Simplify complex algebraic fractions 1

When we want to simplify a fraction, whether it be an everyday fraction with integer values, or more difficult algebraic fractions, the process is still the same.

Let's start with an easy one.

Example 1:

Simplify the expression $\frac{\frac{1}{6}}{\frac{-9}{8}}$16​−98​​.

Firstly, when we have one fraction divided by another, we can multiply the first by the reciprocal of the second.

$=\frac{1}{6}\times\frac{8}{-9}$=16​×8−9​

Now we want to simplify. We look vertically and diagonally for numbers that have highest common factors. Doing this we see that $6$6 and $8$8 can be divided by $2$2.

$=\frac{1}{3}\times\frac{4}{-9}$=13​×4−9​

Now that we've simplified everything we can see, we multiply across horizontally.

$=\frac{4}{-27}$=4−27​

Example 2:

Simplify the expression $\frac{-\frac{12}{x}}{-\frac{3}{x}}$−12x​−3x​​.

Similar to Example 1, we want to multiply the fraction in the numerator by the reciprocal of the fraction in the denominator.

$=-\frac{12}{x}\times-\frac{x}{3}$=−12x​×−x3​

Now we search vertically and diagonally for any common factors. Note that $x$x and $3$3 are two common factors.

$=4$=4

Remember, the product of two negative numbers is a positive number.

Worked Examples

QUESTION 1

QUESTION 2

QUESTION 3

question 4