Simplify: 18x^2y/(8xy^2) = □x/(□y) Fill in each blank

9, 4. Divide the top and the bottom by 2xy: x^2y ÷ xy = x, xy^2 ÷ xy = y, 18 ÷ 2 = 9, 8 ÷ 2 = 4.

4x/(36x^2) = 1/(11x). True or false?

False. Divide the top and the bottom by their common factor 4x: 4x/(36x^2) = 1/(9x).

Simplify: (x^2 + 9x + 14)/(x + 7) = x + □

2. 7 × 2 = 14 and 7 + 2 = 9, so x^2 + 9x + 14 = (x + 7)(x + 2). Cancel x + 7: x + 2.

Formulae & algebraic fractions · Ages 13–14

Simplifying algebraic fractions

Factorise first; cancel factors, never terms.

How to do it

Method

Factorise first; cancel factors, never terms

3x + 6x² + 2x = 3x + 2x(x + 2) = 3x

Another way

Check with a number

x = 2: 128 = 32, 3x = 32

In full

An algebraic fraction has an expression on top and below. To simplify it, factorise the top and the bottom first, then cancel the factors they share. Only factors that multiply can cancel, never terms that add: x + 33 is not x. 3x + 6x² + 2x = 3x + 2x(x + 2) = 3x. Watch the minus sign: 3 − x = −(x − 3), so x − 33 − x = −1. Then check with a number: at x = 2, 3 × 2 + 62² + 2 × 2 = 128 = 32, and 3x = 32 too.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Simplify: 18x²y/(8xy²) = xy
Fill in each blank
Show the answer and working
Answer: 9, 4
Divide the top and the bottom by 2xy: x²y ÷ xy = x, xy² ÷ xy = y, 18 ÷ 2 = 9, 8 ÷ 2 = 4.
Example 2
4x36x² = 111x.
True or false?
Show the answer and working
Answer: False
Divide the top and the bottom by their common factor 4x: 4x36x² = 19x.
Example 3
Simplify: x² + 9x + 14x + 7 = x +
Show the answer and working
Answer: 2
7 × 2 = 14 and 7 + 2 = 9, so x² + 9x + 14 = (x + 7)(x + 2). Cancel x + 7: x + 2.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Simplify: 12x²y/(16xy²) = xy
Fill in each blank
Answer:
2.15x + 156x + 6 = (in its lowest terms)
Fill in each blank
Answer:
3.−2x + 168 − x =
Answer:
4.What is 4x + 127x² + 21x in its simplest form?
- A. 4x7
- B. 4 + 127x + 21
- C. 47x
- D. 47
Choose the right answer
Answer:
5.Simplify: x² + 13x + 36x + 9 = x +
Answer:

All the answers

1. 3, 4
2. 5, 2
3. 2
4. C. 47x
5. 4

Free worksheet: Simplifying algebraic fractionsWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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