a) Divide numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Divide a negative whole number by a fraction. Simplifying is discussed in the advice but not required to get full marks.

Write the following question down on paper and evaluate it without using a calculator. Write your answer as a fraction or whole number (not a decimal). Use / to signify a fraction or division, for example $\\frac{2}{3}$ is written 2/3.

Instead of dividing by the second fraction, we multiply by the reciprocal of the second fraction (that is, the second fraction flipped upside-down), then look for common factors to cancel.

\\begin{align}\\displaystyle\\frac{\\var{a}}{\\var{b}}\\div \\frac{\\var{d}}{\\var{c}}&=\\frac{\\var{a}}{\\var{b}}\\times \\frac{\\var{c}}{\\var{d}}\\\\[3pt]&=\\frac{\\var{a}\\times\\var{c}}{\\var{b}\\times\\var{d}}\\\\[3pt]&=\\frac{\\var{ac}}{\\var{bd}}\\end{align}

We can write this fraction on the computer using the slash, that is, $\\var{ac}/\\var{bd}$.

This answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{ac}$ and $\\var{bd}$ have a common divisor of $\\var{gcda}$. So we divide the top and bottom numbers by $\\var{gcda}$ to write our fraction in a simpler way.

\\begin{align}\\displaystyle\\frac{\\var{ac}}{\\var{bd}}&=\\frac{\\var{ac}\\div\\var{gcda}}{\\var{bd}\\div\\var{gcda}}\\\\[3pt]&=\\frac{\\var{rednuma}}{\\var{reddena}}\\end{align}

Therefore a better answer to give would be $\\displaystyle\\frac{\\var{rednuma}}{\\var{reddena}}$, which we can enter as $\\var{rednuma}/\\var{reddena}$ .

Actually, ideally we would write our answer as $\\var{rednuma}$.

We actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcda}$ comes from in the original question.

Recall that whole numbers can be written as fractions by putting them over $1$. Instead of dividing by the second fraction, we multiply by the reciprocal of the second fraction (that is, the second fraction flipped upside-down), then look for common factors to cancel.

\\begin{align}\\displaystyle-\\var{h}\\div\\frac{\\var{g}}{\\var{f}}&=-\\frac{\\var{h}}{1}\\div\\frac{\\var{g}}{\\var{f}}\\\\[3pt]&=-\\frac{\\var{h}}{\\var{1}}\\times \\frac{\\var{f}}{\\var{g}}\\\\[3pt]&=-\\frac{\\var{h}\\times\\var{f}}{1\\times \\var{g}}\\\\[3pt]&=-\\frac{\\var{fh}}{\\var{g}}\\end{align}

We can write this fraction on the computer using the slash, that is, $-\\var{fh}/\\var{g}$.

This answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{fh}$ and $\\var{g}$ have a common divisor of $\\var{gcdb}$. So we divide the top and bottom numbers by $\\var{gcdb}$ to write our fraction in a simpler way.

\\begin{align}\\displaystyle-\\frac{\\var{fh}}{\\var{g}}&=-\\frac{\\var{fh}\\div\\var{gcdb}}{\\var{g}\\div\\var{gcdb}}\\\\[3pt]&=-\\frac{\\var{rednumb}}{\\var{reddenb}}\\end{align}

Therefore a better answer to give would be $\\displaystyle-\\frac{\\var{rednumb}}{\\var{reddenb}}$, which we can enter as $-\\var{rednumb}/\\var{reddenb}$ .

Actually, ideally we would write our answer as $-\\var{rednumb}$.

$\\displaystyle\\frac{\\var{a}}{\\var{b}}\\div \\frac{\\var{d}}{\\var{c}}=$$\\displaystyle-\\var{h}\\div\\frac{\\var{g}}{\\var{f}}=$[[0]]