The second question:
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
