Penjumlahan dan Pengurangan Pecahan
Penjumlahan dan Pengurangan Pecahan
Dalam penjumlahan maupun pengurangan pecahan, penyebut harus sama
Contoh:
\begin{equation*} \begin{split} &\text{Hitung}\:\: 1\frac{1}{2} + 2\frac{3}{5} – \frac{4}{7}\\\\ &1 + \frac{1}{2} + 2 + \frac{3}{5} – \frac{4}{7}\\\\ &3 + \left(\frac{1}{2} + \frac{3}{5} – \frac{4}{7}\right)\:\:\:\:\: \color {blue} \text{ubah setiap pecahan sehingga memiliki penyebut yang sama}\\\\ &3 + \left(\frac{1 \times \color{red} 35}{2 \times \color{red} 35} + \frac{3 \times \color{red} 14}{5 \times \color{red} 14 } – \frac{4 \times\color{red} 10 }{7\times \color{red} 10}\right)\:\:\:\:\: \color {blue} \text{KPK dari 2, 5, dan 7 adalah 70}\\\\ &3 + \left(\frac{35}{70} + \frac{42}{70} – \frac{40}{70}\right)\\\\ &3 + \frac{35 + 42 – 40}{70}\\\\ &3 + \frac{37}{70}\\\\ &3 \frac{37}{70} \end{split} \end{equation*}
SOAL LATIHAN
[s2If current_user_can(access_s2member_level1)]
\(5\dfrac{1}{2} + 3\dfrac{2}{3} – 1\dfrac{1}{5}\)
\(5\dfrac{1}{2} + 3\dfrac{2}{3} – 1\dfrac{1}{5}\)
Pembahasan:
\begin{equation*} \begin{split} & 5\frac{1}{2} + 3\frac{2}{3} – 1\frac{1}{5}\\\\ & 5 + \frac{1}{2} + 3 + \frac{2}{3} – 1 – \frac{1}{5}\\\\ & (5 + 3 – 1) + \left(\frac{1}{2} + \frac{2}{3} – \frac{1}{5}\right)\\\\ & 7 + \left(\frac{1 \times \color{red} 15 }{2 \times\color{red} 15} + \frac{2 \times \color{red} 10}{3 \times \color{red} 10} – \frac{1 \times \color{red} 6 }{5 \times \color{red} 6 }\right)\\\\ & 7 + \frac{15 + 20 – 6}{30}\\\\ & 7 + \frac{29}{30}\\\\ & 7\frac{29}{30} \end{split} \end{equation*}
\(2\dfrac{3}{4} – 1\dfrac{1}{8} – \dfrac{5}{12}\)
\(2\dfrac{3}{4} – 1\dfrac{1}{8} – \dfrac{5}{12}\)
Pembahasan:
\begin{equation*} \begin{split} & 2\frac{3}{4} – 1\frac{1}{8} – \frac{5}{12}\\\\ & 2 + \frac{3}{4} – (1 + \frac{1}{8}) – \frac{5}{12}\\\\ & 2 – 1 + \frac{3}{4} – \frac{1}{8} – \frac{5}{12}\\\\ & 1 + \left(\frac{3}{4} – \frac{1}{8} – \frac{5}{12}\right)\\\\ & 1 + \left(\frac{3 \times \color{red} 6}{4 \times \color{red} 6 } – \frac{1 \times \color{red} 3 }{8 \times \color{red} 3 } – \frac{5 \times \color{red} 2}{12 \times \color{red} 2}\right)\\\\ & 1 + \frac{18 – 3 – 10}{24}\\\\ & 1 + \frac{5}{24}\\\\ & 1\frac{5}{24} \end{split} \end{equation*}
\(-2\dfrac{3}{4} + \left(-1\dfrac{1}{2}\right)-\left(- 1\dfrac{2}{3}\right)\)
\(-2\dfrac{3}{4} + \left(-1\dfrac{1}{2}\right)-\left(- 1\dfrac{2}{3}\right)\)
Pembahasan:
\begin{equation*} \begin{split} & -2\frac{3}{4} – 1\frac{1}{2} + 1\frac{2}{3}\\\\ & -2 – \frac{3}{4} – 1 – \frac{1}{2} + 1 + \frac{2}{3}\\\\ & (-2 -1 + 1) + \left(\frac{2}{3} – \frac{3}{4} – \frac{1}{2}\right)\\\\ & -2 + \left(\frac{2 \times \color{red} 4 }{3 \times \color{red} 4} – \frac{3 \times \color{red} 3 }{4 \times \color{red} 3 } -\frac{1 \times \color{red} 6 }{2 \times \color{red} 6}\right)\\\\ & -2 + \frac{8 – 9 – 6}{12}\\\\ & -2 + \left(-\frac{7}{12}\right)\\\\ & – 2 -\frac{7}{12}\\\\ & -2\frac{7}{12} \end{split} \end{equation*}
\(\dfrac{4}{5} -\left(\dfrac{7}{8} – \dfrac{7}{4}\right) + \dfrac{31}{40}\)
\(\dfrac{4}{5} -\left(\dfrac{7}{8} – \dfrac{7}{4}\right) + \dfrac{31}{40}\)
Pembahasan:
\begin{equation*} \begin{split} & \frac{4}{5} – \frac{7}{8} + \frac{7}{4} + \frac{31}{40}\\\\ & \frac{4 \times \color{red} 8 }{5 \times \color{red} 8 } – \frac{7 \times \color{red} 5}{8 \times \color{red} 5} + \frac{7 \times \color{red} 10}{4 \times \color{red} 10} + \frac{31}{40}\\\\ & \frac{32}{40} – \frac{35}{40} + \frac{70}{40} + \frac{31}{40}\\\\ & \frac{32 – 35 + 70 + 31}{40}\\\\ & \frac{98 \div \color{red} 2}{40 \div \color{red} 2}\\\\ & \frac{49}{20}\\\\ & \frac{40}{20} + \frac{9}{20}\\\\ & 2 + \frac{9}{20}\\\\ & 2\frac{9}{20} \end{split} \end{equation*}
[else]
[/s2If]