1.2 Exercises

From Förberedande kurs i matematik 1

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{{Ej vald flik|[[1.2 Bråkräkning|Teori]]}}
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{{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
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{{Vald flik|[[1.2 Övningar|Övningar]]}}
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{{Selected tab|[[1.2 Exercises|Exercises]]}}
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===Övning 1.2:1===
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===Exercise 1.2:1===
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Skriv på gemensamt bråkstreck
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Express as a single fraction
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||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
||<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===
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Bestäm minsta gemensamma nämnare
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Determine the lowest common denominator of
{| width="100%" cellspacing="10px"
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|| <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
|| <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 1.2:3===
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===Exercise 1.2:3===
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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"
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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 1.2:4===
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===Exercise 1.2:4===
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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"
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|a)
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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 1.2:5===
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===Exercise 1.2:5===
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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"
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|a)
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|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 1.2:6===
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===Exercise 1.2:6===
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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) \displaystyle \displaystyle \frac{7}{4}+\frac{11}{7} b) \displaystyle \displaystyle \frac{2}{7}-\frac{1}{5} c) \displaystyle \displaystyle \frac{1}{6}-\frac{2}{5}
d) \displaystyle \displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5} e) \displaystyle \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}
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


Exercise 1.2:2

Determine the lowest common denominator of

a) \displaystyle \displaystyle \frac{1}{6}+\frac{1}{10} b) \displaystyle \displaystyle \frac{1}{4}-\frac{1}{8}
c) \displaystyle \displaystyle \frac{1}{12}-\frac{1}{14} d) \displaystyle \displaystyle \frac{2}{45}+\frac{1}{75}
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


Exercise 1.2:3

Calculate the following by using the lowest common denominator.

a) \displaystyle \displaystyle\frac{3}{20}+\frac{7}{50}-\frac{1}{10} b) \displaystyle \displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}
Answer
Answer 1.2:3
Solution a
Solution 1.2:3a
Solution b
Solution 1.2:3b


Exercise 1.2:4

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

a) \displaystyle \displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}} b) \displaystyle \displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}} c) \displaystyle \displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}
Answer
Answer 1.2:4
Solution a
Solution 1.2:4a
Solution b
Solution 1.2:4b
Solution c
Solution 1.2:4c


Exercise 1.2:5

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

a) \displaystyle \displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}} b) \displaystyle \displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}} c) \displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}
Answer
Answer 1.2:5
Solution a
Solution 1.2:5a
Solution b
Solution 1.2:5b
Solution c
Solution 1.2:5c


Exercise 1.2:6

Simplify \displaystyle \ \,\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}}}

Answer
Answer 1.2:6
Solution
Solution 1.2:6
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