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Rules of Algebra (Economics)

Rules of Algebra

The rules for manipulating numbers (see arithmetic) also apply to algebraic symbols. The only difference is that some of the notation is slightly different. For example, for variables $a$ and $b$, we typically write $a\div b$ as $\frac{a}{b}$ and $a\times b$ as $ab$.

Note: When we multiply variables, together, we typically write variables in alphabetic order. For example, we would write $a\times m \times b$ as $abm$.

Worked Exercises

Example 1

Write the following algebraic expressions in their simplest forms and find the numerical value of each when $a=2$, $b=3$ and $c=1$:

a) $-10a+5a+a$

b) $25c+10c-bc$

Solution

a) $-10a+5a+a=-4a$. When $a=2$ this is equal to $-4\times 2=-8$.

b) $25c+10c-bc=35c-bc$. When $b=3$ and $c=1$ this is equal to $35\times 1-3\times 1=32$.

Note: We could simplify the expression in part b) further by factorising it: \[35c-bc=c(35-b)\]

Example 2

Rewrite the following without using the $\times$ and $\div$ signs in their simplest form: a) $-a\times b+4b-3b\times a$ b) $f\div cf$ c) $-b\div a\times 2m$

Solution

a) $-a\times b+4b-3b\times a=4b-4ab$

b) $ f\div cf=\frac{1}{c}$

c) $-b\div a\times 2m=-\dfrac{2bm}{a}$

Whiteboard maths

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