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Write the algebraic expression for each of the following statements or phrases using numbers, literals and the basic operations:
(i) The sum of $ x $ and 5 is added to $ y $.
(ii) $x$ less than the sum of $ y $ and $ z $.
(iii) 4 times the sum of $ x $ and $ y $.
(iv) The quotient of $ x $ by $ y $ is added to the product of $ x $ and $ y $.
Given:
(i) The sum of \( x \) and 5 is added to \( y \).
(ii) $x$ less than the sum of \( y \) and \( z \).
(iii) 4 times the sum of \( x \) and \( y \).
(iv) The quotient of \( x \) by \( y \) is added to the product of \( x \) and \( y \).
To do:
We have to write the algebraic expression for each of the given statements or phrases using numbers, literals and the basic operations.
Solution:
(i) Sum of \( x \) and 5 $=x+5$
The sum of \( x \) and 5 added to \( y \)$=(x+5)+y=x+y+5$.
(ii) Sum of \( y \) and \( z \)$=y+z$
$x$ less than the sum of \( y \) and \( z \)$=(y+z)-x=y+z-x$.
(iii) Sum of \( x \) and \( y \)$=x+y$
4 times the sum of \( x \) and \( y \)$=4\times(x+y)=4(x+y)$.
(iv) Product of \( x \) and \( y \)$=x\times y=xy$
The quotient of \( x \) by \( y \)$=\frac{x}{y}$
The quotient of \( x \) by \( y \) added to the product of \( x \) and \( y \)$=xy+\frac{x}{y}$.
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