etain's copy of Find numbers modulo a base

Error

There was an error loading the page.

Contributors

etain kiely

Feedback

From users who are members of etain's workspace :

etain kiely

said

Ready to use

7 years, 1 month ago

History

○

etain kiely 7 years, 1 month ago

Gave some feedback: Ready to use

○

etain kiely 7 years, 1 month ago

Created this as a copy of Find numbers modulo a base.

Name	Status	Author	Last Modified
Find numbers modulo a base	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Numbers Week 2 -1	draft	Mark Hodds	16/10/2016 20:41
Inbbavathie's copy of Find numbers modulo a base	draft	Inbbavathie Ravi	24/07/2017 14:31
etain's copy of Find numbers modulo a base	Ready to use	etain kiely	04/03/2018 20:43

There is one other version that you do not have access to.

Question statement

Find the following numbers modulo the given number $n$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	172
r1	integer	90
r2	integer	12
m	integer	12
n	integer	14
a1	integer	7566
r	integer	4
m1	integer	4
m2	integer	3
n1	integer	1869
n2	integer	513
a2	integer	1551

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
m*n+r

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

172

← Depends on:

→ Used by:

Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\var{a} \bmod \var{n}=$ Gap 0.
Input your answer as an integer $a$ , $0 \le a \le \var{n-1}$ .
$\var{a1} \bmod \var{n1}=$ Gap 1.
Input your answer as an integer $b$ , $0 \le b \le \var{n1-1}$ .
$\var{a2} \bmod \var{n2}=$ Gap 2.
Input your answer as an integer $c$ , $0 \le c \le \var{n2-1}$ .

Advice

a)

We seek a number

$r=\var{a} \bmod \var{n} \implies \var{a} = m\var{n}+r$

where $m$ is a positive integer and $0 \le r \le \var{n-1}$ .

This is achieved by dividing $\var{a}$ by $\var{n}$ and we find that:

$\begin{align} \frac{\var{a}}{\var{n}} &= \var{m}+\frac{\var{r}}{\var{n}} \\ \implies \var{a} &= \var{m}\times \var{n}+\var{r} \end{align}$

on multiplying through by $\var{n}$ .

Hence $r=\var{r}$ and $\var{a} \bmod \var{n}=\var{r}$ .

You can use your calculator to find this as follows:

Divide $\var{a}$ by $\var{n}$ to get

$\frac{\var{a}}{\var{n}}=\var{a/n}=\var{m}+\var{a/n-m}$

Then multiplying $\var{a/n-m}$ by $\var{n}$ gives the remainder, i.e.

$\var{a/n-m}\times \var{n} = \var{r}$

This must be an integer if no error is introduced, but the calculator result will be either an integer or very close to an integer – so you need to round to the integer in that case.

b)

As in a),

$\frac{\var{a1}}{\var{n1}}=\var{m1}+\frac{\var{r1}}{\var{n1}}$

So $\var{a1} \bmod \var{n1} = \var{r1}$

c)

$\frac{\var{a2}}{\var{n2}}=\var{m2}+\frac{\var{r2}}{\var{n2}}$

So $\var{a2} \bmod \var{n2} = \var{r2}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

etain kiely 7 years, 1 month ago

etain kiely 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

Loading...

Error

etain's copy of Find numbers modulo a base

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

etain kiely 7 years, 1 month ago

etain kiely 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`