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1.2 Exercises

From Förberedande kurs i matematik 1

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@@ Line 1: / Line 1: @@
 __NOTOC__
+{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
+| style="border-bottom:1px solid #000" width="5px" | &nbsp;
+{{Not selected tab|[[1.2 Fractional arithmetic|Theory]]}}
+{{Selected tab|[[1.2 Exercises|Exercises]]}}
+| style="border-bottom:1px solid #000"  width="100%"| &nbsp;
+|}
-===Övning 1.2:1===
+===Exercise 1.2:1===
 <div class="ovning">
-Skriv på gemensamt bråkstreck
+Express as a single fraction
 {| width="100%" cellspacing="10px"
 |a)
 |width="33%" | <math>\displaystyle \frac{7}{4}+\frac{11}{7}</math>
 |b)
-|width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5</math>
+|width="33%"  | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
 |c)
-|width="33%" | <math>\displaystyle \frac{2}{7}-\frac{1}{5}</math>
+|width="33%" | <math>\displaystyle \frac{1}{6}-\frac{2}{5}</math>
 |-
 |d)
-|| \displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}</math>
+|| <math>\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}</math>
 |e)
-|| \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
+||<math> \displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}</math>
 |}
-</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}}
+</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}}
-===Övning 1.2:2===
+===Exercise 1.2:2===
 <div class="ovning">
-Bestäm minsta gemensamma nämnare
+Determine the lowest common denominator of
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 32: / Line 39: @@
 || <math>\displaystyle \frac{1}{12}-\frac{1}{14}</math>
 |d)
-|| \displaystyle \frac{2}{45}+\frac{1}{75}</math>
+|| <math>\displaystyle \frac{2}{45}+\frac{1}{75}</math>
 |}
-</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}}
+</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}}
-===Övning 1.1:3===
+===Exercise 1.2:3===
 <div class="ovning">
-Beräkna följande uttryck genom att använda minsta gemensamma nämnare:
+Calculate the following by using the lowest common denominator.
 {| width="100%" cellspacing="10px"
 |a)
@@ Line 46: / Line 53: @@
 |width="50%"| <math>\displaystyle\frac{1}{24}+\frac{1}{40}-\frac{1}{16}</math>
 |}
-</div>{{#NAVCONTENT:Svar|Svar 1.2:3|Lösning a|Lösning 1.2:3a|Lösning b|Lösning 1.2:3b}}
+</div>{{#NAVCONTENT:Answer|Answer 1.2:3|Solution a|Solution 1.2:3a|Solution b|Solution 1.2:3b}}
-===Övning 1.1:4===
+===Exercise 1.2:4===
 <div class="ovning">
-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.
+Simplify the following by writing each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"
 |a)
-|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}}</math>
+|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}</math>
 |b)
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}</math>
@@ Line 60: / Line 67: @@
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}</math>
 |}
-</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}}
+</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}}
-===Övning 1.1:5===
+===Exercise 1.2:5===
 <div class="ovning">
-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.
+Simplify the following by writing  each part as one fraction. The fraction should be in the simplest possible form.
 {| width="100%" cellspacing="10px"
 |a)
 |width="33%"| <math>\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}</math>
 |b)
-|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}}</math>
+|width="33%"| <math>\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}</math>
 |c)
 |width="33%"| <math>\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}</math>
 |}
-</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}}
+</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}}
-===Övning 1.1:6===
+===Exercise 1.2:6===
 <div class="ovning">
-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>
+Simplify
-</div>{{#NAVCONTENT:Svar|Svar 1.2:6|Lösning |Lösning 1.2:6}}
+<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>
+</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

Answer 1.2:1

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Solution a

Solution 1.2:1a

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Solution b

Solution 1.2:1b

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Solution c

Solution 1.2:1c

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Solution d

Solution 1.2:1d

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Solution e

Solution 1.2:1e

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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

Answer

Answer 1.2:2

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Solution a

Solution 1.2:2a

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Solution b

Solution 1.2:2b

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Solution c

Solution 1.2:2c

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Solution d

Solution 1.2:2d

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Exercise 1.2:3

Calculate the following by using the lowest common denominator.

320+750−110

124+140−116

Answer | Solution a | Solution b

Answer

Answer 1.2:3

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Solution a

Solution 1.2:3a

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Solution b

Solution 1.2:3b

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Exercise 1.2:4

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

53710

8372

31041−51

Answer | Solution a | Solution b | Solution c

Answer

Answer 1.2:4

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Solution a

Solution 1.2:4a

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Solution b

Solution 1.2:4b

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Solution c

Solution 1.2:4c

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Exercise 1.2:5

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

271−115

31−2121+31

\displaystyle \displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}

Answer | Solution a | Solution b | Solution c

Answer

Answer 1.2:5

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Solution a

Solution 1.2:5a

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Solution b

Solution 1.2:5b

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Solution c

Solution 1.2:5c

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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 | Solution

Answer

Answer 1.2:6

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Solution

Solution 1.2:6

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3. Roots and logarithms

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1.2 Exercises

From Förberedande kurs i matematik 1

Current revision

Exercise 1.2:1

Exercise 1.2:2

Exercise 1.2:3

Exercise 1.2:4

Exercise 1.2:5

Exercise 1.2:6