J. Richard's copy of Decimals to fractions

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J. Richard Snape

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6 years, 5 months ago

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Anna Strzelecka was given access to the J. Richard's copy of Decimals to fractions 5 years, 7 months ago

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J. Richard Snape 6 years, 5 months ago

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J. Richard Snape 6 years, 5 months ago

Created this as a copy of Decimals to fractions.

Name	Status	Author	Last Modified
Decimals to fractions	Ready to use	Lauren Richards	20/11/2019 14:47
J. Richard's copy of Decimals to fractions	Ready to use	J. Richard Snape	05/12/2022 15:24
Dezimalzahlen in Bruchzahlen umwandeln	Ready to use	Ulrich Görtz	17/11/2024 18:33

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Question statement

Fractions can be equivalently represented as decimals and vice versa. One form may be more useful in a context than another and it is useful to practise how to change between them.

Have a go at these questions involving fractions and decimals, remembering to write your answer in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	0.9
b	number	0.25
c	integer	6
d	number	0.4
b_	number	25
b_coprime	number	1
d_coprime	number	2
answer	integer	54
cround	rational	2

			Name	Type	Generated Value

f	number	0.228
f2	number	228
mygcd	number	4
h	integer	3
j	integer	2
k	integer	7
f3	number	57
f4	number	250
f1000	integer	1000
numerator	integer	324
g	integer	99
gcd1	number	9
numerator_coprime	number	36
g_coprime	number	11

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.1,0.3,0.7,0.9)

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: `number`

0.9

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Gap 0." - Minimum accepted value
"Part a)" → "Gap 0." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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8. Gap Gap 7. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

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

Express these common decimals as their fraction equivalent.

$\var{a}=$ Gap 0. Gap 1.

ii)

$\var{b}=$ Gap 2. Gap 3.

iii)

$\var{d}=$ Gap 6. Gap 7.

iv)

$0.\dot{\var{c}}=$ Gap 4. Gap 5.

Advice

a)

To convert a decimal into a fraction, firstly place the decimal over $1$ as a fraction, and then multiply both the numerator and denominator by $10$ for however many decimal places the decimal has. For example, if the decimal was $0.1$ , you would multiply the fraction by $10$ as there is one decimal place. If the decimal was $0.01$ , you would multiply it by $100$ , as there are two decimal places.

$\var{a}$

$\frac{\var{a}}{1}\times\frac{10}{10}=\frac{\var{10a}}{10}\text{.}$

ii)

$\var{b}$

$\frac{\var{b}}{1}\times\frac{100}{100}=\frac{\var{100b}}{100}=\simplify{{100b}/{100}}\text{.}$

iii)

$\var{d}$

$\frac{\var{d}}{1}\times\frac{10}{10}=\frac{\var{10d}}{10}=\simplify{{10d}/{10}}\text{.}$

iv)

$0.\dot{\var{c}}$

To convert a recurring decimal to a fraction, the first step is to set up a simple equation where

$x=0.\dot{\var{c}}\text{.}$

By multiplying both sides by $10$ , we can gain another simple equation where

$10x=\var{c}.\dot{\var{c}}\text{.}$

By subtracting one equation from the other, we can find the fraction equivalent of the recurring decimal.

$\begin{align} &&\var{c}.\dot{\var{c}}&={10}x\\ -&&{0.\dot{\var{c}}}&=x\\ &&\overline{\qquad} & \overline{\qquad}\\ &&{\var{c}}&=9x\\ \\ &&\frac{\var{c}}{9}&=x \end{align}$

$\displaystyle\frac{\var{c}}{9}$ simplifies to $\simplify{{{c}}/{9}}$ by dividing by $3$ and therefore, $0.\dot{\var{c}}=\simplify{{{c}}/{9}}$ in its fractional form.}

b)

$\displaystyle\var{f}$

$\var{f}\times\frac{\var{f1000}}{\var{f1000}}=\frac{\var{f2}}{\var{f1000}}\text{.}$

From this, we can look to see if we can cancel down the fraction by finding the highest common divisor between the numerator and denominator. This is $\var{mygcd}$ .

Therefore, it is not possible to simplify the answer any further and the final answer is

Simplifying by this amount gives the final answer

$\frac{\var{f3}}{\var{f4}}.$

c)

$\var{h}.\dot{\var{j}}\dot{\var{k}}.$

To convert a recurring decimal to a fraction, the first step is to set up a simple equation where,

$x=\var{h}.\dot{\var{j}}\dot{\var{k}}.$

By multiplying both sides by $100$ to isolate the recurring section on the left hand side of the decimal point, we can gain another simple equation

$100x=\var{h}\var{j}\var{k}.\dot{\var{j}}\dot{\var{k}}.$

Now that we have two equations in terms of $x$ , we can subtract one from the other and solve to get a value of $x$ .

$\begin{align} &&\var{h}\var{j}\var{k}.\dot{\var{j}}\dot{\var{k}}&=100x\\ -&&\var{h}.\dot{\var{j}}\dot{\var{k}}&=x\\ &&\overline{\qquad} & \overline{\qquad} \\ &&{{\var{h}}\var{j}\var{k-h}}&=99x\\ \\ &&\frac{\var{numerator}}{\var{g}}&=x\text{.}\\ \end{align}$

From this, we should look to see if it is possible to simplify by finding the greatest common divisor of the numerator and the denominator. The greatest common divisor is $\var{gcd1 }.$

Therefore, it is not possible to simplify and so

Simplifying by this value gives the fraction $\displaystyle\simplify{{{numerator}}/{g}}$ and so

$\begin{align} \var{h}.\dot{\var{j}}\dot{\var{k}}=\simplify{{{numerator}}/{g}}\text{ in its fractional form.}\\ \end{align}$

Give a worked solution to the whole question.

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This question is used in the following exam:

Initial maths test by J. Richard Snape in J. Richard's workspace.

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Taxonomy: mathcentre

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Checkpoint description

Anna Strzelecka was given access to the J. Richard's copy of Decimals to fractions 5 years, 7 months ago

J. Richard Snape 6 years, 5 months ago

J. Richard Snape 6 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `number`

Parts

Gap-fill

a)

b)

c)

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J. Richard's copy of Decimals to fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Anna Strzelecka was given access to the J. Richard's copy of Decimals to fractions 5 years, 7 months ago

J. Richard Snape 6 years, 5 months ago

J. Richard Snape 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

a)

b)

c)

Generated value: `number`