IGCSEMaths A: HigherEdexcelFlashcards

Algebraic Fractions (Edexcel IGCSE Maths A)

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    What is an algebraic fraction?

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Cards in this collection (17)

  • What is an algebraic fraction?

    An algebraic fraction is a fraction with an algebraic expression on the top (numerator) and/or the bottom (denominator).

  • What are the common steps for simplifying an algebraic fraction?

    To simplify an algebraic fraction, you should:

    1. Factorise fully top and bottom

    2. Then cancel common factors (including common brackets)

  • True or False?

    If asked to simplify an algebraic fraction in an exam question, one factor will likely be the same on the top and bottom, which can help you to factorise difficult quadratics.

    True.

    If asked to simplify an algebraic fraction in an exam question, one factor will likely be the same on the top and bottom, which can help you to factorise difficult quadratics.

  • Describe lowest common denominator (LCD) in the context of algebraic fractions.

    With algebraic fractions, the lowest common denominator (LCD) is found by multiplying the denominators together if they do not share any factors, or by taking the denominator that already includes the other(s) if they do share factors.

  • True or False?

    If x and 2 x are the denominators of two algebraic fractions, then the lowest common denominator is found by multiplying xand 2 x together.

    False.

    2 x already includes the factor x.

    If x and 2 x are the denominators of two algebraic fractions, then the lowest common denominator is 2 x.

  • What does it mean to 'write each fraction over the LCD'?

    'To write each fraction over the LCD' means to multiply the numerator of each fraction by the same expression that its denominator was multiplied by to obtain the LCD.

  • Why is it useful to leave an algebraic fraction in factorised form.

    Factorised form means leaving the top and bottom of the fraction each expressed as the product of its factors.

    This is useful because it makes it easier to see if anything cancels at the end.

  • What is the process for multiplying algebraic fractions?

    To multiply algebraic fractions:

    1. Simplify both fractions first by factorising and cancelling common factors

    2. Multiply the numerators together

    3. Multiply the denominators together

    4. Check for further factorising and cancelling

  • What is the process for dividing algebraic fractions?

    To divide algebraic fractions:

    1. Flip (find the reciprocal of) the second fraction and replace divided by with cross times

    2. Then follow the rules for multiplying two algebraic fractions

    Note that this is the same thing you do when dividing normal fractions.

  • Define reciprocal of a fraction.

    The reciprocal of a fraction is the fraction 'flipped', i.e. with the original denominator divided by the numerator.

    For example the reciprocal of fraction numerator x minus 4 over denominator x squared plus 3 end fraction is fraction numerator x squared plus 3 over denominator x minus 4 end fraction.

  • What is a common factor?

    A common factor is a factor that is shared between two or more expressions.

  • What is cancelling in algebraic fractions?

    Cancelling in algebraic fractions means removing common factors that appear in both the numerator and denominator.

  • What are the two main methods for solving equations with algebraic fractions?

    The two main methods for solving equations with algebraic fractions are:

    1. Deal with algebraic fractions first by adding/subtracting, then solve the equation

    2. Multiply everything by the common denominator to eliminate fractions, then solve the resulting equation

  • What are the steps to solve an equation with algebraic fractions by multiplying through by the common denominator?

    The steps to solve an equation with algebraic fractions by multiplying through by the common denominator are:

    1. Multiply every term by each denominator

    2. Expand brackets

    3. Collect like terms

    4. Rearrange into standard equation form

    5. Solve the equation.

  • True or False?

    Multiplying by two denominators at once can speed up solving an algebraic fractions equation.

    True.

    Multiplying by two denominators at once can speed up solving an algebraic fractions equation.

    But you need to be really careful with the algebra!

  • What is the first step in the method of dealing with fractions first before solving an algebraic fractions equation?

    The first step in the method of dealing with fractions first before solving an algebraic fractions equation is to add or subtract the fractions (according to the rules for operating with algebraic fractions).

  • True or False?

    When solving by dealing with fractions first, you follow the same rules as solving linear equations with fractions on one or both sides.

    True.

    When solving by dealing with fractions first, you follow the same rules as solving linear equations with fractions on one or both sides.

1. Numbers & the Number System
2. Equations, Formulae & Identities
3. Sequences, Functions & Graphs
4. Geometry & Trigonometry
5. Vectors & Transformation Geometry
6. Statistics & Probability