The second question:
Consider the division expression 
. Select all multiplication equations that correspond to this division expression.
Answer:
1. See Explanation
2. and
Step-by-step explanation:
Solving (a):
Given
Required
Interpret 
in 2 ways
<u>Interpretation 1:</u> Number of groups if there are 5 students in each
<u>Interpretation 2:</u> Number of students in each group if there are 5 groups
<u>Solving the quotient</u>
<u>For Interpretation 1:</u>
The quotient means: 12 groups
<u>For Interpretation 2:</u>
The quotient means: 12 students
Solving (b):
Given
Required
Select all equivalent multiplication equations
Let ? be the quotient of t
So, we have:
Multiply through by 2
Rewrite as:
--- This is 1 equivalent expression
Apply commutative law of addition:
--- This is another equivalent expression
Answer:
2
Step-by-step explanation:
C is too small to have more.
In order to solve this, you have to set up a systems of linear equations.
Let's say that children = c and adults = a
30a + 12c = 19,080
a + c = 960
I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.
a + c = 960
- c - c
---------------------- ⇒ Step 1: Solve for either a or c in either equation.
a = 960 - c
20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
19,200 - 8c = 19,080
- 19,200 - 19,200
---------------------------------- ⇒ Step 2: Substitute in the value you got for a or c
8c = -120 into the opposite equation.
------ ---------
8 8
c = -15
30a + 12(-15) = 19,080
30a - 180 = 19,080
+ 180 + 180
-------------------------------
30a = 19,260
------- -----------
30 30
a = 642
__________________________________________________________
I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong.
Answer: 
Step-by-step explanation:
Since you did not indicate what you need to do, I assume that you have to write an expression using the sentence given in the problem.
In order to solve this exercise, it is importat to remember the following information:
1. The quotient is the result of a division.
2. The sum is the result of an addition.
3. The word "twice" indicates a multiplicatio by 2.
4. The word "cube" indicates an exponent 3.
Then, keeping on mind the explained above and the data given in the exercise, you know that:
-The sum of 
and 
can be expressed as:
- Twice the cube of 
can be expressed in the following form:
Therefore, you can dermine that "the quotient of the sum of and and twice the cube of " is represented with the following expression:
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