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

Consider the division expression [tex]7\frac{1}{2} / 2[/tex]. Select all multiplication equations that correspond to this division expression.

[tex]2 * ? = 7\frac{1}{2}[/tex] [tex]7\frac{1}{2} * ?= 2[/tex] [tex]? * 2 = 7\frac{1}{2}[/tex]

[tex]2* 7\frac{1}{2} = ?[/tex] [tex]? * 7\frac{1}{2} = 2[/tex]

Answer:

1. See Explanation

2. [tex]2 * ? = 7\frac{1}{2}[/tex] and [tex]? * 2 = 7\frac{1}{2}[/tex]

Step-by-step explanation:

Solving (a):

Given

[tex]Students = 60[/tex]

[tex]Group = Equal\ Sized[/tex]

Required

Interpret [tex]\frac{60}{5}[/tex] 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

[tex]Quotient = \frac{60}{5}[/tex]

[tex]Quotient = 12[/tex]

For Interpretation 1:

The quotient means: 12 groups

For Interpretation 2:

The quotient means: 12 students

Solving (b):

Given

[tex]7\frac{1}{2} / 2[/tex]

Required

Select all equivalent multiplication equations

Let ? be the quotient of t [tex]7\frac{1}{2} / 2[/tex]

So, we have:

[tex]7\frac{1}{2}/2 = ?[/tex]

Multiply through by 2

[tex]2 * 7\frac{1}{2}/2 = ? * 2[/tex]

[tex]7\frac{1}{2} = ? * 2[/tex]

Rewrite as:

[tex]? * 2 = 7\frac{1}{2}[/tex] --- This is 1 equivalent expression

Apply commutative law of addition:

[tex]2 * ? = 7\frac{1}{2}[/tex] --- This is another equivalent expression