بِسْـــــــمِ اللّٰهِ الرَّحْمٰنِ الرَّحِيْمِ
..
Cara menyelesaikan operasi hitung pecahan:
[tex] \frac{a}{b} + \frac{c}{ d} + \frac{e}{f} [/tex]
[tex]= \small\frac{(bdf \div b) \times a}{bdf} + \frac{(bdf \div d) \times c}{bdf} + \frac{(bdf \div f) \times e}{bdf} [/tex]
atau
[tex]\footnotesize{ = \frac{(KPK \:dari \:b, d, f \: \div b) \times a}{KPK \:dari \:b, d, f} + \frac{(KPK \:dari \:b, d, f \: \div d) \times c}{KPK \:dari \:b, d, f} + \frac{(KPK \:dari \: b, d, f \: \div f) \times e}{KPK \:dari \:b, d, f} }[/tex]
[tex]\begin{aligned}1. \: ~ & \frac{1}{8} + \frac{1}{6} - \frac{1}{12} \\ \\& = \frac{3}{24} + \frac{4}{24} - \frac{2}{24} \\ \\& = \frac{3 + 4 - 2}{24} \\ \\& = \frac{7 - 2}{24} \\ \\& = \frac{5}{24} \end{aligned} [/tex]
[tex]\begin{aligned}2.~~& \frac{1}{3} - \frac{1}{8} + \frac{1}{6} \\ \\& = \frac{8}{24} - \frac{3}{24} + \frac{4}{24} \\ \\& = \frac{8 - 3 + 4}{24} \\ \\& = \frac{5 + 4}{24} \\ \\& = \frac{9}{24} \end{aligned} [/tex]
[tex]\begin{aligned}3.~~& \frac{3}{7} - \frac{5}{14} + \frac{11}{21} \\ \\& = \frac{18}{42} - \frac{15}{42} + \frac{22}{42} \\ \\& = \frac{18 - 15 + 22}{42} \\ \\& = \frac{3 + 22}{42} \\ \\& = \frac{25}{42} \end{aligned} [/tex]
[tex]\begin{aligned}4.~~& \frac{5}{8} - \frac{5}{16} + \frac{3}{4} \\ \\&= \frac{10}{16} - \frac{5}{16} + \frac{12}{16} \\ \\&= \frac{10-5+12}{16} \\ \\& = \frac{5 +12}{16} \\ \\&= \frac{17}{16}\\\\&= 1\frac{1}{16}\end{aligned} [/tex]
[tex]\begin{aligned}5.~~& \frac{5}{6} - \frac{3}{4} + \frac{1}{6} \\ \\&= \frac{10}{12} - \frac{9}{12} + \frac{2}{12} \\ \\&= \frac{10 - 9 + 2}{12} \\ \\&= \frac{1 + 2}{12} \\ \\ &=\frac{3 \div 3}{12 \div 3} \\ \\&= \frac{1}{4} \end{aligned} [/tex]
وَاللّٰهُ اَعْلَمُ بِاالصَّوَافَ
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
بِسْـــــــمِ اللّٰهِ الرَّحْمٰنِ الرَّحِيْمِ
..
Pembahasan
Cara menyelesaikan operasi hitung pecahan:
[tex] \frac{a}{b} + \frac{c}{ d} + \frac{e}{f} [/tex]
[tex]= \small\frac{(bdf \div b) \times a}{bdf} + \frac{(bdf \div d) \times c}{bdf} + \frac{(bdf \div f) \times e}{bdf} [/tex]
atau
[tex] \frac{a}{b} + \frac{c}{ d} + \frac{e}{f} [/tex]
[tex]\footnotesize{ = \frac{(KPK \:dari \:b, d, f \: \div b) \times a}{KPK \:dari \:b, d, f} + \frac{(KPK \:dari \:b, d, f \: \div d) \times c}{KPK \:dari \:b, d, f} + \frac{(KPK \:dari \: b, d, f \: \div f) \times e}{KPK \:dari \:b, d, f} }[/tex]
Penyelesaian:
[tex]\begin{aligned}1. \: ~ & \frac{1}{8} + \frac{1}{6} - \frac{1}{12} \\ \\& = \frac{3}{24} + \frac{4}{24} - \frac{2}{24} \\ \\& = \frac{3 + 4 - 2}{24} \\ \\& = \frac{7 - 2}{24} \\ \\& = \frac{5}{24} \end{aligned} [/tex]
[tex]\begin{aligned}2.~~& \frac{1}{3} - \frac{1}{8} + \frac{1}{6} \\ \\& = \frac{8}{24} - \frac{3}{24} + \frac{4}{24} \\ \\& = \frac{8 - 3 + 4}{24} \\ \\& = \frac{5 + 4}{24} \\ \\& = \frac{9}{24} \end{aligned} [/tex]
[tex]\begin{aligned}3.~~& \frac{3}{7} - \frac{5}{14} + \frac{11}{21} \\ \\& = \frac{18}{42} - \frac{15}{42} + \frac{22}{42} \\ \\& = \frac{18 - 15 + 22}{42} \\ \\& = \frac{3 + 22}{42} \\ \\& = \frac{25}{42} \end{aligned} [/tex]
[tex]\begin{aligned}4.~~& \frac{5}{8} - \frac{5}{16} + \frac{3}{4} \\ \\&= \frac{10}{16} - \frac{5}{16} + \frac{12}{16} \\ \\&= \frac{10-5+12}{16} \\ \\& = \frac{5 +12}{16} \\ \\&= \frac{17}{16}\\\\&= 1\frac{1}{16}\end{aligned} [/tex]
[tex]\begin{aligned}5.~~& \frac{5}{6} - \frac{3}{4} + \frac{1}{6} \\ \\&= \frac{10}{12} - \frac{9}{12} + \frac{2}{12} \\ \\&= \frac{10 - 9 + 2}{12} \\ \\&= \frac{1 + 2}{12} \\ \\ &=\frac{3 \div 3}{12 \div 3} \\ \\&= \frac{1}{4} \end{aligned} [/tex]
..
وَاللّٰهُ اَعْلَمُ بِاالصَّوَافَ