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1.2 Exercises

From Förberedande kurs i matematik 1

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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
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| style="border-bottom:1px solid #000" width="5px" |  
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{{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
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{{Selected tab|[[1.2 Exercises|Exercises]]}}
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| style="border-bottom:1px solid #000" width="100%"|  
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|}
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===Övning 1.2:1===
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===Exercise 1.2:1===
<div class="ovning">
<div class="ovning">
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Skriv på gemensamt bråkstreck
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Express as a single fraction
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%" | <math>\displaystyle \frac{7}{4}+\frac{11}{7}</math>
|width="33%" | <math>\displaystyle \frac{7}{4}+\frac{11}{7}</math>
|b)
|b)
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|width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5</math>
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|width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
|c)
|c)
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|width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
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|width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
|-
|-
|d)
|d)
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|| \displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}</math>
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|| <math>\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}</math>
|e)
|e)
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|| \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
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||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:1|Lösning a|Lösning 1.2:1a|Lösning b|Lösning 1.2:1b|Lösning c|Lösning 1.2:1c|Lösning d|Lösning 1.2:1d|Lösning e|Lösning 1.2:1e}}
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</div>{{#NAVCONTENT:Answer|Answer 1.2:1|Solution a|Solution 1.2:1a|Solution b|Solution 1.2:1b|Solution c|Solution 1.2:1c|Solution d|Solution 1.2:1d|Solution e|Solution 1.2:1e}}
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===Övning 1.2:2===
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===Exercise 1.2:2===
<div class="ovning">
<div class="ovning">
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Bestäm minsta gemensamma nämnare
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Determine the lowest common denominator of
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|| <math>\displaystyle \frac{1}{12}-\frac{1}{14}</math>
|| <math>\displaystyle \frac{1}{12}-\frac{1}{14}</math>
|d)
|d)
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|| \displaystyle \frac{2}{45}+\frac{1}{75}</math>
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|| <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:2|Lösning a|Lösning 1.2:2a|Lösning b|Lösning 1.2:2b|Lösning c|Lösning 1.2:2c|Lösning d|Lösning 1.2:2d}}
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</div>{{#NAVCONTENT:Answer|Answer 1.2:2|Solution a|Solution 1.2:2a|Solution b|Solution 1.2:2b|Solution c|Solution 1.2:2c|Solution d|Solution 1.2:2d}}
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===Övning 1.1:3===
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===Exercise 1.2:3===
<div class="ovning">
<div class="ovning">
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Beräkna följande uttryck genom att använda minsta gemensamma nämnare:
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Calculate the following by using the lowest common denominator.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
|width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}}
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</div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
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===Övning 1.1:4===
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===Exercise 1.2:4===
<div class="ovning">
<div class="ovning">
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F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.
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Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}}</math>
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|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}</math>
|b)
|b)
|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}</math>
|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}</math>
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|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:4|Lösning a|Lösning 1.2:4a|Lösning b|Lösning 1.2:4b|Lösning c|Lösning 1.2:4c}}
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</div>{{#NAVCONTENT:Answer|Answer 1.2:4|Solution a|Solution 1.2:4a|Solution b|Solution 1.2:4b|Solution c|Solution 1.2:4c}}
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===Övning 1.1:5===
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===Exercise 1.2:5===
<div class="ovning">
<div class="ovning">
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F&ouml;renkla f&ouml;ljande uttryck genom att skriva p&aring; gemensamt br&aring;kstreck. Br&aring;ket ska vara f&auml;rdigf&ouml;rkortat.
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Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%"| <math>\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}</math>
|width="33%"| <math>\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}</math>
|b)
|b)
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|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}}</math>
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|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}</math>
|c)
|c)
|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.2:5|Lösning a|Lösning 1.2:5a|Lösning b|Lösning 1.2:5b|Lösning c|Lösning 1.2:5c}}
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</div>{{#NAVCONTENT:Answer|Answer 1.2:5|Solution a|Solution 1.2:5a|Solution b|Solution 1.2:5b|Solution c|Solution 1.2:5c}}
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===Övning 1.1:6===
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===Exercise 1.2:6===
<div class="ovning">
<div class="ovning">
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F&ouml;renkla <math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
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Simplify
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</div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}}
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<math>\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}</math>
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</div>{{#NAVCONTENT:Answer|Answer 1.2:6|Solution |Solution 1.2:6}}

Current revision

       Theory          Exercises      


Exercise 1.2:1

Express as a single fraction

a) 47+711 b) 72−51 c) 61−52
d) 31+41+51 e) 78+43−34

Answer | Solution a | Solution b | Solution c | Solution d | Solution e


Exercise 1.2:2

Determine the lowest common denominator of

a) 61+110 b) 41−81
c) 112−114 d) 245+175

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.2:3

Calculate the following by using the lowest common denominator.

a) 320+750−110 b) 124+140−116

Answer | Solution a | Solution b


Exercise 1.2:4

Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.

a) 53710 b) 8372 c) 31041−51

Answer | Solution a | Solution b | Solution c


Exercise 1.2:5

Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.

a) 271−115 b) 31−2121+31 c) 87−316310−51

Answer | Solution a | Solution b | Solution c


Exercise 1.2:6

Simplify  21−32−7223+21+2141−31

Answer | Solution

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