To simplify an expression is to write it in a more efficient form without affecting the value of the original expression. Fully simplifying means the expression cannot be simplified further.

To factorise is to express a term as the product of its factors.

Simplifying algebraic fractions

Maths

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

Algebraic fractions

What is the simplest form of the fraction $$18x^2y^6\over 12x^5y^2$$?

Write the fraction $$8a + 24\over 4a + 12$$ in its simplest form. 

Simplify $$3x^2 -6x\over x^2 - 7x + 10$$.

Simplify $$3x^2 +17x + 10\over 6x^2 + 25x + 14$$.

Which fractions simplify to $$4\over 5$$?

Which of these is the highest common factor of $$12a^2b$$ and $$6a^3b^2$$?

Which of these is equivalent to $$a^6 \div a^3$$?

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