Question

Write the following using literals, numbers and signs of basic operations:
(i) x increased by 12
(ii) y decreased by 7
(iii) The difference of a and b, when a > b
(iv) The product of x and y added to their sum
(v) One-third of x multiplied by the sum of a and b
(vi) 5 times x added to 7 times y
(vii) Sum of x and the quotient of y by 5
(viii) x taken away from 4
(ix) 2 less than the quotient of x by y
(x) x multiplied by itself
(xi) Twice x increased by y
(xii) Thrice x added to y squared
(xiii) x minus twice y
(xiv) x cubed less than y cubed
(xv) The quotient of x by 8 is multiplied by y

Answer 1

(i) x increased by 12 is (x + 12).
(ii) y decreased by 7 is (y - 7).
(iii) The difference of a and b, when a>b is (a - b).
(iv) The product of x and y is xy.
The sum of x and y is (x + y).
So, product of x and y added to their sum is xy + (x + y).
(v) One third of x is $\frac{x}{3}$.
The sum of a and b is (a + b).
$\therefore$ One-third of x multiplied by the sum of a and b = $\frac{\mathrm{x}}{3}\times (\mathrm{a}+\mathrm{b})=\frac{\mathbf{x}\mathbf{(}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{)}}{\mathbf{3}}\mathbf{}$
(vi) 5 times x added to 7 times y = $(5\times \mathrm{x})+(7\times \mathrm{y}),\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathbf{5}\mathbf{x}\mathbf{+}\mathbf{7}\mathbf{y}.$

(vii) Sum of x and the quotient of y by 5 is $\mathbf{x}\mathbf{+}\frac{\mathbf{y}}{\mathbf{5}}$.
(viii) x taken away from 4 is (4-x).
(ix) 2 less than the quotient of x by y is $\frac{\mathbf{x}}{\mathbf{y}}\mathbf{-}\mathbf{2}$.
(x) x multiplied by itself is $\mathrm{x}\times \mathrm{x}={\mathbf{x}}^{\mathbf{2}}$.
(xi) Twice x increased by y is $(2\times \mathrm{x})+\mathrm{y}=2\mathrm{x}+\mathrm{y}$.
(xii) Thrice x added to y squared is $(3\times \mathrm{x})+(\mathrm{y}\times \mathrm{y})=\mathbf{3}\mathbf{x}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}$.
(xiii) x minus twice y is $\mathrm{x}-(2\times \mathrm{y})=\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}$.
(xiv) x cubed less than y cubed is $(\mathrm{y}\times \mathrm{y}\times \mathrm{y})-(\mathrm{x}\times \mathrm{x}\times \mathrm{x})={\mathbf{y}}^{\mathbf{3}}\mathbf{-}{\mathbf{x}}^{\mathbf{3}}\mathbf{.}$
(xv) The quotient of x by 8 is multiplied by y is $\frac{\mathrm{x}}{8}\times \mathrm{y}=\frac{\mathbf{xy}}{\mathbf{8}}$.