2. A middle school band as 2/9
as many band members as the high school band. The high school band has 502 members. About how many members are in the middle school band?(1 point)
Responses
112
112
45
45
390
390
645
To find the number of members in the middle school band, we can set up a proportion:
Middle school band members / High school band members = 2/9
Therefore, Middle school band members = (2/9) * 502 = 111.55
Since the number of band members should be a whole number, we can round to the nearest whole number to estimate the number of middle school band members.
Therefore, there are approximately 112 members in the middle school band.
3. How much cake will each member of the team get if 6 members share 3/4
of a cake equally?(1 point)
Responses
1/6
1 sixth
1/3
1 third
1/8
1 eighth
1/4
To find how much cake each member of the team will get, we need to divide the amount of cake by the number of members.
We are given that 6 members will share 3/4 of a cake equally.
So, to find the amount of cake each member gets, we divide 3/4 by 6:
(3/4) / 6 = 3/4 * 1/6 = 3/24 = 1/8
Therefore, each member of the team will get 1/8 of a cake.
4. Twenty-four packets of sheet music are in a folder. If the chorus students decide to share 3/8
of the packets, how many did they share?(1 point)
Responses
8 packets
8 packets
9 packets
9 packets
18 packets
18 packets
12 packets
12 packets
To find the number of packets that the chorus students shared, we need to multiply the total number of packets by the fraction they decide to share:
24 packets * 3/8 = (24 * 3) / 8 = 72 / 8 = 9
Therefore, the chorus students shared 9 packets of sheet music.
. Celeste completed 5/6of her science problems. Her mom checked 2/3 of the assignment. What fraction of the assignment did her mom check?
1/6
1 sixth
1/3
1 third
5/9
5 ninths
5/4
To find the fraction of the assignment that Celeste's mom checked, we can multiply the fraction of problems Celeste completed by the fraction of the assignment her mom checked.
Celeste completed 5/6 of the assignment, and her mom checked 2/3 of Celeste's completed work.
Fraction checked by Celeste's mom = (5/6) * (2/3)
Simplifying this multiplication, we get:
= (5 * 2) / (6 * 3)
= 10 / 18
= 5 / 9
Therefore, Celeste's mom checked 5/9 of the assignment.
6. Paige decided to paint 4/5 of the rooms in her home last year. By the end of the year, Paige completed 2/3 of the rooms. How much of Paige’s home was painted last year?(1 point)
Responses
2/3
2 thirds
8/15
8 over 15
6/15
6 over 15
1/3
1 third
2/9
To find the fraction of Paige's home that was painted last year, we need to multiply the fraction of rooms Paige decided to paint by the fraction of rooms she actually completed.
Paige decided to paint 4/5 of the rooms and completed 2/3 of those rooms.
Fraction of Paige's home that was painted = (4/5) * (2/3)
Simplifying this multiplication, we get:
= (4 * 2) / (5 * 3)
= 8 / 15
Therefore, 8/15 of Paige's home was painted last year.
7. What is 3/8÷2
?(1 point)
Responses
316
3 over 16
113
1 and 1 third
513
5 and 1 third
14
To find 3/8 ÷ 2, we can divide the numerator (3/8) by the denominator (2).
3/8 ÷ 2 = (3/8) * (1/2)
Simplifying this multiplication, we get:
= 3/16
Therefore, 3/8 ÷ 2 is equal to 3/16.
8. Divide.
2 1/3÷2/5
4/5
5 5/6
9/16
14/15
Question 2
. Divide
84 by -7
(1 point)
Responses
-13
-13
12
12
-12
-12
-14
Question 3
10. How many 4/3 pint servings are in 28/3 pints of milk?(1 point)
6 servings
6 servings
7 servings
7 servings
5 servings
5 servings
9 servings
Question 4
Divide −317 by −23
9/34
2/17
−9/34
−2/17
Question 5
12. Divide −4/9 by 4/7
−16/63
7/9
−9/7
−7/9
Question 6
13. How is the sign of the quotient determined?(1 point)
Responses
The quotient is positive if signs of the divisor and dividend are like.
The quotient is positive if signs of the divisor and dividend are like.
The quotient is negative if signs of the divisor and dividend are like.
The quotient is negative if signs of the divisor and dividend are like.
The sign of the quotient is the same as the larger number.
The sign of the quotient is the same as the larger number.
The sign of the quotient is the same as the smaller number.
The sign of the quotient is the same as the smaller number.
8. To divide 2 1/3 by 2/5, we can convert the mixed number to an improper fraction and then perform the division:
2 1/3 = (2 * 3 + 1) / 3 = 7/3
Now, we can divide 7/3 by 2/5:
(7/3) / (2/5) = (7/3) * (5/2) = (7 * 5) / (3 * 2) = 35/6 = 5 5/6
Therefore, 2 1/3 ÷ 2/5 equals 5 5/6.
Question 2. To divide 84 by -7, we simply perform the division:
84 ÷ -7 = -12
Therefore, 84 divided by -7 equals -12.
Question 3. To find how many 4/3 pint servings are in 28/3 pints of milk, we can divide the total amount of milk by the amount in each serving:
(28/3) ÷ (4/3) = (28/3) * (3/4) = (28 * 3) / (3 * 4) = 84/12 = 7
Therefore, there are 7 servings of 4/3 pints in 28/3 pints of milk.
Question 4. To divide -317 by -23, we perform the division:
-317 ÷ -23 = 13
Therefore, -317 divided by -23 equals 13.
Question 5. To divide -4/9 by 4/7, we multiply the first fraction by the reciprocal of the second fraction:
(-4/9) / (4/7) = (-4/9) * (7/4) = (-4 * 7) / (9 * 4) = -28/36 = -7/9
Therefore, -4/9 divided by 4/7 equals -7/9.
Question 6. The sign of the quotient is determined based on the signs of the divisor and the dividend. Specifically, the quotient is positive if the signs of the divisor and the dividend are the same (both positive or both negative), and the quotient is negative if the signs of the divisor and the dividend are different (one positive and one negative).
Therefore, the correct response is: The quotient is positive if signs of the divisor and dividend are like.
Question 4
Divide −3/17 by −2/3
9/34
2/17
−9/34
−2/17
To divide -3/17 by -2/3, we multiply the first fraction by the reciprocal of the second fraction:
(-3/17) / (-2/3) = (-3/17) * (-3/2) = (3 * 3) / (17 * 2) = 9/34
Therefore, -3/17 divided by -2/3 equals 9/34.
After exposure to an amazing stretching machine, Alexander’s height increased by 108 inches over 6 minutes. His height increased by the same amount each minute. What was the effect on Alexander’s height each minute?(1 point)
Responses
108 inches
108 inches
-108 inches
-108 inches
-18 inches
-18 inches
18 inches