Sammanställning övningar
Sommarmatte 1
(Skillnad mellan versioner)
Versionen från 21 juni 2007 kl. 14.04 (redigera) KTH.SE:u1xsetv1 (Diskussion | bidrag) (→Övning 1.2:1) ← Gå till föregående ändring |
Nuvarande version (17 juli 2007 kl. 13.17) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) |
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(48 mellanliggande versioner visas inte.) | |||
Rad 1: | Rad 1: | ||
__NOTOC__ | __NOTOC__ | ||
- | ==Övning 1.1:1== | + | [[övn 1|1 Numerisk räkning]] |
- | <div class="ovning"> | + | |
- | Beräkna (utan hjälp av räknedosa) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$3-7-4+6-5$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$3-(7-4)+(6-5)$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$3-(7-(4+6)-5)$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$3-(7-(4+6))-5$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | <div class="svar"> | + | [[övn 2|2 Algebra]] |
- | <table width="100%" cellspacing="10px"> | + | [[övn 3|3 Rötter och algoritmer]] |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$-7$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$1$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$11$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$1$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | [[övn 4|4 Trigonometri]] |
- | + | ||
- | ==Övning 1.1:2== | + | |
- | <div class="ovning"> | + | |
- | Beräkna (utan hjälp av räknedosa) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$(3-(7-4))(6-5)$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$3-(((7-4)+6)-5)$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$3\cdot(-7)-4\cdot(6-5)$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$3\cdot(-7)-(4+6)/(-5)$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$0$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$-1$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$-25$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$-19$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.1:3== | + | |
- | <div class="ovning"> | + | |
- | Vilka av följande tal tillhör de naturliga talen? heltalen? | + | |
- | rationella talen? irrationella talen? Förenkla först! | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">$8$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">$-4$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">$8-4$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="33%">$4-8$</td> | + | |
- | <td class="ntext">e)</td> | + | |
- | <td class="ntext" width="33%">$8(-4)$</td> | + | |
- | <td class="ntext">f)</td> | + | |
- | <td class="ntext" width="33%">$(-8)(-4)$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">g)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{4}{-8}$</td> | + | |
- | <td class="ntext">h)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{-8}{-4}$</td> | + | |
- | <td class="ntext">i)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{\sqrt{2}}{3}$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">j)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2$</td> | + | |
- | <td class="ntext">k)</td> | + | |
- | <td class="ntext" width="33%">$-\pi$</td> | + | |
- | <td class="ntext">l)</td> | + | |
- | <td class="ntext" width="33%">$\pi+1$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | <tr align="left" valign="top"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">heltalen, rationella talen</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | + | |
- | </tr> | + | |
- | <tr align="left" valign="top"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="33%">heltalen, rationella talen</td> | + | |
- | <td class="ntext">e)</td> | + | |
- | <td class="ntext" width="33%">heltalen, rationella talen</td> | + | |
- | <td class="ntext">f)</td> | + | |
- | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | + | |
- | </tr> | + | |
- | <tr align="left" valign="top"> | + | |
- | <td class="ntext">g)</td> | + | |
- | <td class="ntext" width="33%">rationella talen</td> | + | |
- | <td class="ntext">h)</td> | + | |
- | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | + | |
- | <td class="ntext">i)</td> | + | |
- | <td class="ntext" width="33%">irrationella talen</td> | + | |
- | </tr> | + | |
- | <tr align="left" valign="top"> | + | |
- | <td class="ntext">j)</td> | + | |
- | <td class="ntext" width="33%">naturliga talen, heltalen, rationella talen</td> | + | |
- | <td class="ntext">k)</td> | + | |
- | <td class="ntext" width="33%">irrationella talen</td> | + | |
- | <td class="ntext">l)</td> | + | |
- | <td class="ntext" width="33%">irrationella talen</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.1:4== | + | |
- | <div class="ovning"> | + | |
- | Ordna följande tal i storleksordning | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle 2,\ \frac{3}{5},\ \frac{5}{3}\ $ och $\ \displaystyle \frac{7}{3}$</td> | + | |
- | </tr> | + | |
- | <tr> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle -\frac{1}{2},\ -\frac{1}{5},\ -\frac{3}{10}\ $ och $\ \displaystyle -\frac{1}{3}$</td> | + | |
- | </tr> | + | |
- | <tr> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle \frac{1}{2},\ \frac{2}{3},\ \frac{3}{5},\ \frac{5}{8}\ $ och $\ \displaystyle \frac{21}{34}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle \frac{3}{5}<\frac{5}{3}<2<\frac{7}{3}$</td> | + | |
- | </tr> | + | |
- | <tr> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle -\frac{1}{2}<-\frac{1}{3}<-\frac{3}{10}<-\frac{1}{5}$</td> | + | |
- | </tr> | + | |
- | <tr> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="100%">$\displaystyle \frac{1}{2}<\frac{3}{5}<\frac{21}{34}<\frac{5}{8}<\frac{2}{3}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.1:5== | + | |
- | <div class="ovning"> | + | |
- | Ange decimalutvecklingen med tre korrekta decimaler till | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="25%">$\displaystyle \frac{7}{6}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="25%">$\displaystyle \frac{9}{4}$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="25%">$\displaystyle \frac{2}{7}$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="25%">$\sqrt{2}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="25%">$1{,}167$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="25%">$2{,}250$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="25%">$0{,}286$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="25%">$1{,}414$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.1:6== | + | |
- | <div class="ovning"> | + | |
- | Vilka av följande tal är rationella? Ange dem som en kvot mellan heltal. | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="100%">$3,14$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="100%">$3{,}1416\,1416\,1416\,\dots$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="100%">$0{,}2\,001\,001\,001\,\dots\,$ (därefter är var tredje decimal en 1:a och övriga 0)</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="100%">$0{,}10\,100\,1000\,10000\,1\dots\, $ (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.)</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="100%">Talet är rationellt och lika med $\,314/100 = 157/50\,$.</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="100%">Talet är rationellt och är lika med $\,31413/9999 = 10471/3333\,$.</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="100%">Talet är rationellt och lika med $\,1999/9990\,$.</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="100%">Talet är irrationellt.</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | + | ||
- | ==Övning 1.2:1== | + | |
- | <div class="ovning"> | + | |
- | Skriv på gemensamt bråkstreck | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{7}{4}+\frac{11}{7}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{2}{7}-\frac{1}{5}$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{1}{6}-\frac{2}{5}$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$</td> | + | |
- | <td class="ntext">e)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{8}{7}+\frac{3}{4}-\frac{4}{3}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class="svar"> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{93}{28}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{3}{35}$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle -\frac{7}{30}$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{47}{60}$</td> | + | |
- | <td class="ntext">e)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{47}{84}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.2:2== | + | |
- | <div class="ovning"> | + | |
- | Bestäm minsta gemensamma nämnare | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{1}{6}+\frac{1}{10}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{1}{4}-\frac{1}{8}$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{1}{12}-\frac{1}{14}$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{2}{45}+\frac{1}{75}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Facit </div> | + | |
- | <div class=NavContent> | + | |
- | Facit till alla delfrågor | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle {30}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle {8}$</td> | + | |
- | </tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle {84}$</td> | + | |
- | <td class="ntext">d)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle {225}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning a) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga a) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_2a.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning b) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga b) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_2b.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning c) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga c) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_2c.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning d) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga d) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_2d.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | + | ||
- | + | ||
- | ==Övning 1.2:3== | + | |
- | <div class="ovning"> | + | |
- | Beräkna följande uttryck genom att använda minsta gemensamma nämnare: | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{3}{20}+\frac{7}{50}-\frac{1}{10}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{1}{24}+\frac{1}{40}-\frac{1}{16}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Facit </div> | + | |
- | <div class=NavContent> | + | |
- | + | ||
- | Facit till alla delfrågor | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{19}{100}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="50%">$\displaystyle \frac{1}{240}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning a </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga a) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_3a.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning b) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga b) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_3b.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | ==Övning 1.2:4== | + | |
- | <div class="ovning"> | + | |
- | Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</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" width="33%">$\displaystyle\frac{\displaystyle\frac{2}{7}}{\displaystyle\frac{3}{8}}$</td> | + | |
- | <td class="ntext">c)</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> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Facit </div> | + | |
- | <div class=NavContent> | + | |
- | Facit till alla delfrågor<br\> | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{6}{7}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{16}{21}$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{1}{6}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning a) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga a) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_4a.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning b) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga b) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_4b.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning c) </div> | + | |
- | <div class=NavContent> | + | |
- | 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> | + | |
- | + | ||
- | ==Övning 1.2:5== | + | |
- | <div class="ovning"> | + | |
- | Förenkla följande uttryck genom att skriva på gemensamt bråkstreck. Bråket ska vara färdigförkortat. | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</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" 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" width="33%">$\displaystyle\frac{\displaystyle\frac{3}{10}\displaystyle-\frac{1}{5}}{\displaystyle\frac{7}{8}\displaystyle-\frac{3}{16}}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | + | ||
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Facit </div> | + | |
- | <div class=NavContent> | + | |
- | Facit till alla delfrågor | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | <tr align="left"> | + | |
- | <td class="ntext">a)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{105}{4}$</td> | + | |
- | <td class="ntext">b)</td> | + | |
- | <td class="ntext" width="33%">$-5$</td> | + | |
- | <td class="ntext">c)</td> | + | |
- | <td class="ntext" width="33%">$\displaystyle \frac{8}{55}$</td> | + | |
- | </tr> | + | |
- | <tr><td height="5px"/></tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning a) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga a) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_5a.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning b) </div> | + | |
- | <div class=NavContent> | + | |
- | Lösning till delfråga b) | + | |
- | <table width="100%" cellspacing="10px"> | + | |
- | <tr> | + | |
- | <td align="center"> | + | |
- | [[Bild:1_2_5b.gif]] | + | |
- | </td> | + | |
- | </tr> | + | |
- | </table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning c) </div> | + | |
- | <div class=NavContent> | + | |
- | 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> | + | |
- | + | ||
- | ==Övning 1.2:6== | + | |
- | + | ||
- | <div class="ovning"> | + | |
- | Förenkla $\ \,\displaystyle \frac{\displaystyle \frac{2}{\displaystyle 3+\frac{1}{2}}\displaystyle + \frac{\displaystyle \frac{1}{2}}{\displaystyle \frac{1}{4}\displaystyle -\frac{1}{3}}}{\displaystyle \frac{1}{2}\displaystyle - \frac{3}{\displaystyle 2-\frac{2}{7}}}$ | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Facit </div> | + | |
- | <div class=NavContent> | + | |
- | <table align="center" width="100%"><tr><td class="ntext" align="center">$\displaystyle \frac{152}{35}$</td></tr></table> | + | |
- | </div> | + | |
- | </div> | + | |
- | + | ||
- | <div class=NavFrame style="CLEAR: both"> | + | |
- | <div class=NavHead>Lösning </div> | + | |
- | <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> | + |