The answer to this question is 3,3
So we are given the expression:
÷ 
When we divide fractions, we must flip the second term and change the sign to multiplication:
And then we multiply across:
Then we can break apart all of the like variables for simplification:
When we simplify variables through division, we subtract the exponent of the numerator from the exponent of the denominator. So we then have:
So then we multiply all of these simplified parts together:
So now we know that the simplified form of the initial expression is: 
.
Step-by-step explanation:
I know you've already done parts a and b, but I'll show the work for that before I do c.
Draw two free body diagrams, one for the car and one for the trailer. The car pulls the trailer forward with a tension force T, so the trailer pulls backward on the car with an equal and opposite force T.
The car also has a 1200 N forward force from the engine, and a 200 N backwards force from resistance.
The trailer has a backwards resistance force of 100 N.
Sum of forces on the car:
∑F = ma
1200 − 200 − T = 900a
1000 − T = 900a
Sum of forces on the trailer:
∑F = ma
T − 100 = 300a
To solve the system of equations, first add the equations together.
1000 − 100 = 1200a
900 = 1200a
a = 0.75 m/s²
Plug back into either equation to find the tension force:
T = 325 N
Now for part c, draw new free body diagrams for the car and trailer. This time, the car is pushing back on the trailer to slow it down. So the trailer is pushing forward on the car with an equal and opposite force. The magnitude of that tension force is given to be 100 N.
The car also has a backwards 200 N force from resistance, and a backwards brake force F.
The trailer has a backwards 100 N force from resistance.
Sum of forces on the car:
∑F = ma
100 − 200 − F = 900a
-100 − F = 900a
Sum of forces on the trailer:
∑F = ma
-100 − 100 = 300a
-200 = 300a
a = -⅔
Plugging into the first equation:
-100 − F = 900 (-⅔)
-100 − F = -600
F = 500 N
Answer:
C) 1 quart
Step-by-step explanation:
So I think maybe the example for the first problem created some confusion, and you may want to have your child take another look.
If we numbered the top half 1 to 9 going from left to right, numbers 1, 2, 6, 7 and 8 are right. They worked because the top number (numerator) perfectly fit into the bottom number (denominator). This is not true for the rest.
The key is to find the largest number that you can think of that will go into BOTH the top and the bottom evenly.
So for number 3: 18/24; 18 does not fit evenly into 24. The highest number that will fit into both is 6, so you divide both top and bottom by 6 and your answer is 3/4.
Number 4: 45/54; the highest number that goes into both is 9, so you divide both top and bottom by 9 and your answer is 5/6.
Number 5: 55/66; the highest number that can go into both is 11, so the answer is 5/6.
Is this making sense?
The bottom, numbering 1 to 9 from left to right. The correct ones are 1, 6 and 9.
For 2: 14/41 is about 15/40. Both can be divided by 5, so the answer is 3/8.
For 3: 20/81 is about 20/80, and 2/8 is close, but can still be divided by 2, so the answer is 1/4.
For 4: 24/49 is closer to 25/50 than 20/50. 25/50 can be divided by 25, so the answer is 1/2.
For 5: it was all correct, but the answer can be further reduced from 2/8 to 1/4.
For 7: 23/72 is about 25/75, and 25 goes into both, so it reduces to 1/3.
For 8: 13/21 is about 15/20, and 5 goes into both, so the answer is 3/4.
As your child continues to learn this, remember that if he or she gets an answer like 2/6 or 6/12, they should ask themselves if they can further reduce the fractions- 2/6 reduces to 1/3, and 6/12reduces to 1/2. I know it's confusing, but they do get the hang of it with practice
