Penjumlahan dan Pengurangan Pecahan

Pecahan Biasa

• Penyebut sama
$\large \frac{a}{p}+\frac{b}{p}=\frac{a+b}{p}$

Contoh : $\large \frac{1}{5}+\frac{3}{5}=\frac{1+3}{5}=\frac{4}{5}$

• Penyebut berbeda
• Mengalikan penyebut
$\large \frac{a}{p}+\frac{b}{q}=\frac{(a\times q)+(b\times p)}{p\times q}$

Contoh : $\large \frac{2}{3}+\frac{1}{4}=\frac{(2\times 4)+(1\times 3)}{3\times 4}=\frac{8+3}{12}=\frac{11}{12}$

• Mencari KPK penyebut

Contoh :

$\large \frac{2}{3}+\frac{5}{6}=\frac{\big((6\div 3)\times 2\big)+\big((6\div 6)\times 5\big)}{6}$$\large \hspace{2.25em} =\frac{(2\times 2)+(1\times 5)}{6}$$\large \hspace{2.25em} =\frac{4+5}{6}$$\large \hspace{2.25em} =\frac{9}{6}=1\frac{3}{6}=1\frac{1}{2}$

Pecahan Campuran

• Penyebut sama
$\large m\frac{a}{p}+n\frac{b}{p}=(m+n)+\frac{a+b}{p}$

Contoh : $3\frac{3}{8}+5\frac{2}{8}=(3+5)+\frac{3+2}{8}=8\frac{5}{8}$

• Penyebut berbeda
$\large m\frac{a}{p}+n\frac{b}{q}=(m+n)+\frac{(a\times q)+(b\times p)}{p\times q}$
Contoh :
$\large 2\frac{5}{6}+4\frac{3}{4}=(2+4)+\frac{(5\times 4)+(3\times 6)}{6\times 4}$$\large \hspace{3.25em} =6+\frac{20+18}{24}$$\large \hspace{3.25em} =6+\frac{38}{24}$$\large \hspace{3.25em} =6+1\frac{14}{24}$$\large \hspace{3.25em} =7\frac{14}{24}$$\large \hspace{3.25em} =7\frac{7}{12} \to \footnotesize\textsf{12 adl KPK dari 6 dan 4}$

Pecahan Desimal

Menghitung secara bersusun dengan meluruskan tanda koma.

Contoh : $0,25+1,5$

Pecahan Biasa

• Penyebut sama
$\large \frac{a}{p}-\frac{b}{p}=\frac{a-b}{p}$

Contoh : $\large \frac{3}{5}-\frac{1}{5}=\frac{3-1}{5}=\frac{2}{5}$

• Penyebut berbeda
• Mengalikan penyebut
$\large \frac{a}{p}-\frac{b}{q}=\frac{(a\times q)-(b\times p)}{p\times q}$

Contoh : $\large \frac{2}{3}-\frac{1}{4}=\frac{(2\times 4)-(1\times 3)}{3\times 4}=\frac{8-3}{12}=\frac{5}{12}$

• Mencari KPK penyebut

Contoh :

$\large \frac{2}{3}-\frac{3}{6}=\frac{\big((6\div 3)\times 2\big)-\big((6\div 6)\times 3\big)}{6}$$\large \hspace{2.25em} =\frac{(2\times 2)-(1\times 3)}{6}$$\large \hspace{2.25em} =\frac{4-3}{6}$$\large \hspace{2.25em} =\frac{1}{6}$

Pecahan Campuran

• Penyebut sama
$\large m\frac{a}{p}-n\frac{b}{p}=(m-n)+\frac{a-b}{p}$

Contoh : $5\frac{3}{8}-3\frac{2}{8}=(5-3)+\frac{3-2}{8}=2\frac{1}{8}$

• Penyebut berbeda
$\large m\frac{a}{p}-n\frac{b}{q}=(m-n)+\frac{(a\times q)-(b\times p)}{p\times q}$
Contoh :
$\large 4\frac{5}{6}-2\frac{3}{4}=(4-2)+\frac{(5\times 4)-(3\times 6)}{6\times 4}$$\large \hspace{3.25em} =2+\frac{20-18}{24}$$\large \hspace{3.25em} =2\frac{2}{24}$$\large \hspace{3.25em} =2\frac{1}{12} \to \footnotesize\textsf{12 adl KPK dari 6 dan 4}$

Pecahan Desimal

Contoh : $1,5 - 0,25$