Operasi Penjumlahan dan Pengurangan
Soal 01
\(5x + 11x \:-\: 2x = \dotso\)
(A) \(10x\)
(B) \(12x\)
(C) \(14x\)
(D) \(15x\)
Jawaban: C
\(5x + 11x \:-\: 2x = (5 + 11\:-\:2)x\)
\(5x + 11x \:-\: 2x = (16\:-\:2)x\)
\(5x + 11x \:-\: 2x = \color{blue}14x\)
Soal 02
\(2x + 5y \:-\: x + 4y = \dotso\)
(A) \(2x + 3y\)
(B) \(x + 9y\)
(C) \(x + 10y\)
(D) \(3x + 2y\)
Jawaban: B
Kelompokkan suku-suku sejenis terlebih dahulu
\(2x + 5y \:-\: x + 4y\)
\(2x\:-\:x + 5y + 4y\)
\((2\:-\:1)x + (5 + 4)y\)
\(1x + 9y\)
\(x + 9y\)
Soal 03
\(2x^2 + 3xy \:-\:2xy + y^2 = \dotso\)
(A) \(2x^2 + xy + y^2\)
(B) \(3x^2y^2 + xy\)
(C) \(2x^2 + y^2 + 3xy\)
(D) \(x^2 + y^2 + 2xy\)
Jawaban: A
\(2x^2 + 3xy \:-\:2xy + y^2\)
\(2x^2 + (3\:-\:2)xy + y^2\)
\(2x^2 + xy + y^2\)
Ingat!
Yang dapat dijumlah atau dikurang hanyalah suku-suku yang sejenis.
Soal 04
\(3x + 12y \:-\:(7x + 5y + z) = \dotso\)
(A) \(-3x + 7y \:-\:z\)
(B) \(-4x + 7y \:-\:z\)
(C) \(-4x + 8y + z\)
(D) \(4x + 7y + z\)
Jawaban: B
\(3x + 12y \:-\:(7x + 5y + z)\)
Buka kurung
\(3x + 12y \:-\:7x \:-\:5y \:-\:z\)
Kelompokkan suku-suku yang sejenis
\(3x \:-\: 7x + 12y \:-\:5y \:-\:z\)
\((3\:-\:7)x + (12 \:-\:5)y \:-\:z\)
\(-4x + 7y \:-\:z\)
Soal 05
\(2(x\:-\:3y) + 5(x + 4y) = \dotso\)
(A) \(4x + 10y\)
(B) \(5x + 12y\)
(C) \(7x + 13y\)
(D) \(7x + 14y\)
Jawaban: D
\(2(x\:-\:3y) + 5(x + 4y)\)
Buka kurung
Kalikan angka yang berada di luar kurung dengan angka di dalam kurung sesuai arah panah di atas
\(2x \:-\:6y + 5x + 20y\)
Kumpulkan suku-suku yang sejenis
\(2x + 5x \:-\:6y + 20y\)
\((2 + 5)x + (-6 + 20)y\)
\(7x + 14y\)
Operasi perkalian dan Pembagian
Soal 06
\(5x \times 2x = \dotso\)
(A) \(8x\)
(B) \(8x^2\)
(C) \(10x\)
(D) \(10x^2\)
Jawaban: D
\(5x \times 2x = (5\times 2)x^2\)
Note: \(\color{blue}x \cdot x = x^{1 + 1} = x^2\)
\(5x \times 2x = \color{blue} 10x^2\)
Soal 07
\(7x \times 8y = \dotso\)
(A) \(15xy\)
(B) \(25xy\)
(C) \(56xy\)
(D) \(60xy\)
Jawaban: C
\(7x \times 8y = (7 \times 8)xy\)
\(7x \times 8y = \color{blue} 56xy\)
Soal 08
\(2x(x + y) = \dotso\)
(A) \(2x^2 + 2xy\)
(B) \(2x + 2y\)
(C) \(2x + 2xy\)
(D) \(2x^2 + 2y\)
Jawaban: A
\(2x(x + y) = 2x\cdot x + 2x \cdot y\)
\(2x(x + y) = 2x^2 + 2xy\)
Note:
\(\color{red} x \cdot x = x^2\)
Soal 09
\(25x \div 5x = \dotso\)
(A) 4
(B) 5
(C) 6
(D) 7
Jawaban: B
\(25x \div 5x\) dapat ditulis menjadi \(\dfrac{25x}{5x}\)
\(\dfrac{25\cancel{x}}{5\cancel{x}}\)
\(\dfrac{25}{5} = 5\)
Soal 10
\(8x^3 \div 2x^2 = \dotso\)
(A) \(2x\)
(B) \(3x\)
(C) \(4x\)
(D) \(5x\)
Jawaban: C
\(8x^3 \div 2x^2\) dapat ditulis menjadi \(\dfrac{8x^3}{2x^2}\)
\(\dfrac{\cancelto{4}{8}x^3}{\cancel{2}x^2}\)
\(\dfrac{4x^3}{x^2}\)
selanjutnya gunakan rumus eksponen berikut:
\(\color{red} \dfrac{x^m}{x^n} = x^{m\:-\:n}\)
\(4x^{3\:-\:2}\)
\(4x^1\)
\(4x\)
Soal 11
\(\dfrac{6x^3y^2}{3x^2y} = \dotso\)
(A) \(2xy\)
(B) \(3xy\)
(C) \(4xy\)
(D) \(5xy\)
Jawaban: A
\(\dfrac{\cancelto{2}{6}x^3y^2}{\cancel{3}x^2y}\)
\(\dfrac{2x^3y^2}{x^2y^1}\)
selanjutnya gunakan rumus eksponen berikut:
\(\color{red} \dfrac{x^m}{x^n} = x^{m\:-\:n}\)
\(2x^{3\:-\:2} y^{2\:-\:1}\)
\(2x^1 y^1\)
\(2xy\)
Soal 12
\(\dfrac{12x}{15y} \div \dfrac{3x}{5y} = \dotso\)
(A) \(\dfrac{4}{3}\)
(B) \(\dfrac{5}{7}\)
(C) \(\dfrac{1}{15}\)
(D)\(\dfrac{4}{11}\)
Jawaban: A
\(\dfrac{12x}{15y} \div \dfrac{3x}{5y}\) dapat ditulis \(\dfrac{12x}{15y} \times \dfrac{5y}{3x}\)
\(\dfrac{12x}{15y} \times \dfrac{5y}{3x} = \dfrac{12x \cdot 5y}{15y \cdot 3x}\)
\(\dfrac{12x}{15y} \times \dfrac{5y}{3x} = \dfrac{60xy}{45xy}\)
\(\dfrac{12x}{15y} \times \dfrac{5y}{3x} = \dfrac{60\cancel{xy}}{45\cancel{xy}}\)
\(\dfrac{12x}{15y} \times \dfrac{5y}{3x} = \dfrac{60}{45}\)
\(\dfrac{12x}{15y} \times \dfrac{5y}{3x} = \dfrac{4}{3}\)