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)
To find out how many members are in the middle school band, we can set up a proportion using the given ratio:
Middle school band members / High school band members = 2/9.
Since the high school band has 502 members, we can set up the proportion as:
x / 502 = 2/9, where x represents the number of members in the middle school band.
To solve for x, we multiply both sides of the equation by 502:
502 * (x / 502) = (2/9) * 502
x = (2/9) * 502
Multiplying 2/9 by 502, we find that x is approximately:
x ≈ 111.56
Therefore, there are about 112 members in the middle school band.
1. Yesterday, Sarah spent 35 1/2
minutes studying for a test. Emma spent 1 1/2
times that amount studying for a different test. How many minutes did Emma spend studying?
To find out how many minutes Emma spent studying, we start by calculating 1 1/2 times the amount that Sarah spent.
First, let's convert 35 1/2 minutes to an improper fraction for easier calculations. To do this, we multiply the whole number (35) by the denominator (2) and add the numerator (1). This gives us:
35 * 2 = 70
70 + 1 = 71
So, 35 1/2 minutes as an improper fraction is 71/2.
Now, let's calculate 1 1/2 times 71/2.
To multiply a whole number by a fraction, we multiply the whole number by the numerator and divide the result by the denominator. So, we have:
(1 * 71) / 2 = 71/ 2
Therefore, Emma spent 71/2 minutes studying.
How much cake will each member of the team get if 6 members share 3/4
of a cake equally?(1 point)
To determine how much cake each member of the team will get, we need to divide 3/4 of a cake by the number of team members, which is 6.
First, let's convert 3/4 to a decimal. We divide 3 by 4:
3 ÷ 4 = 0.75
So, 3/4 as a decimal is 0.75.
Now, we can divide 0.75 by 6 to find out how much cake each member will get:
0.75 ÷ 6 = 0.125
Therefore, each member of the team will get 0.125 of a cake.
3. How much cake will each member of the team get if 6 members share 3/4
of a cake equally?(1 point)
1/4
1/8
1/3
1/6
To determine how much cake each member of the team will get if 6 members share 3/4 of a cake equally, we need to divide the amount of cake (3/4) by the number of team members (6).
Dividing fractions involves multiplying the numerator of the first fraction by the reciprocal of the second fraction.
So, 3/4 ÷ 6 becomes (3/4) * (1/6).
Multiplying the numerators and denominators, we get (3 * 1) / (4 * 6) = 3/24.
Simplifying the fraction, we have 1/8.
Therefore, each member of the team will get 1/8 of the cake.
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?
To determine how many packets of sheet music the chorus students shared, we need to calculate 3/8 of 24.
To find 3/8 of a number, we multiply that number by 3/8.
So, 3/8 * 24 = (3 * 24) / 8 = 72/8 = 9.
Therefore, the chorus students shared 9 packets of sheet music.
5. Celeste completed 5/6
of her science problems. Her mom checked 2/3
of the assignment. What fraction of the assignment did her mom check?(1 point)
Responses
To determine the fraction of the assignment Celeste's mom checked, we need to multiply the fraction of the assignment Celeste completed (5/6) by the fraction her mom checked (2/3).
Multiplying fractions involves multiplying the numerators together and multiplying the denominators together.
So, (5/6) * (2/3) = (5 * 2) / (6 * 3) = 10/18.
The fraction 10/18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Dividing 10 by 2 and 18 by 2, we get 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)
To determine how much of Paige's home was painted last year, we need to calculate the fraction of the rooms that Paige completed by painting last year.
First, we need to find out what fraction of the rooms Paige completed based on the fraction she decided to paint (4/5) and the fraction she actually completed (2/3).
To find the fraction of completed rooms, we multiply the fraction decided to paint (4/5) by the fraction completed (2/3).
(4/5) * (2/3) = (4 * 2) / (5 * 3) = 8/15.
Therefore, Paige painted 8/15 of her home last year.
what is 3/8 ÷ 2?
To divide 3/8 by 2, we need to multiply 3/8 by the reciprocal of 2, which is 1/2.
So, (3/8) ÷ 2 = (3/8) * (1/2).
To multiply fractions, we multiply the numerators together and the denominators together:
(3 * 1) / (8 * 2) = 3/16.
Therefore, 3/8 ÷ 2 equals 3/16.
2 1/3 ÷ 2/5
To divide 2 1/3 by 2/5, we need to convert the mixed number 2 1/3 into an improper fraction.
To do this, we multiply the whole number (2) by the denominator (3) and add the numerator (1), then place the result over the denominator:
2 * 3 = 6
6 + 1 = 7
So, 2 1/3 as an improper fraction is 7/3.
Now, we can divide 7/3 by 2/5:
(7/3) ÷ (2/5).
To divide fractions, we multiply the first fraction by the reciprocal (inverted form) of the second fraction:
(7/3) * (5/2).
Multiplying the numerators and denominators, we have:
(7 * 5) / (3 * 2) = 35/6.
Therefore, 2 1/3 ÷ 2/5 equals 35/6.
Divide 84 by -7
To divide 84 by -7, we perform the division operation:
84 ÷ -7 = -12.
Therefore, 84 divided by -7 equals -12.
how many 4/3 pint servings are in 28/3 pints of milk?
To determine the number of 4/3 pint servings in 28/3 pints of milk, we need to divide the total amount of milk by the size of each serving.
Dividing 28/3 pints by 4/3 pints, we can multiply the first fraction by the reciprocal (inverted form) of the second fraction:
(28/3) ÷ (4/3).
Multiplying the numerators and denominators, we have:
(28 * 3) / (3 * 4) = 84/12.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 12:
84 ÷ 12 = 7.
Therefore, there are 7 servings of 4/3 pints in 28/3 pints of milk.
divide - 3/17 by -2/3
To divide -3/17 by -2/3, we can multiply the first fraction by the reciprocal (inverted form) of the second fraction:
(-3/17) ÷ (-2/3) = (-3/17) * (3/-2).
Multiplying the numerators and denominators, we have:
(-3 * 3) / (17 * -2) = -9/-34.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 1:
-9 ÷ -34 = 9/34.
Therefore, -3/17 divided by -2/3 equals 9/34.
divide -4/9 by 4/7
To divide -4/9 by 4/7, we can multiply the first fraction by the reciprocal (inverted form) of the second fraction:
(-4/9) ÷ (4/7) = (-4/9) * (7/4).
Multiplying the numerators and denominators, we have:
(-4 * 7) / (9 * 4) = -28/36.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 4:
-28 ÷ 36 = -7/9.
Therefore, -4/9 divided by 4/7 equals -7/9.
How is the sign of the quotient determined?(1 point)
The sign of the quotient is determined by the signs of the dividend (the number being divided) and the divisor (the number dividing the dividend).
If both the dividend and divisor have the same sign (either both positive or both negative), then the quotient will be positive.
If the dividend and divisor have different signs (one positive and one negative), then the quotient will be negative.
In summary, the sign of the quotient is determined by the combination of the signs of the dividend and the divisor.
multiply -1/3 x -5/8
To multiply -1/3 by -5/8, we simply multiply the numerators together and the denominators together.
(-1/3) x (-5/8) = (-1 x -5) / (3 x 8) = 5/24.
Therefore, -1/3 multiplied by -5/8 equals 5/24.
-5(-10)(12) find the product
To find the product of -5, -10, and 12, we multiply the numbers together:
-5 x -10 x 12 = 50 x 12 = 600.
Therefore, the product of -5, -10, and 12 is 600.
16. If the Walkers deducted $850 each month last year from their checking account to pay for childcare, what was the effect on their checking account balance?(1 point)
Responses
To determine the effect on the Walkers' checking account balance, we need more information. Specifically, we need to know the starting balance of their checking account and whether any other deposits or withdrawals were made during the year.
Without this information, we cannot determine the exact effect on their checking account balance. However, we can conclude that each month, $850 was deducted from their checking account for childcare expenses. This means that their account balance would likely decrease by $850 each month as a result of these deductions. The total effect on their balance for the entire year would depend on the starting balance and any other activities in the account.
16. If the Walkers deducted $850 each month last year from their checking account to pay for childcare, what was the effect on their checking account balance?(1 point)
$850
$10,200
-$850
-$10,200
If the Walkers deducted $850 each month last year from their checking account to pay for childcare, the effect on their checking account balance would be a reduction of $850 each month.
Therefore, the correct answer is: -$850.
17. Deborah hired Nick to remove leaves, aerate the lawn, and plant 3 flower beds. If Nick spends 4.2 hours working on Deborah’s lawn, what is his hourly earnings for the job?
Hint: Each price listed in the chart is a flat fee for the service.
To determine Nick's hourly earnings for the job, we need to know the total amount he was paid for the job and the number of hours he worked.
If we are given the total amount he was paid, we can then divide it by the number of hours worked to find his hourly earnings.
However, in this case, we do not have the total amount Nick was paid for the job. Without this information, we cannot determine his hourly earnings for the job.
We would need additional information to calculate Nick's hourly earnings, such as the total amount he was paid for the job or an hourly rate that was agreed upon beforehand.
17. Deborah hired Nick to remove leaves, aerate the lawn, and plant 3 flower beds. If Nick spends 4.2 hours working on Deborah’s lawn, what is his hourly earnings for the job?
Hint: Each price listed in the chart is a flat fee for the service.
375.00
79,76
93.75
89.29
To determine Nick's hourly earnings for the job, we need to have the total amount he was paid for the job. However, none of the provided answer options specify the total payment.
Without knowing the total amount Nick was paid, we cannot calculate his hourly earnings. Therefore, we cannot determine the correct answer based on the given information.
weed control: 70.00
leaf removal: 165.00
lawn cleanup: 225.00
aeration: 90.00
flower planting: 40.00 per flower bed
17. Deborah hired Nick to remove leaves, aerate the lawn, and plant 3 flower beds. If Nick spends 4.2 hours working on Deborah’s lawn, what is his hourly earnings for the job?
Hint: Each price listed in the chart is a flat fee for the service.
375.00
79.76
93.75
89.29
To calculate Nick's hourly earnings for the job, we need to determine the total amount he was paid and divide it by the number of hours he worked.
First, let's calculate the total payment for the services provided by Nick:
Leaf removal: $165.00
Aeration: $90.00
Flower planting (3 beds at $40.00 per bed): $40.00 x 3 = $120.00
Total payment = $165.00 + $90.00 + $120.00 = $375.00
Now, we can calculate Nick's hourly earnings by dividing the total payment by the number of hours worked:
$375.00 ÷ 4.2 hours = $89.29 (rounded to the nearest cent)
Therefore, Nick's hourly earnings for the job would be $89.29.
18. Over the past 8 months, Devon made payments for a total of $936 to pay for internet service. The service is the same amount each month. What was the change in Devon’s account each month after paying for the service?(1 point)
Responses
To find the change in Devon's account each month after paying for the internet service, we need to divide the total payments made ($936) by the number of months (8).
$936 ÷ 8 = $117.
Therefore, the change in Devon's account each month after paying for the service is $117.
19. 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
To find the effect on Alexander's height each minute, we need to divide the total increase in height (108 inches) by the number of minutes (6).
108 inches ÷ 6 minutes = 18 inches.
Therefore, the effect on Alexander's height each minute was an increase of 18 inches.
Find the product
-4/7(-11/2)
To find the product of -4/7 and -11/2, we simply multiply the two fractions together:
(-4/7) * (-11/2) = (4/7) * (11/2).
To multiply fractions, we multiply the numerators together and the denominators together:
(4 * 11) / (7 * 2) = 44/14.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 2:
44 ÷ 14 = 22/7.
Therefore, the product of -4/7 and -11/2 is 22/7.
9 (-3/7)(-1/3)
To find the product of 9, -3/7, and -1/3, we multiply all the numbers together:
9 x (-3/7) x (-1/3).
Multiplying the numbers, we have:
(9) x (-3/7) x (-1/3) = (-27/7) x (-1/3).
To multiply fractions, we multiply the numerators together and the denominators together:
(-27 * -1) / (7 * 3) = 27/21.
Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3:
27 ÷ 21 = 9/7.
Therefore, the product of 9, -3/
Convert 5 18/25
to a decimal.(1 point)