During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Find the quotient. Explain what the quotient would mean in each of the two interpretations you described. Consider the division expression 712÷2 7 1 2 ÷ 2 . Select all multiplication equations that correspond to this division expression. 2⋅?=712 2 ⋅ ? = 7 1 2 712⋅?=2 7 1 2 ⋅ ? = 2 2⋅712=? 2 ⋅ 7 1 2 = ? ?⋅712=2 ? ⋅ 7 1 2 = 2 ?⋅2=712

The second question:

Consider the division expression . Select all multiplication equations that correspond to this division expression.

1. See Explanation

2.     and    

Step-by-step explanation:

Solving (a):

Given

Required

Interpret in 2 ways

Interpretation 1: Number of groups if there are 5 students in each

Interpretation 2: Number of students in each group if there are 5 groups

Solving the quotient

For Interpretation 1:

The quotient means: 12 groups

For Interpretation 2:

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

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.