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
Simplify the expression $\frac{-\frac{3}{8}}{-\frac{9}{4}}$−38−94.
QUESTION 2
Fill in the empty boxes to simplify the expression.
$\frac{\frac{4}{n}}{\frac{5}{n^2}}$4n5n2$=$=$\frac{\editable{}\left(\frac{4}{n}\right)}{\editable{}\left(\frac{5}{n^2}\right)}=\frac{\editable{}}{\editable{}}$(4n)(5n2)=
QUESTION 3
Simplify the expression $\frac{\frac{28uv^2}{25}}{\frac{49u^2v}{15}}$28uv22549u2v15.
question 4
Simplify the expression $\frac{\frac{4y-6}{10}}{\frac{6y-9}{5}}$4y−6106y−95.