judith's copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)

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judith metz

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judith metz 7 years, 5 months ago

Created this as a copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic).

Name	Status	Author	Last Modified
Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)	Ready to use	Ben Brawn	11/02/2025 23:39
judith's copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)	draft	judith metz	23/10/2017 21:52
Brüche/Divisionen und Multiplikationen, verschiedene Arten den gleichen Wert darzustellen (non-algebraic)	draft	Helge Münnich	02/12/2020 15:42
Merryn's copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)	Ready to use	Merryn Horrocks	07/03/2024 01:07

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Question statement

Without the use of a calculator and without actually calculating the values of each answer, which of the following are equal to $\displaystyle \var{c}\times \frac{\var{a}}{\var{b}}$ ?

Give any introductory information the student needs.

			Name	Type	Generated Value

primes	list	List of 32 items
a	integer	37
b	integer	101
c	integer	73
choices	list	List of 15 items
marks	list	List of 15 items

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shuffle([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131])

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

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Generated value: `list`

[ 37, 101, 73, 47, 19, 71, 41, 2, 79, 11, 23, 13, 97, 17, 89, 61, 113, 109, 31, 7, 131, 67, 127, 53, 59, 5, 103, 3, 107, 43, 29, 83 ]

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Advice

Recall the following:

the bar in a fraction is really just division. For example, $\frac{1}{2}=1\div 2$ .
the order of operations dictates that if a term contains multiplication and division, then you do the operations from left to right. For example, $4\div 1 \times 4 = (4\div 1 )\times 4=16$ .
the order of multiplication is irrelevant. For example, $3\times 4=4\times 3$ .
a whole number can be written as a fraction over 1. For example, $3=\frac{3}{1}$ .
division by a number is equivalent to multiplication by that numbers reciprocal. For example, $12\div 3=12\times \frac{1}{3}$ , and $3 \div \frac{2}{3}=3\times \frac{3}{2}$ .
multiplication by a number is equivalent to division by that numbers reciprocal. For example, $10\times \frac{1}{5}=10\div 5$ .

The above gives us (amoung other things) that

$\displaystyle \var{c}\times \frac{\var{a}}{\var{b}}$	$=\displaystyle\var{c}\times\var{a}\div\var{b}$
	$=\displaystyle\frac{\var{a}}{\var{b}}\times\var{c}$
	$=\displaystyle(\var{a}\div\var{b})\times\var{c}$
	$=\displaystyle\frac{\var{a}}{\var{b}}\times\frac{\var{c}}{1}$
	$=\displaystyle\frac{\var{a}\times\var{c}}{\var{b}}$
	$=\displaystyle\frac{\var{c}\times\var{a}}{\var{b}}$
	$=\displaystyle\frac{\var{c}}{\var{b}}\times\var{a}$
	$=\displaystyle\var{c}\div\var{b}\times\var{a}$
	$=\displaystyle\var{a}\times\frac{\var{c}}{\var{b}}$
	$=\displaystyle\var{a}\times\var{c}\div\var{b}$
	$=\displaystyle\var{a}\times\var{c}\times\frac{1}{\var{b}}$

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This question is used in the following exam:

test your understanding multiplication and division of algebraic terms by Lyn Armstrong in Lyn's workspace.

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judith's copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)

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Taxonomy: mathcentre

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Taxonomy: Context

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judith metz 7 years, 5 months ago

Error in variable testing condition

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Generated value: `list`

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judith's copy of Fractions/division and multiplication, different ways of presenting the same thing (non-algebraic)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

judith metz 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Choose several from a list

Advanced settings

Generated value: `list`