my daughter is doing homework using greatest common factor, greatest common divisor, and prime factorization. She has this problem: Computers in the research room of the history museum are 30 wide, 30 inches apart and at either end of a row 30 inches from the wall. How many computers can fit across a room that is 25 feet wide?
I can do the problem in my head but I don't know how to explain it to her or to tell her how to show her work. What is the teacher looking for on how to solve this problem? I've tried to read the chapter over and over again and it doesn't make sense to me whatsoever.
I also don't quite see how that problem ties in with common factoring, etc.
Unless the teacher is looking for multiples of 5 feet that go into 75
each computer needs 30 inches plus 30 inches to one side, for a total of 60 inches or 5 feet.
So starting with 30 inches on one side of the room we could mark off 5 feet at a time until we reach 25 feet.
so we have 5,10,15,20,25
but that would mean that the first computer would have to be right against the wall.
a rather confusing question for a grade 5
find the prime fractorization of each number .20
To solve this problem, the teacher is likely looking for the application of the concept of greatest common factor and prime factorization to find the maximum number of computers that can fit across the room. Let's break down the steps to solve this problem and explain them in a way that you can explain to your daughter:
Step 1: Understand the problem
First, make sure your daughter understands the dimensions given in the problem. The computers are 30 inches wide, 30 inches apart, and 30 inches from the wall. The room itself is 25 feet wide.
Step 2: Convert units
Since the room width is given in feet and the computer dimensions are given in inches, we need to convert the units to be consistent. There are 12 inches in a foot, so the room width is 25 feet * 12 inches/foot = 300 inches.
Step 3: Find the greatest common factor (GCF)
The greatest common factor (GCF) represents the largest number that divides both the number of computers that can fit across the room width and the number of inches in the room width.
To find the GCF, we need to factorize both numbers, which means expressing them as products of their prime factors.
For the number of computers, which is 30 inches, we can break it down into its prime factors. It can be written as 2 * 3 * 5.
For the room width, which is 300 inches, the prime factorization is 2 * 2 * 3 * 5 * 5.
Step 4: Determine the common factors
Next, we need to find the common factors between the number of computers and the room width. The common factors are the prime factors that both numbers share.
Looking at the prime factorizations, we find that the common factors are 2, 3, and 5.
Step 5: Calculate the GCF
To calculate the GCF, multiply the common factors together. In this case, GCF = 2 * 3 * 5 = 30.
Step 6: Apply the GCF to solve the problem
To find the maximum number of computers that can fit across the room width, divide the width of the room by the GCF. In this case, that would be 300 inches / 30 = 10 computers.
So, the answer is that 10 computers can fit across the room that is 25 feet wide.
To show her work, your daughter can write down the prime factorization of both numbers, find the common factors, calculate the GCF, and then demonstrate the division to find the final answer.
I hope this explanation helps both you and your daughter understand how to solve this problem using greatest common factor and prime factorization.