Mr. Bryan's class has 60 students. 1/4
of the students stay for tutoring on Monday. If Mr. Bryan equally divides the students that stay for tutoring into 5 groups, how many students are in each group
1/4 of 60 students is (1/4)*60 = <<1/4*60=15>>15 students.
Therefore, there are 15 students/5 groups = <<15/5=3>>3 students in each group. Answer: \boxed{3}.
Mr. Bryan's class has 60 students. 1/4
of the students stay for tutoring on Monday. If Mr. Bryan equally divides the students that stay for tutoring into 5 groups, how many students are in each group?
Responses
A 33
B 55
C 1212
D 1515
1/4 of 60 students is equal to (1/4) * 60 = 15 students.
If Mr. Bryan equally divides the students into 5 groups, each group will have 15 students / 5 = 3 students.
Therefore, the answer is 3 students per group, which is option A.
Factor this expression completely.
35x − 40
Responses
A 5(7x − 8)5(7x − 8)
B 5(7x + 8)5(7x + 8)
C 7(5x + 8)7(5x + 8)
D 7(5x − 8)
To factor the expression 35x - 40, we need to look for the greatest common factor (GCF) of the two terms.
The GCF of 35x and 40 is 5.
We can then factor out the GCF from each term:
35x - 40 = 5(7x) - 5(8)
This can be further simplified:
35x - 40 = 5(7x - 8)
Therefore, the expression is factored completely as option A: 5(7x - 8).
Which expression is equivalent to 2.2 − 0.5(0.6x − 1.8) ?
Responses
A 0.3x + 1.30.3x + 1.3
B 0.3x + 3.10.3x + 3.1
C 1.3 − 0.3x1.3 − 0.3x
D 3.1 − 0.3x
We can start simplifying the expression by distributing the -0.5 to the terms inside the parentheses:
2.2 - 0.5(0.6x - 1.8) = 2.2 - 0.5*0.6x + 0.5*1.8
Simplifying further:
2.2 - 0.3x + 0.9
Combining like terms:
(2.2 + 0.9) - 0.3x = 3.1 - 0.3x
Therefore, the expression is equivalent to 3.1 - 0.3x, which is option D.
(h + 12) + (p + 24)
Responses
The expression (h + 12) + (p + 24) can be simplified by combining like terms:
(h + 12) + (p + 24) = h + p + 12 + 24
Simplifying further:
h + p + 36
Therefore, the simplified form of the expression is h + p + 36.
Which number sentence shows how the distributive property can be used to represent the area of the blue rectangle?
Responses
A (9 + 6) × (9 + 11)(9 + 6) × (9 + 11)
B (9 × 6) + (9 × 11)(9 × 6) + (9 × 11)
C 11(6 + 9)11(6 + 9)
D 9 × 6 × 11
The distributive property states that a(b + c) = ab + ac. In this case, we are trying to represent the area of the blue rectangle.
The area of a rectangle with length 9 and width 6 can be represented as 9 × 6.
If we add the width of the blue rectangle (11) to the length of the blue rectangle (9), we get (9 + 11). Using the distributive property, we can expand this expression as 9 × (9 + 11).
Therefore, the number sentence that shows how the distributive property can be used to represent the area of the blue rectangle is option C: 11(6 + 9).
A board 6 1/8
feet in length is shortened by having 2 1/12
feet cut off one end. The length of the shortened board is
To find the length of the shortened board, we need to subtract the amount that was cut off from the original length.
The original length of the board is 6 1/8 feet, which can be written as an improper fraction: 49/8 feet.
The amount that was cut off is 2 1/12 feet, which can be written as an improper fraction: 25/12 feet.
To subtract the fractions, we need a common denominator. The least common multiple of 8 and 12 is 24.
Converting the fractions to have a denominator of 24:
49/8 = (49/8) * (3/3) = 147/24
25/12 = (25/12) * (2/2) = 50/24
Subtracting the fractions:
147/24 - 50/24 = 97/24
Converting the resulting fraction back to a mixed number:
97/24 = 4 1/24
Therefore, the length of the shortened board is 4 1/24 feet.
Factor this expression completely.
45x − 18y + 36
To factor the expression completely, we look for the greatest common factor (GCF) of the terms. The GCF of 45x, -18y, and 36 is 9.
Factoring out the GCF from each term:
45x - 18y + 36 = 9(5x) - 9(2y) + 9(4)
Simplifying further:
45x - 18y + 36 = 9(5x - 2y + 4)
Therefore, the expression is factored completely as 9(5x - 2y + 4).
Simplify 3 - (4x - 5) + 6.
To simplify the expression 3 - (4x - 5) + 6, we can begin by simplifying the expression inside the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we combine like terms:
3 - 4x + 5 + 6 = (3 + 5 + 6) - 4x
Simplifying further:
(3 + 5 + 6) - 4x = 14 - 4x
Therefore, the simplified form of the expression is 14 - 4x.
Simplify 3 - (4x - 5) + 6.
Responses
A 12x + 2112x + 21
B 4x + 144x + 14
C 4x + 44x + 4
D -4x + 14-4x + 14
E -4x + 4
To simplify the expression 3 - (4x - 5) + 6, we need to distribute the negative sign to the terms inside the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we can combine like terms:
3 - 4x + 5 + 6 = (3 + 5 + 6) - 4x = 14 - 4x
Therefore, the simplified form of the expression is 14 - 4x. None of the given responses match with this simplified form, so the correct answer would be none of the above.
Simplify 3 - (4x - 5) + 6.
Responses
A 12x + 21
B 4x + 14
C 4x + 4
D -4x + 14
E -4x + 4
To simplify the expression 3 - (4x - 5) + 6, we need to distribute the negative sign to the terms inside the parentheses:
3 - (4x - 5) + 6 = 3 - 4x + 5 + 6
Next, we can combine like terms:
3 - 4x + 5 + 6 = -4x + 14
Therefore, the simplified form of the expression is -4x + 14, which matches with option D: -4x + 14.
Divide -4/17 by - 3/4
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of -3/4 is -4/3.
So, we have (-4/17) / (-3/4) = (-4/17) * (-4/3).
Multiplying the numerators and denominators:
(-4*-4)/(17*3) = 16/51.
Therefore, -4/17 divided by -3/4 is equal to 16/51.
Cindy bought 5 dresses for $20 each and 3 pairs of shoes for $20 each. She used this expression to calculate the total amount she spent.
(5 × 20) + (3 × 20)
What is another expression to calculate the total amount spent?
Responses
A (5 + 3) × 20(5 + 3) × 20
B 5 × (20 + 3)5 × (20 + 3)
C 5 × 20 × 35 × 20 × 3
D (5 + 20) × (3 + 20)
Another expression to calculate the total amount spent can be obtained by using the distributive property to multiply the quantities separately:
(5 × 20) + (3 × 20) = 5 × 20 + 3 × 20 = (5 + 3) × 20
Therefore, the equivalent expression to calculate the total amount spent is option A: (5 + 3) × 20.