Algebraic Fractions
Lipi Shorts
Karnataka · KSEEB · Class 10 · Mathematics
Swipe up to begin ↑
Algebraic Fractions
Central idea
An algebraic fraction is an ordinary fraction wearing a disguise: the numbers have been swapped for letters, but every rule you learned for 3/4 still works for (x+1)/(x-2).
Central idea
Replace the 3 in 3/4 with (x+1) and the 4 with (x−2): you get (x+1)/(x−2). Every fraction rule from primary school still applies.
Swap the numbers in a fraction for letters and you have an algebraic fraction.
What they are
You may only cancel factors (things multiplied), never terms (things added). So (x²+x)/(x+1) becomes x(x+1)/(x+1) = x.
Factorise top and bottom, then cancel any factor that appears in both.
Simplifying
Factorise and cancel before multiplying to keep the algebra small. For division use KFC: Keep, Flip, Change.
Multiply tops and bottoms; to divide, flip the second fraction and multiply.
Multiply and divide
If the bottoms share no factor, the common denominator is their product. Take care with the minus sign when subtracting.
Find a common denominator first, then combine the numerators.
Add and subtract
See it in a diagram
1/3
Myth vs truth
✕ Myth
You can cancel the x in (x²+x)/(x+1) straight away.
✓ Truth
x is a term on top, not a factor. Factorise to x(x+1) first, then cancel.
Myths vs truth
1/4
Word meanings
numerator
the expression on the top of a fraction
denominator
the expression on the bottom of a fraction
factor
an expression that is multiplied with others; only factors can be cancelled
term
a part of an expression separated by + or −; terms cannot be cancelled
Word meanings
1/2
Themes & message
•
An algebraic fraction obeys exactly the same rules as a number fraction.
•
Factorising is the key skill: it lets you cancel and simplify.
•
Always state restrictions: values of x that make a denominator zero.
Themes & message
Key facts at a glance
What it is
A fraction with algebra on top and/or bottom, e.g. (x+1)/(x−2)
Simplify
Factorise top and bottom, then cancel common FACTORS
Cancel rule
Cancel factors (multiplied), never terms (added)
Key facts at a glance
1/3
You finished this chapter's Shorts!