Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

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Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

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Simple word-problem reinforcement of fractions.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

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

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Add/subtract fractions and reduce to lowest form.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

Educational calculation tool rather than "question".

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Division (Rationalising) complex numbers in rectangular (Cartesian) Form.

Thanks are due to Christian for his Gap Fills in Fractions code and method

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

Given a sum of logs, all numbers are integers,

$\log_b(a_1)+\alpha\log_b(a_2)+\beta\log_b(a_3)$ write as $\log_b(a)$ for some fraction $a$.

Also calculate to 3 decimal places $\log_b(a)$. 

Dividing powers of x - set out as a fraction

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.