Simplifying Algebraic Fractions (Cambridge (CIE) IGCSE International Maths: Core): Flashcards

Exam code: 0607

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Define an algebraic fraction.
An algebraic fraction is a fraction whose numerator or denominator, or both, contain an algebraic term.
So $\frac{x}{4}$ , $\frac{48}{y^{2}}$ and $\frac{2 p^{3}}{4 p^{2} + 1}$ are all algebraic fractions.
Why does writing out the powers in full help you simplify $\frac{n^{5}}{n^{2}}$ ?
Because you can then see each matching $n$ on the top and the bottom and cancel them in pairs.
Writing $\frac{n \times n \times n \times n \times n}{n \times n}$ and cancelling two pairs leaves $n \times n \times n$ , which is $n^{3}$ .
When you simplify $\frac{m^{2}}{m^{3}}$ , every factor in the numerator cancels. What is left on the top?
A 1 is left on the top, so the answer is $\frac{1}{m}$ .
Cancelling removes factors rather than deleting them, so once every factor on the top has gone the number 1 remains.
Fill in the two gaps to show two other ways of writing the same fraction.
$\frac{5}{6 y} = 5 \times \frac{1}{______} = \frac{5}{6} \times \frac{1}{______}$
The completed statement is:
$\frac{5}{6 y} = 5 \times \frac{1}{6 y} = \frac{5}{6} \times \frac{1}{y}$
The number and the letter in a denominator can be separated, because dividing by $6 y$ is the same as dividing by $6$ and then by $y$ .
True or False?
$\frac{3 x}{4}$ can also be written as $0.75 x$ .
True.
The fraction $\frac{3 x}{4}$ means $\frac{3}{4}$ multiplied by $x$ , and $\frac{3}{4}$ written as a decimal is $0.75$ .

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