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

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

= \(2x-5\)

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

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

=\(5\)

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

=\(\frac{2×5×y×3(2y+7)}{5(2y+7)}=6y\)

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

= \(\frac{xy×3(z-8)}{3(z-8)}=xy\)

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

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

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