To perform the partial-quotients algorithm, follow these steps:
1. Determine the largest multiple of the divisor that fits into the dividend without exceeding it. This multiple becomes the partial quotient.
2. Multiply the divisor by the partial quotient and write the product below the dividend.
3. Subtract the product from the dividend to find the remainder.
4. Bring down the next digit of the dividend (if there is one) to the right of the remainder, forming a new dividend.
5. Repeat steps 1-4 until there are no more digits to bring down or the remainder is less than the divisor.
6. The sum of the partial quotients is the quotient, and the final remainder is the remainder of the division.
Let's apply these steps to an example division: dividing 154 by 3.
1. The largest multiple of 3 that fits into 15 is 15 (5 groups of 3), so the first partial quotient is 5.
2. Multiply 3 by 5 to get 15, and write it below the 15 in the dividend.
3. Subtract 15 from 15 to get a remainder of 0.
4. Bring down the next digit, 4, to get a new dividend of 04.
5. The largest multiple of 3 that fits into 4 is 3 (1 group of 3), so the second partial quotient is 1.
6. Multiply 3 by 1 to get 3, and write it below the 4 in the dividend.
7. Subtract 3 from 4 to get a final remainder of 1.
The quotient is the sum of the partial quotients, which is 5 + 1 = 6, and the remainder is 1. So, 154 divided by 3 is 6 with a remainder of 1.
The partial-quotients algorithm is particularly useful for dividing large numbers because it breaks down the division into more manageable parts. It also helps with understanding the concept of division as a process of repeated subtraction.
PLEASE HELP URGENT PLEASE HELP apply the definition of subtraction and properties of operations to find the result. 1/8 - 3/7 - 3/8
2. A pool company is trying out several new drains. Drain A empties a pool at a rate of 2 gal/min. Drain B empties a pool at a rate of 5 gal/min. One pool has 108 gal of water in it. Write an equation for each drain that shows the amount of time it takes to empty the pool. Then solve each equation showing your work.
108/2=54*60= 34min40sec then 108/5=21*60=13min
sorry if this is incorrect your question was a little confusing
The Equations are 2x = 108 and 3y = 108.
Drain A takes 54 minutes and Drain B takes 36 minutes to empties the pool.
What is Unit rate?When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another.
Given:
Drain A empties a pool at a rate of 2 gal/min.
Drain B empties a pool at a rate of 5 gal/min.
One pool has 108 gal of water in it.
So, let Drain A empties the pool in x minutes and Drain B in y minutes.
Then, Drain A:
2x = 108
x= 54 minutes
and, Drain B:
3y = 108
y= 36 minutes
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There are two buildings bisede each ather that are 47feet and 31 feet high. The buildings are 12 feet apart. What is the distance between the rooftop of the bluilfings
The distance between the rooftops of two buildings, one 47 feet high and the other 31 feet high with a 12 feet gap between them, is 20 feet, as calculated using the Pythagorean theorem.
To determine the distance between the rooftops of two buildings with different heights, we should envision a right-angled triangle where the buildings form the two vertical legs, and the distance between them forms the base.
The height difference of the buildings gives us one leg of the triangle (47 feet - 31 feet = 16 feet), and the distance between them gives us the other leg (12 feet).
Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, we can calculate the length of the hypotenuse, which is the distance between the rooftops.
The formula is c = ( √{a² + b²} ), where a and b represent the legs of the triangle, and c represents the hypotenuse.
For our problem:
Leg a (height difference): 16 feet
Leg b (distance apart): 12 feet
Plug the values into the formula:
c = √{16² + 12²}
c = √{256 + 144}
c = √{400}
c = 20 feet
So, the distance between the rooftops of the buildings is 20 feet.
show two ways five people can share a 3 segment chewy fruit
Jordan and Jake each work during the summer. Jordan earns $9 per hour at her job. Jordan also gets a $10 weekly allowance. Jordan displayed her earnings in a table.
Hours: 0 1 2 3 4 5 6 7 8
Earnings: 10 19 28 37 46 55 64 73 82
Jake earns $6.50 per hour at his job. Jake also gets a $15 weekly allowance. Jake displayed his earnings in a graph. How many hours will it take for Jordan and Jake to earn the same amount of money?
I am desperate!!!
To find out when Jordan and Jake will earn the same amount, we need to set their earnings equations equal to each other and solve for the number of hours worked. The resulting value will be the number of hours at which they both earn the same amount.
Explanation:To determine the number of hours it will take for Jordan and Jake to earn the same amount of money, we need to solve an equation that sets their earnings equal to each other.
For Jordan, her earnings (EJ) are calculated as $9 per hour plus a $10 allowance. So, we write this as an equation:
EJ = 9h + 10.
Similarly, for Jake, his earnings (EJk) are calculated as $6.50 per hour plus a $15 allowance. So, his earning equation is given by:
EJk = 6.5h + 15.
To find when they earn the same, we set the two equations equal to each other:
9h + 10 = 6.5h + 15
By simplifying the equation, it results in 'h', which represents the number of hours needed for Jordan and Jake to earn the same amount of money.
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Brand X costs $2.40 for 16 ounces. Brand Y costs $1.92 for 12 ounces. Find the unit price of each brand. Which brand is the better buy? Please Help! Thanks
To find the unit price, divide the cost by the number of ounces for each brand. Brand X has a unit price of $0.15 per ounce, while Brand Y has a unit price of $0.16 per ounce. Brand X is the better buy because it has a lower unit price.
Explanation:To find the unit price of each brand, we need to divide the cost by the number of ounces for each brand.
Brand X: Unit Price = $2.40 / 16 ounces = $0.15 per ounce
Brand Y: Unit Price = $1.92 / 12 ounces = $0.16 per ounce
Therefore, Brand X is the better buy because it has a lower unit price.
What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3,−4) ?
HELP ME ON THESE THREE QUESTIONS!!!!!!!!!!!!!!!!!!!!!!
Octavio used a brand new 6-hour tape to record some television shows. He recorded a movie that is 1 16/32 hours long and a cooking show that is 1 2/8 hours long. How much time is left on the tape?
Betty is making punch for a party. She needs a total of 9/10 gallon of water to add to fruit juice. In one container she has 1/3 gallons of water, and in another she has 2/5 gallons of water. How much more water does she need?
Zac moved 1/5 of the things from his old bedroom to his new dorm room in 32 6/12 minutes. How long will it take in hours, minutes, and seconds?
**Use hr for hour, min for minutes, and sec for seconds.
Josh is training to run in a half-marathon. So far this week, he has run 6 3/8 miles on each of the three days of training. Assuming Josh keeps this up, what is the total distance Josh runs in 3 weeks?
Sally has 6 boxes of colored pencils only three of the boxes contain 12 colored pencils each .the remaining boxes each contain 20 colored pencils.she packs the colored pencils into 8 packets.how many pencils are there in each packet??
The number of people that belong to a certain social website is 412 and growing at a rate of 5% every month. How many members will there be in 9 months? (round to the nearest whole number)
Any and all help is appreciated!
Answer: 639
Step-by-step explanation:
Given: The number of people that belong to a certain social website=412
Since they are increasing at the rate of 5% every month .
The number of members of after x months is given by exponential growth function, i.e. [tex]y=A(1+r)^x[/tex], where A is the initial amount , r is the growth rate
From question, A=412
r=5%=0.05
x=9 months
Therefore, [tex]y=412(1+0.05)^9=412(1.05)^9=412\times1.551=639.1356\approx639[/tex]
hence, there will be 639 members agter 9 months.
45% of $432 =
Show work
what is 2/300 as a fraction and decimal
Fractional equivalent of 2/300 is 1/150 .
Decimal equivalent of 2/300 is 0.0066.
Given,
2/300
Here,
To get the fractional equivalent of 2/300
Divide numerator and denominator by the common factor,
2 / 2= 1
300 / 2= 150
Simplified fractional form,
= 1/150.
Decimal equivalent of 2/300,
Divide 2 by 300
So,
2/300 = 0.0066
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City A: 3% City B: 4.1% City C: 2.9% City D: 3.2% Tom wants to buy a sweater for $30. In witch city will it be lest expensive?
Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not correct. Find the correct answer.
A mule deer can run one over four of a mile in 25 seconds. At this rate, which expression can be used to determine how fast a mule deer runs in miles per hour?
twenty-five seconds over one-fourth mile = 36 miles per hour
one-fourth mile over twenty-five seconds = 36 miles per hour
one-fourth mile over twenty-five seconds = 100 miles per hour
twenty-five seconds over one-fourth mile = 100 miles per hour
The correct expression to determine how fast a mule deer runs in miles per hour is one-fourth mile over twenty-five seconds = 36 miles per hour.
To find the speed of the mule deer in miles per hour, we need to convert the time from seconds to hours and then use the formula for speed, which is distance divided by time.
First, let's convert 25 seconds into hours. There are 3600 seconds in an hour, so:
25 seconds * (1 hour / 3600 seconds) = 25/3600 hours
Now, we know that the mule deer runs one-fourth of a mile in 25 seconds. To find the speed in miles per hour, we divide the distance by the time in hours:
Speed (mph) = Distance (miles) / Time (hours)
Using the conversion above, we have:
Speed (mph) = (1/4 mile) / (25/3600 hours)
To simplify this, we multiply the numerator and denominator by 4 to get rid of the fraction in the numerator:
Speed (mph) = (1 mile) / (25/900 hours)
Now, we multiply the denominator by 900 to get the time in hours:
Speed (mph) = (1 mile) / (25/900 * 900 hours)
Speed (mph) = (1 mile) / (25 hours)
Next, we need to find out how many 25-hour intervals there are in one hour. To do this, we divide 1 by 25:
Speed (mph) = 1 mile * (1/25 hours)
Speed (mph) = 1/25 miles per hour
Since there are 25 intervals of 1/25 hours in one hour, the mule deer can cover 25 intervals of 1/4 mile in one hour:
Speed (mph) = 25 * (1/4 mile) per hour
Speed (mph) = 25/4 miles per hour
Speed (mph) = 6.25 miles per hour
However, this result does not match any of the options given in the question. It seems there was a mistake in the calculation. Let's correct it:
Speed (mph) = (1/4 mile) / (25/3600 hours)
Speed (mph) = (1/4) / (25/3600)
Speed (mph) = (1 * 3600) / (4 * 25)
Speed (mph) = 3600 / 100
Speed (mph) = 36 mph
This is the correct calculation. Therefore, the expression that represents the speed of the mule deer in miles per hour is one-fourth mile over twenty-five seconds equals 36 miles per hour.
Use division to rename 8/10
if one banch of cookies call for 5 eggs, how many banches can you make with 24 eggs.will there be any left over.
For a house call, a veterinarian charges $70, plus $40 an hour.
a. Write an equation that represents the total fee yy (in dollars) the veterinarian charges for a visit lasting xx hours.
daphne was given a riddle to solve the sum of two consecutive positive integers is 71 find the two positive integers
Two consecutive positive integers that sum to 71, a simple equation can be used leading to the solution that the integers are 35 and 36.
Tasked with finding two consecutive positive integers whose sum is 71. To solve this, let's represent the smaller integer as n, which means the next consecutive integer is n+1. According to the riddle, the sum of these two integers is 71:
n + (n + 1) = 71
Solving this equation:
2n + 1 = 71
2n = 71 - 1
2n = 70
n = 35
The smaller integer is 35, and the next consecutive integer is 36. Therefore, the two consecutive positive integers are 35 and 36.
Without dividing how can you decide wether the quotient of 7.16 * 4 will be less than or greater than 2
write a word problem that involves dividing by a decimal .include a picture of solution using a model
A word problem is,
"A member of the school track team ran for a total of 179.3 miles in practice over 61.5 days. About how many miles did he average per day?
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
a word problem that involves dividing by a decimal .include a picture of solution using a model
given by,
"A member of the school track team ran for a total of 179.3 miles in practice over 61.5 days. About how many miles did he average per day?"
(Explanation is attached)
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what is 3/22 tines 33
179.4 ÷ 2.3 plz help meh
To make a dark orange color , Ron Mixes 3 oz of red paint woth 2 oz of yellow paint . Write the ratio of red paint to yellow paint three ways .
Sarah and her friends picked 3 3/4 pints of blueberries. After they ate some of the blueberries, only 2 1/3 pints remained.
How many pints of blueberries did Sarah and her friends eat?
Answer: 1 5/12
Step-by-step explanation:
2 1/3 = 7/4
3 3/4 = 15 / 4
The amount they eat = The amount they picked - The amount they remained
The amount they eat = 15 / 4 - 7/3
=45-28 / 12
=17/12
= 1 5/12
John swam 0.86 km each day for 3 weeks. How many meters did he swim in those 3 weeks?
In a shipment of 850 widgets, 32 are found to be defective. At this rate, how many defective widgets could be expected in 22,000 widgets? Round to the nearest whole number.
What equation is graphed in this equation?
A. Y-3= 3/2(x+1)
B. Y+2= -3/2(x-2)
C. Y+1= -2/3(x-3)
D. Y-4= -2/3(x+2)
4 • 2 - 3 = -2 • 2 + 9
Edgar used 10 x d to represent the number of pennies in d dollars. Is this reasonable?