Question

Work out the following divisions.

1. $(10x – 25) ÷ 5$
2. $(10x – 25) ÷ (2x – 5)$
3. $10y(6y + 21) ÷ 5(2y + 7)$
4. $9x^ 2 y^ 2 (3z – 24) ÷ 27xy(z – 8)$
5. $96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)$

Answer 1

(i) $\frac{(10x-25)}{5} = \frac{2 ×5×x-5×5}{5}$

=$\frac{ 5(2x-5)}{5}$

= $2x-5$

---

(ii) $\frac{(10x-25)}{(2x-5)} = \frac{2×5×x-5×5}{(2x-5)}$

=$\frac{5(2x-5)}{2x-5}$

=$5$

---

(iii) $\frac{10y(6y+21)}{5(2y+7)}=\frac{2×5×y[2×3×y+3×7]}{5(2y+7)}$

=$\frac{2×5×y×3(2y+7)}{5(2y+7)}=6y$

---

(iv) $\frac{9x^2y^2(3z-24)}{27xy(z-8)}=\frac{9x^2y^2[3×z-2×2×2×3]}{27xy(z-8)}$

= $\frac{xy×3(z-8)}{3(z-8)}=xy$

---

(v) $\frac{96 abc(3a - 12) (5b - 30) }{ 144 (a - 4) (b - 6) }$

= $\frac{96abc(3×a-3×4)(5×b-2×3×5)}{144(a-4)(b-6)}$

=$\frac{2abc×3(a-4)×5(b-6)}{3(a-4)(b-6)}=10abc$