Checking and securing understanding of solving with simple algebraic fractions
I can solve equations involving simple algebraic fractions.
Checking and securing understanding of solving with simple algebraic fractions
I can solve equations involving simple algebraic fractions.
Lesson details
Key learning points
- The product of a number and its reciprocal is 1
- The product of a term and its reciprocal is 1
- Equivalence can be maintained by multiplying the connected statements by the same reciprocal.
- This step can help you simplify an equation so you can solve it.
Common misconception
When solving equations with fractional coefficients, pupils may divide by the reciprocal rather than multiply. E.g. $$\frac{1}{2}x = 8$$ pupils may just halve $$8$$
Start with integer coefficients, and get pupils used to the idea of multiplying by the reciprocal (not just dividing by the coefficient). This step should be written as part of the working. Answers can be checked by substitution.
Keywords
Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
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).
Video
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Starter quiz
6 Questions
$$2$$ -
$$1\over 2$$
$$1\over 2$$ -
$$2$$
$$3\over 2$$ -
$$2\over 3$$
$$-{1\over 2}$$ -
$$-2$$
$$-{2\over 3}$$ -
$$-{3\over 2}$$
$$1\over 6$$ -
$$6$$
$$2(3x-6)$$ -
$$6x-12$$
$$6(x-1)$$ -
$$6x-6$$
$$2(x-6)$$ -
$$2x-12$$
$$-6(-2-x)$$ -
$$6x+12$$
$$3(2x-6)$$ -
$$6x-18$$
$$6(3-x)$$ -
$$-6x+18$$
Exit quiz
6 Questions
$${1\over 4}a + 3 = 10$$ -
$$a = 28$$
$${1\over 4}(a + 3)=10$$ -
$$a = 37$$
$${4\over 7} a = 1$$ -
$$a = {7\over 4}$$
$${7\over 4}a=14$$ -
$$a = 8$$
$$\frac{a+3}{7} = 2$$ -
$$a = 11$$
$${2\over 3}x$$ -
$$2x\over 3$$
$$2\over 3x$$ -
$$2({1\over 3x})$$
$${2\over 3}\times {1\over 3x}$$ -
$$2\over 9x$$
$$2x \times {1\over 9}$$ -
$$2x\over 9$$
$${3\over 2}\times {1\over x}$$ -
$$3\over 2x$$