New
New
Year 11
Higher

Operations with algebraic fractions

I can multiply, divide, add and subtract with algebraic fractions.

New
New
Year 11
Higher

Operations with algebraic fractions

I can multiply, divide, add and subtract with algebraic fractions.

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Lesson details

Key learning points

  1. When multiplying/dividing, it can be easier to fully factorise every expression first.
  2. When dividing by an expression, it is equivalent to multiplying by the reciprocal of that expression.
  3. When adding/subtracting with algebraic fractions, a common denominator is required.

Keywords

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

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

Common misconception

Trying to simplify a division calculation by identifying common factors before calculating.

Pupils need to understand why this works with multiplication questions to understand why this does not work with division. Encourage pupils to write their division as a multiplication of the reciprocal before identifying common factors.

A reminder of operations with numerical fractions before starting this lesson will help pupils see that operations with algebraic fractions are exactly the same.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

6 Questions

Q1.
Calculate 35×23.
Correct answer: 25
34
58
715
6
Q2.
Calculate 910÷125.
12
13
32
Correct answer: 38
5425
Q3.
Calculate 3816.
Correct answer: 524
1324
248
1148
Q4.
Which of these is the fully factorised form of 2436x?
2(18x+12)
4(9x+6)
6(6x+4)
Correct answer: 12(3x+2)
24(13x)
Q5.
Factorise x22x24.
(x3)(x+8)
(x4)(x+6)
Correct answer: (x6)(x+4)
(x8)(x+3)
(x12)(x+2)
Q6.
What is the simplest form of the fraction 14x3y615x4y3?
14y215x
14y215x3
14xy315
14x315y3
Correct answer: 14y315x

6 Questions

Q1.
Simplify 5x6x×4x3x.
52
Correct answer: 109
9x10
20x218x
20x221x2
Q2.
Simplify 2a÷3a4.
23
32
83a
23a2
Correct answer: 83a2
Q3.
Write 3a+2a5 in its simplest form.
65
152a2
3+2a5a
2a+1510a
Correct answer: 2a2+155a
Q4.
Which of these are equivalent to 2x+105×xx2+8x+15?
2x+3
x5x+10
Correct answer: 2x5x+15
2x5x+50
4x+28x+15
Q5.
Which of these are equivalent to x2x62x÷x2+x12x?
x+2x+4
x3x4
Correct answer: x+22x+8
x2+6x+82x2
Q6.
Write 53x+12+x5x+20 in its simplest form.
x+58x+32
28x5x+20
13x+405x+20
Correct answer: 3x+2515x+60
5x+1515x+60
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