Distributing the –1, we get:
–1 * 4 + –1 * (–c)
Simplifying each term, we have:
–4 + c
Therefore, the correct answer is:
–4 + c
Use the Distributive Property to simplify the expression.
4(2x ‒ 4)
(1 point)
Responses
8x + 4
8 x + 4
8x – 4
8 x – 4
8x – 16
8 x – 16
4x – 16
To simplify the expression 4(2x - 4) using the Distributive Property, we need to multiply each term inside the parentheses by 4.
Distributing the 4, we get:
4 * 2x - 4 * 4
Simplifying each term, we have:
8x - 16
Therefore, the correct answer is:
8x - 16.
Use the Distributive Property to simplify the expression.
(10 + 4y) one-half
(1 point)
Responses
5 + 2y
5 + 2 y
20 + 8y
20 + 8 y
5 + 4y
5 + 4 y
10 + 2y
To simplify the expression (10 + 4y) one-half using the Distributive Property, we need to distribute the one-half to each term inside the parentheses.
Distributing the one-half, we get:
(10 * one-half) + (4y * one-half)
Simplifying each term, we have:
5 + 2y
Therefore, the correct answer is:
5 + 2y.
To which subsets of real numbers does the number –22 belong? Choose all subsets that apply.
(1 point)
Responses
whole numbers
whole numbers
rational numbers
rational numbers
integers
integers
irrational numbers
irrational numbers
natural numbers
The number -22 belongs to the following subsets of real numbers:
- Integers
- Rational numbers
Integers include all whole numbers (positive, negative, and zero) and their opposites. Since -22 is a negative whole number, it is also an integer.
Rational numbers include all numbers that can be expressed as a fraction or ratio of two integers. -22 can be expressed as -22/1, which is a fraction, making it a rational number.
Therefore, the correct responses are:
- Integers
- Rational numbers
What is an algebraic expression for the following word phrase: "6 times the difference of b and p"?
(1 point)
Responses
6b – p
6 b – p
6(b – p)
6( b – p )
6 – bp
6 – bp
6bp
The algebraic expression for the word phrase "6 times the difference of b and p" is 6(b - p).
Therefore, the correct response is:
6(b - p)
What is the simplified form of the expression?
Start Fraction 5 left-parenthesis 14 minus 2 right-parenthesis squared over 2 End Fraction
(1 point)
Responses
60
60
30
30
72
72
360
To simplify the expression 5(14 - 2)^2 / 2, we need to follow the order of operations (PEMDAS).
First, we simplify the expression inside the parentheses:
14 - 2 = 12
Next, we square the result:
12^2 = 144
Now, we can substitute the simplified expression back into the original expression:
5 * 144 / 2
Next, we perform the multiplication:
5 * 144 = 720
Finally, we perform the division:
720 / 2 = 360
Therefore, the simplified form of the expression is 360.
Correct response:
360
Evaluate u + xy, if u = 18, x = 10, and y = 8.
(1 point)
Responses
188
188
36
36
98
98
224
To evaluate the expression u + xy, we substitute the given values for u, x, and y:
u = 18, x = 10, and y = 8.
Substituting these values into the expression, we have:
18 + 10 * 8
Next, we perform the multiplication:
10 * 8 = 80
Substituting this result back into the expression, we have:
18 + 80
Finally, we perform the addition:
18 + 80 = 98
Therefore, u + xy equals 98.
Correct response:
98
Essay
Note: Your teacher will grade your response ensure that you receive proper credit for your answer.
A square field has an area of 479 ft2. What is the approximate length of a side of the field? Give your answer to the nearest foot. Explain your response.
(2 points)
To find the length of a side of the square field, we can use the formula for the area of a square, which is side length squared.
Given that the area of the field is 479 ft^2, we can set up the equation:
side length^2 = 479
To solve for the side length, we need to find the square root of both sides of the equation:
√(side length^2) = √479
This simplifies to:
side length = √479
Now, we need to approximate the value of √479 to the nearest foot.
Using a calculator, we find that √479 is approximately 21.88.
To find the length of a side of the field to the nearest foot, we round 21.88 to the nearest whole number, which is 22.
Therefore, the approximate length of a side of the field is 22 feet.