Laske
a) \(\dfrac{2}{3}+\dfrac{4}{3}\)
b) \(\dfrac{2}{3}-\dfrac{4}{3}\)
c) \(\dfrac{2}{3} \cdot \dfrac{4}{3}\)
d) \(\dfrac{2}{3}: \dfrac{4}{3}\)
e) \(3+ \dfrac{3}{4}\)
f) \(\dfrac{1}{6}-\dfrac{5}{4}\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{color} \begin{align*} \textbf{a)} \quad&\dfrac{2}{3}+\dfrac{4}{3} \\\\ =&\dfrac{2+4}{3} =\dfrac{6}{3}= \underline{\underline{\ 2\ }} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{b)}\quad&\dfrac{2}{3}-\dfrac{4}{3} \\\\ =&\dfrac{2-4}{3}=\dfrac{-2}{3}= \underline{\underline{-\dfrac{2}{3}}} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)}\quad&\dfrac{2}{3} \cdot \dfrac{4}{3} \\\\ =&\dfrac{2 \cdot 4}{3 \cdot 3} =\underline{\underline{\ \dfrac{8}{9}\ }} && \color{red}\text{(+1p)} \end{align*}\)
\(\require{cancel}\require{color} \begin{align*} \textbf{d)}\quad & \dfrac23:\dfrac43 && \Big| \Big| \dfrac{a}{b}:\dfrac{c}{d}=\dfrac{a}{b} \cdot \dfrac{d}{c} \\\\ =& \dfrac23 \cdot \dfrac34 && \color{red}{\text{(+1p)}}\\\\ =&\dfrac{2\cdot\overset{1}{\cancel{3}}}{\underset{1}{\cancel{3}}\cdot4}=\dfrac24= \underline{\underline{\ \dfrac{1}{2}\ }} && \color{red}{\text{(+1p)}} \end{align*} \)
\(\require{color} \begin{align*} \textbf{e)} \phantom{x}^{4)}&3+\dfrac{3}{4} \\\\ =&\dfrac{4 \cdot 3}{4\cdot 1}+\dfrac{3}{4} \\\\ =&\dfrac{12}{4}+\dfrac{3}{4} =\underline{\underline{\ \dfrac{15}{4}\ }} && \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{f)}\quad &\phantom{\Big)}^{2)}{}{\dfrac{1}{6}}- \phantom{\Big)}^{3)}{}{\dfrac{5}{4}} \\\\ &=\dfrac{2 \cdot 1}{2 \cdot 6}- \dfrac{3 \cdot 5}{3 \cdot 4} \\\\ &=\dfrac{2}{12}-\dfrac{15}{12} =\underline{\underline{-\dfrac{13}{12}}} && \color{red}{\text{(+1p)}} \end{align*}\)
Laske
a) \(\dfrac{5}{3}-\dfrac{5}{3} \cdot \dfrac{1}{2}\)
b) \(\dfrac{8}{5}:4-4\)
c) \(\dfrac{\dfrac{3}{5}}{\dfrac{1}{4}}\)
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{color} \begin{align*} \textbf{a)}\quad &\dfrac{5}{3}-\dfrac{5 \cdot 1}{3 \cdot 2} \\ \\ =&\phantom{\Big|}^{2)}{}{\dfrac{5}{3}}-\dfrac{5}{6} && \color{red}{\text{(+1p)}} \\ \\ =&\dfrac{2 \cdot 5}{2 \cdot 3}-\dfrac{5}{6} \\ \\ =&\dfrac{10}{6}-\dfrac{5}{6} =\underline{\underline{\ \dfrac{5}{6}\ }} && \color{red}{(\text{+1p})} \end{align*}\)
\(\require{color} \begin{align*} \textbf{b)}\quad &\dfrac{8}{5}:4-4 \\ \\ =&\dfrac{8}{5} \cdot \dfrac{1}{4}-4 && \color{red}{(\text{+1p})} \\\\ =&\dfrac{8 \cdot 1}{5 \cdot 4} - 4 =\dfrac{8}{20}^{(4}-4 \\\\ =&\dfrac{2}{5}-\phantom{\Big|}^{5)}{}{4} =\dfrac{2}{5}-\dfrac{20}{5} =\underline{\underline{-\dfrac{18}{5}}} && \color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)}\quad &\dfrac{\dfrac{3}{5}}{\dfrac{1}{4}}= \dfrac{3}{5}:\dfrac{1}{4} \\\\ =&\dfrac{3}{5}\cdot \dfrac{4}{1} && \color{red}{\text{(+1p)}} \\\\ =&\dfrac{3 \cdot 4}{5 \cdot 1} =\underline{\underline{\dfrac{12}{5} }}&& \color{red}{\text{(+1p)}} \end{align*}\)
a) Laske lukujen \(4\) ja \(-\tfrac{4}{7}\) käänteislukujen erotus.
b) Laske lukujen \(-\tfrac{1}{3}\) ja \(7\) käänteislukujen osamäärä.
c) Laske \(2\dfrac{2}{3}-3\dfrac{3}{4}+4 \dfrac{5}{6}\).
Merkitse vihkoosi värikynällä pisteesi ja puuttuvat välivaiheet.
\(\require{color} \begin{align*} \textbf{a)}\quad&\dfrac{1}{4}-\Big(- \dfrac{7}{4}\Big) && \color{red}{\text{(+1p)}} \\ \\ =&\dfrac{1}{4}+\dfrac{7}{4} \\\\ =&\dfrac{8}{4}= \underline{\underline{\ 2 \ }}&&\color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{b)}\quad&-3: \dfrac{1}{7} && \color{red}{\text{(+1p)}} \\ \\ =&-3 \cdot \dfrac{7}{1} \\\\ =&\underline{\underline{-21}} &&\color{red}{\text{(+1p)}} \end{align*}\)
\(\require{color} \begin{align*} \textbf{c)}\quad2 &\dfrac{2}{3}-3\dfrac{3}{4}+4 \dfrac{5}{6}\\ \\ =&\phantom{\Big|}^{3)}{}{2}+\dfrac{2}{3}+\phantom{\Big|}^{4)}{}{3} +\dfrac{3}{4}-\Big(\phantom{\Big|}^{6)}{}{4}+\dfrac{5}{6}\Big) \\ \\ =&\phantom{\Big|}^{4)}{}{\dfrac{8}{3}}+\phantom{\Big|}^{3)}{}{\dfrac{15}{4}}-\phantom{\Big|}^{2)}{}{\dfrac{29}{6}} \\ \\ =&\dfrac{32}{12}-\dfrac{45}{12}+\dfrac{58}{12} \qquad\qquad \ \ \color{red}{\text{(+1p)}} \\ \\ =&\dfrac{45}{12} =\dfrac{36}{12}+\dfrac{9}{12} \\\\ =&3 \dfrac{9}{12} =\underline{\underline{3 \dfrac{3}{4}}} \qquad \qquad \qquad \color{red}{\text{(+1p)}} \end{align*}\)
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