Here is the problem: Identify which of the following situations can be represented by 4 divided by 3/4, and explain your reasoning. A) Sue had 3/4 of a room to paint in 4 hours. How much of the room must she paint each hour to finish on time? B) Kendra has 4 yards of electrical wiring to use in setting up her science fair experiment. She needs to cut it into lengths of 3/4 yard. How many pieces will she be able to make from the 4 yards? C) A rotating video camera in the parking garage goes through 4 complete rotations in 3/4 hour. How many rotations will it make in 1 hour? D) In a local farmers' market, 3/4 of the profits are cycled back into the local farming community. If you spend $4 there, how much of your money goes to local farmers? Here are my answers: A) 4 divided by 3/4=3/16 B) 4 divided by 3/4= 16/3= 5 1/3= 5 pieces. C) 4 divided by 3/4 =1/3 D) 3/4 * 4= 3 Is this correct?
Which of your calculations fulfills this requirement?
Identify which of the following situations can be represented by 4 divided by 3/4.
I think it is A, B and C is this correct?
BB -- How can you keep getting different answers for the same problem?
4 / 3/4 = 4 * 4/3 = 16/3 = 5 1/3
5 1/3 makes sense for B and C.
To identify the correct representation for each situation, we need to understand what the division operation is doing in each case and how it relates to the given situation. Let's go through each option one by one:
A) Sue had 3/4 of a room to paint in 4 hours. How much of the room must she paint each hour to finish on time?
In this case, we are dividing the room size by the time taken to paint it. The division represents the amount of work Sue needs to do per hour in order to finish on time. So, to find the answer, we need to divide 4 by 3/4.
To divide a number by a fraction, we multiply the number by the reciprocal (or inverse) of the fraction. The reciprocal of 3/4 is 4/3. Therefore, to divide 4 by 3/4, we multiply 4 by 4/3.
4 * (4/3) = 16/3
So, Sue needs to paint 16/3 (or 5 1/3) parts of the room each hour to finish on time.
B) Kendra has 4 yards of electrical wiring to use in setting up her science fair experiment. She needs to cut it into lengths of 3/4 yard. How many pieces will she be able to make from the 4 yards?
In this case, we are dividing the total length of the wiring by the length needed for each piece. The division will give us the number of pieces Kendra can make from the given amount of wiring. Therefore, to find the answer, we divide 4 by 3/4.
To divide a number by a fraction, we again multiply the number by the reciprocal of the fraction. So, we multiply 4 by 4/3.
4 * (4/3) = 16/3
So, Kendra will be able to make 16/3 (or 5 1/3) pieces from the 4 yards of wiring.
C) A rotating video camera in the parking garage goes through 4 complete rotations in 3/4 hour. How many rotations will it make in 1 hour?
In this case, we are again dividing the total number of rotations by the time taken to determine the rate of rotation per hour. So, to find the answer, we divide 4 by 3/4.
To divide a number by a fraction, we multiply the number by the reciprocal of the fraction. Therefore, we multiply 4 by 4/3.
4 * (4/3) = 16/3
So, the rotating video camera will make 16/3 (or 5 1/3) rotations in 1 hour.
D) In a local farmers' market, 3/4 of the profits are cycled back into the local farming community. If you spend $4 there, how much of your money goes to local farmers?
In this case, we need to find how much of the money spent goes to the local farmers. We know that 3/4 of the profits go to them. Therefore, to find the answer, we multiply $4 by 3/4.
4 * (3/4) = 12/4 = 3
So, $3 of your money goes to local farmers.
Comparing your answers to these explanations, it seems that only option D) is correctly represented. Options A), B), and C) have incorrect representations.
A) Sue needs to paint 16/3 (or 5 1/3) parts of the room each hour to finish on time, not 3/16.
B) Kendra will be able to make 16/3 (or 5 1/3) pieces from the 4 yards of wiring, not 5 pieces.
C) The rotating video camera will make 16/3 (or 5 1/3) rotations in 1 hour, not 1/3.
Therefore, the correct answer is D) 3.