1.2 Övningar
Sommarmatte 1
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| Rad 1: | Rad 1: | ||
| + | __NOTOC__ | ||
| ==Övning 1.2:1== | ==Övning 1.2:1== | ||
| <div class="ovning"> | <div class="ovning"> | ||
| Rad 4: | Rad 5: | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$\displaystyle \frac{7}{4}+\frac{11}{7}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{7}{4}+\frac{11}{7}$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle \frac{2}{7}-\frac{1}{5}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{2}{7}-\frac{1}{5}$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{6}-\frac{2}{5}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{1}{6}-\frac{2}{5}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$</td> |
| - | <td class="ntext">$\textrm{e) }$</td> | + | <td class="ntext">e)</td> |
| - | <td class="ntext">$\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 31: | Rad 29: | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext"> $\displaystyle \frac{93}{28}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{93}{28}$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle \frac{3}{35}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\displaystyle -\frac{7}{30}$</td> | + | <td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\displaystyle \frac{47}{60}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td> |
| - | <td class="ntext">$\textrm{e) }$</td> | + | <td class="ntext">e)</td> |
| - | <td class="ntext">$\displaystyle \frac{47}{84}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 53: | Rad 48: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a <br\>[[Bild:1_2_1a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_1a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b <br\>[[Bild:1_2_1b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_1b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c <br\>[[Bild:1_2_1c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_1c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d <br\>[[Bild:1_2_1d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_1d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e <br\>[[Bild:1_2_1e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_1e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 92: | Rad 122: | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext"> $\displaystyle \frac{1}{6}+\frac{1}{10}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{6}+\frac{1}{10}$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{4}-\frac{1}{8}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{4}-\frac{1}{8}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{12}-\frac{2}{14}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{12}-\frac{1}{14}$</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\displaystyle \frac{2}{45}+\frac{1}{75}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{2}{45}+\frac{1}{75}$</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 113: | Rad 140: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | + | Facit till alla delfrågor | |
| - | Facit till alla delfrågorna | + | |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext"> $\displaystyle {30}$</td> | + | <td class="ntext" width="50%">$\displaystyle {30}$</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle {8}$</td> | + | <td class="ntext" width="50%">$\displaystyle {8}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">$\displaystyle {84}$</td> | + | <td class="ntext" width="50%">$\displaystyle {84}$</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\displaystyle {225}$</td> | + | <td class="ntext" width="50%">$\displaystyle {225}$</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 137: | Rad 160: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a <br\>[[Bild:1_2_2a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_2a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b <br\>[[Bild:1_2_2b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_2b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c <br\>[[Bild:1_2_2c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_2c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d <br\>[[Bild:1_2_2d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_2d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 170: | Rad 221: | ||
| Beräkna följande uttryck genom att använda minsta gemensamma nämnare: | Beräkna följande uttryck genom att använda minsta gemensamma nämnare: | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a)}$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$</td> |
| - | <td class="ntext">$\textrm{b)}$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 185: | Rad 235: | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a)}$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">$\displaystyle \frac{19}{100}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td> |
| - | <td class="ntext">$\textrm{b)}$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">$\displaystyle \frac{1}{240}$</td> | + | <td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 202: | Rad 252: | ||
| <div class=NavHead>Lösning a </div> | <div class=NavHead>Lösning a </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a <br\>[[Bild:1_2_3a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_3a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b <br\>[[Bild:1_2_3b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_3b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 215: | Rad 279: | ||
| ==Övning 1.2:4== | ==Övning 1.2:4== | ||
| <div class="ovning"> | <div class="ovning"> | ||
| - | Förenkla följande uttrycken genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. | + | Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. |
| - | <table width="100%" cellspacing="5px"> | + | <table width="100%" cellspacing="10px"> |
| - | <tr><td height="5px"/></tr> | + | |
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}$</td> | + | <td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$</td> | + | <td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}$</td> | + | <td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}$</td> |
| </tr><tr><td height="5px"/></tr> | </tr><tr><td height="5px"/></tr> | ||
| </table> | </table> | ||
| Rad 232: | Rad 295: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br\> | + | Facit till alla delfrågor<br\> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{6}{7}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{6}{7}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{16}{21}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{1}{6}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 249: | Rad 311: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a <br\>[[Bild:1_2_4a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_4a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b <br\>[[Bild:1_2_4b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_4b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c <br\>[[Bild:1_2_4c-1(2).gif]]<br\>[[Bild:1_2_4c-2(2).gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_4c-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr align="center"> | ||
| + | <td> | ||
| + | [[Bild:1_2_4c-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 271: | Rad 359: | ||
| ==Övning 1.2:5== | ==Övning 1.2:5== | ||
| <div class="ovning"> | <div class="ovning"> | ||
| - | Förenkla följande uttrycken genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. | + | Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}$</td> | + | <td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$</td> | + | <td class="ntext" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 290: | Rad 377: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{105}{4}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">$-5$</td> | + | <td class="ntext" width="33%">$-5$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\displaystyle \frac{8}{55}$</td> | + | <td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 307: | Rad 394: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_2_5a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_5a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_2_5b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_5b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_2_5c-1(2).gif]]<br\>[[Bild:1_2_5c-2(2).gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_5c-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td> | ||
| + | [[Bild:1_2_5c-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 330: | Rad 443: | ||
| <div class="ovning"> | <div class="ovning"> | ||
| - | Förenkla | + | Förenkla $\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$ |
| - | <table width="100%" align="center"><tr><td class="ntext"> | + | |
| - | $\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$</td></tr></table> | + | |
| </div> | </div> | ||
| Rad 338: | Rad 449: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | <table align="center"><tr><td class="ntext">$\displaystyle \frac{152}{35}$</td></tr></table> | + | <table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> |
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 344: | Rad 455: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| <div class=NavHead>Lösning </div> | <div class=NavHead>Lösning </div> | ||
| - | <div class=NavContent>[[Bild:1_2_6-1(2).gif]]<br \>[[Bild:1_2_6-2(2).gif]] | + | <div class=NavContent> |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_6-1(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_2_6-2(2).gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
Versionen från 12 maj 2007 kl. 15.03
Övning 1.2:1
Skriv på gemensamt bråkstreck
| a) | $\displaystyle \frac{7}{4}+\frac{11}{7}$ | b) | $\displaystyle \frac{2}{7}-\frac{1}{5}$ | c) | $\displaystyle \frac{1}{6}-\frac{2}{5}$ |
| d) | $\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$ | e) | $\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$ | ||
Facit
Facit till alla delfrågorna
| a) | $\displaystyle \frac{93}{28}$ | b) | $\displaystyle \frac{3}{35}$ | c) | $\displaystyle -\frac{7}{30}$ |
| d) | $\displaystyle \frac{47}{60}$ | e) | $\displaystyle \frac{47}{84}$ | ||
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Lösning e)
Lösning till delfråga e)
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Övning 1.2:2
Bestäm minsta gemensamma nämnare
| a) | $\displaystyle \frac{1}{6}+\frac{1}{10}$ | b) | $\displaystyle \frac{1}{4}-\frac{1}{8}$ |
| c) | $\displaystyle \frac{1}{12}-\frac{1}{14}$ | d) | $\displaystyle \frac{2}{45}+\frac{1}{75}$ |
Facit
Facit till alla delfrågor
| a) | $\displaystyle {30}$ | b) | $\displaystyle {8}$ |
| c) | $\displaystyle {84}$ | d) | $\displaystyle {225}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Lösning d)
Lösning till delfråga d)
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Övning 1.2:3
Beräkna följande uttryck genom att använda minsta gemensamma nämnare:
| a) | $\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$ | b) | $\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$ |
Facit
Facit till alla delfrågor
| a) | $\displaystyle \frac{19}{100}$ | b) | $\displaystyle \frac{1}{240}$ |
Lösning a
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Övning 1.2:4
Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat.
| a) | $\displaystyle\frac{\displaystyle\frac{3}{5}}{\displaystyle\frac{7}{10}}$ | b) | $\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$ | c) | $\displaystyle\frac{\displaystyle\frac{1}{4}-\frac{1}{5}}{\displaystyle\frac{3}{10}}$ |
Facit
Facit till alla delfrågor
| a) | $\displaystyle \frac{6}{7}$ | b) | $\displaystyle \frac{16}{21}$ | c) | $\displaystyle \frac{1}{6}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Övning 1.2:5
Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat.
| a) | $\displaystyle \frac{2}{\displaystyle \frac{1}{7}\displaystyle -\frac{1}{15}}$ | b) | $\displaystyle\frac{\displaystyle\frac{1}{2}\displaystyle+\frac{1}{3}}{\displaystyle\frac{1}{3}\displaystyle-\frac{1}{2}}$ | c) | $\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$ |
Facit
Facit till alla delfrågor
| a) | $\displaystyle \frac{105}{4}$ | b) | $-5$ | c) | $\displaystyle \frac{8}{55}$ |
Lösning a)
Lösning till delfråga a)
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Lösning b)
Lösning till delfråga b)
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Lösning c)
Lösning till delfråga c)
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Övning 1.2:6
Förenkla $\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$
Facit
| $\displaystyle \frac{152}{35}$ |
Lösning
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