Formulae & algebraic fractions · Ages 13–14
Multiplying and dividing algebraic fractions
Cancel, then multiply; to divide, multiply by the reciprocal.
How to do it
Method
Cancel, then multiply; to divide, multiply by the reciprocal
4x + 1 × x + 12x = 2x
Another way
Multiply, then simplify
4(x + 1)2x(x + 1) = 2x
In full
To multiply, factorise every top and bottom first, cancel any factor that appears above and below (across the fractions too), then multiply what is left, top by top and bottom by bottom. To divide by a fraction, multiply by its reciprocal: turn the divisor upside down, then multiply. 4x + 1 × x + 12x = 2x: x + 1 cancels, and 4 with 2 leaves 2. Or multiply everything out first, 4(x + 1)2x(x + 1), and simplify at the end: the same answer, a longer line.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
x4 × 5x2 = 54x.
True or false?
Show the answer and working
Answer: True
x4 × 5x2 = 5x4x2; one x cancels, giving 54x.
Example 2
28x × 9x5 =
Answer in simplest form
Show the answer and working
Answer: 920
x cancels above and below, leaving 2 × 98 × 5 = 920.
Example 3
3x + 247 ÷ x + 84 =
Answer in simplest form
Show the answer and working
Answer: 127
Dividing by x + 84 is multiplying by 4x + 8: 3x + 87 × 4x + 8; x + 8 cancels, leaving 3 × 47 = 127.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.What is 4x − 4 ÷ 5(x − 4)2?
- A. 54(x − 4)
- B. 4x − 45
- C. 45
- D. 20(x − 4)3
Choose the right answer
Answer:
2.36x × 6x5 =
Answer in simplest form
Answer:
3.7x6 ÷ (5x29) = x (simplest form)
Fill in each blank
Answer:
4.What is x2 − 17x × 5x2x + 1?
- A. 5xx − 17
- B. 5xx − 17(x + 1)
- C. 5xx + 17
- D. 5x − 17
Choose the right answer
Answer:
5.2x + 183 ÷ x + 94 =
Answer in simplest form
Answer:
All the answers
- 1. B. 4x − 45
- 2. 35
- 3. 21, 10
- 4. A. 5xx − 17
- 5. 83
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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