Add, subtract, multiply and divide algebraic fractions.

Practice with adding, subtracting and dividing basic algebraic fractions

Add, subtract, multiply and divide algebraic fractions.

Practice with adding, subtracting and dividing basic algebraic fractions

Add, subtract, multiply and divide algebraic fractions.

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Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the total hours of work (randomised) and overtime (randomised) and asked to write an expression for the amount of pay earned.

Calculating limits using algebraic techniques

Evaluate $\displaystyle \quad \lim_{x\to a} \frac{ex+d}{ax^2+bx+c} \quad $ algebraically.

Evaluate $\displaystyle \quad \lim_{x\to a} \frac{ax^2+bx+c}{ex+d} \quad $ algebraically.

Evaluate $\displaystyle \quad \lim_{x\to a} \frac{ax+b}{x^2+c} \quad $ algebraically.

Students will solve for x using algebraic maipulation.

Simplificación de expresiones algebraicas

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

Inputting algebraic expressions into Numbas. (Translation to German)

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

German translation of https://numbas.mathcentre.ac.uk/question/12012/solve-an-equation-in-algebraic-fractions/ by Newcastle University Mathematics and Statistics

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Practise solving simultaneous linear equations graphically and algebraically.

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

This quiz contains questions on algebraic fractions, logarithmic equations, exponential equations, quadratic equations and simultaneous equations.

Splitting an algebraic fraction into partial fractions

rebelmaths

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$.

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Express $\displaystyle b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction.