Question

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

Answer 1

The second question:

Consider the division expression
`7(1)/(2) / 2`. Select all multiplication equations that correspond to this division expression.

`2 * ? = 7(1)/(2)`
`7(1)/(2) * ?= 2`
`? * 2 = 7(1)/(2)`

`2* 7(1)/(2) = ?`
`? * 7(1)/(2) = 2`

Answer:

1. See Explanation

2.
`2 * ? = 7(1)/(2)` and
`? * 2 = 7(1)/(2)`

Explanation:

Solving (a):

Given

`Students = 60`

`Group = Equal\ Sized`

Required

Interpret
`(60)/(5)` 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

`Quotient = (60)/(5)`

`Quotient = 12`

For Interpretation 1:

The quotient means: 12 groups

For Interpretation 2:

The quotient means: 12 students

Solving (b):

Given

`7(1)/(2) / 2`

Required

Select all equivalent multiplication equations

Let ? be the quotient of t
`7(1)/(2) / 2`

So, we have:

`7(1)/(2)/2 = ?`

Multiply through by 2

`2 * 7(1)/(2)/2 = ? * 2`

`7(1)/(2) = ? * 2`

Rewrite as:

`? * 2 = 7(1)/(2)` --- This is 1 equivalent expression

Apply commutative law of addition:

`2 * ? = 7(1)/(2)` --- This is another equivalent expression