Buku Teks Matematik Tingkatan 1 (KSSM) – Latih Diri 5.2c

Soalan 1:
Cari hasil darab bagi setiap yang berikut.
(a) \(3 x \times 5 x^3\)
(b) \(-4 m n \times 7 m^2\)
(c) \(\frac{2}{3} p^4 q \times 6 p r\)

Penyelesaian:
(a) \[ \begin{aligned} & 3 x \times 5 x^3 \\ & =(3 \times 5) \times x \times x \times x \times x \\ & =15 x^4 \end{aligned} \]
(b) \[ \begin{aligned} & -4 m n \times 7 m^2 \\ & =(-4 \times 7) \times m \times m \times m \times n \\ & =-28 m^3 n \end{aligned} \]
(c) \[ \begin{aligned} \frac{2}{3} p^4 q \times 6 p r & =\left(\frac{2}{3} \times 6\right) \times p \times p \times p \times p \times p \times q \times r \\ & =4 p^5 q r \end{aligned} \]

Soalan 2:
Cari hasil bahagi bagi setiap yang berikut.
(a) \(8 x^6 y^4 \div 2 x y^3\)
(b) \(4 a b^3 \div 6 a^2 b\)
(c) \(12 p^5 r \div(-10 p q)\)

Penyelesaian:
(a)
$\begin{array}{l}8x^6{y}^4÷2x{y}^3\\ =\frac{8x^6{y}^4}{2x{y}^3}\\ =\frac{{}^4\cancel{8}\times \cancel{x}\times x\times x\times x\times x\times \cancel{y}\times \cancel{y}\times \cancel{y}\times y}{{}^1\cancel{2}\times \cancel{x}\times \cancel{y}\times \cancel{y}\times \cancel{y}}\\ =4x^{5}y\end{array}$


(b)
$\begin{array}{l}4a{b}^3÷6a^{2}b\\ =\frac{4a{b}^3}{6a^{2}b}\\ =\frac{{}^2\bcancel{4}\times \bcancel{a}\times \bcancel{b}\times b\times b}{{}^3\bcancel{6}\times \bcancel{a}\times a\times \bcancel{b}}\\ =\frac{2b^2}{3a}\end{array}$


(c)
$\begin{array}{l}12p^{5}r÷(-10pq)\\ =\frac{12p^{5}r}{-10pq}\\ =\frac{{}^6\sout{1}\sout{2}\times \bcancel{p}\times p\times p\times p\times p\times r}{{}^5-\sout{1}\sout{0}\times \bcancel{p}\times q}\\ =-\frac{6p^{4}r}{5q}\end{array}$

Soalan 3:
Permudahkan setiap yang berikut.
(a) \(2 m n \times 5 m^2 \div 3 n^3\)
(b) \(6 x y \div 20 p x^2 \times\left(-5 p^6 y\right)\)

Penyelesaian:
(a)
$\begin{array}{l}2mn\times 5m^2÷3n^3\\ =\frac{2mn\times 5m^2}{3n^3}\\ =\frac{10\times m\times m\times m\times \bcancel{n}}{3\times \bcancel{n}\times n\times n}\\ =\frac{10m^3}{3n^2}\end{array}$

(b)
$\begin{array}{l}6xy÷20p{x}^2\times (-5p^{6}y)\\ =\frac{6xy\times (-5p^{6}y)}{20p{x}^2}\\ =\frac{{-}^3\sout{3}\sout{0}\times \bcancel{x}\times y\times y\times \bcancel{p}\times p\times p\times p\times p\times p}{{}^2\sout{2}\sout{0}\times \bcancel{p}\times \bcancel{x}\times x}\\ =-\frac{3p^5{y}^2}{2x}\end{array}$