Title: 4. Multiplication and division of fractions
Course: Demonstrating STACK (v4.3.7)

Express [value] as a single fraction \[ [value]x+[value]+\frac[value]{x+1} \]
Feedback: First write each term over a common denominator \[ [value]\] Then expand out brackets on the top and collect like terms to get \[ [value].\]

Write the following expression as a single fraction in it's simplest form:
\[[value]\cdot[value].\]
Feedback: Note that: \[{\frac{a}{b}} \cdot {c}=\frac{{a} \cdot {c}}{b}.\] Therefore in this example: \[[value]\cdot[value]=\frac[value][value].\] Don't forget to simplify your fraction as well by removing common factors from the numerator and denominator. So: \[[value].\]

Simplify the following expression by removing common factors in the numerator and denominator. \[[value]\cdot[value]. \]

Be sure to leave your answer in it's simplest form.
Feedback: Simply multiply the numerators and denominators together respectively. \[\frac{a}{b}\cdot\frac{c}{d} = \frac{a \cdot c}{b \cdot d}\]. Therefore in this example: \[[value]\cdot[value] = \frac{[value]\cdot[value]}{[value]\cdot[value]} = [value] \]

Simplify the following expression by removing common factors from the numerator and denominator: \[[value]\cdot[value].\] Be sure to leave your answer in it's simplest form.
Feedback: In this example there is a common factor in the denominator of the first fraction and the numerator of the second which can be cancelled, before multiplying, which can save time and make the multiplication simpler. In this example: \[ [value]\cdot[value] = [value]\cdot[value] = [value]. \]

Calculate: \[[value]\div[value].\]

Be sure to leave your answer in it's simplest form.
Feedback: When dividing a fraction \(\frac{a}{b}\) by an integer \(c\) you simply multiply the denominator \(b\) by \(c\). Therefore in this example: \[[value]\div[value] = [value].\]

Calculate \[[value]\div[value].\]
Make sure to express your answer as a single fraction in it's simplest form.
Feedback: In order to divide fractions multiply the first fraction by the reciprocal of the second. In this example: \[[value]\div[value],\] \[=[value]\cdot[value],\] \[=[value].\]