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Fractions Toolkit (Cambridge (CIE) IGCSE Maths)

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  • FrontBasic Fractions

    True or False?

    The denominator is the number on the bottom of a fraction.

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  • True or False?

    The denominator is the number on the bottom of a fraction.

    True.

    The denominator is the number on the bottom of a fraction.

    The numerator is the number of the top of a fraction.

  • Define the term equivalent fractions.

    E.g. Find an equivalent fraction to 2 over 5.

    Equivalent fractions are two fractions that represent the same amount.

    If two fractions are equivalent, you can multiply both parts of one fraction by the same value in order to get the second fraction.

    E.g. 2 over 5 equals fraction numerator 2 cross times 3 over denominator 5 cross times 3 end fraction equals 6 over 15

  • How do you simplify a fraction?

    E.g. Simplify 18 over 24.

    To simplify a fraction, divide both parts of the fraction by their highest common factor.

    Alternatively, you can also keep dividing both parts of the fraction by common factors until the two parts have no common factors.

    E.g. 18 over 24 equals fraction numerator 18 divided by 6 over denominator 24 divided by 6 end fraction equals 3 over 4

  • How do you find a fraction of an amount?

    E.g. What is 2 over 5 of 35?

    To find a fraction of an amount, multiply the amount by the fraction.

    This is the same as dividing the amount by the denominator of the fraction and then multiplying by the numerator of the fraction.

    E.g. 2 over 5 of 35

    table row cell 2 over 5 cross times 35 end cell equals cell 35 over 5 cross times 2 end cell row blank equals cell 7 cross times 2 end cell row blank equals 14 end table

  • Define the term top heavy (improper) fraction.

    A top heavy (improper) fraction is one where its numerator is bigger than its denominator.

    E.g. 4 over 3 is a top heavy fraction.

  • Define the term mixed number.

    A mixed number is a whole number added together with a fraction.

    E.g. 2 3 over 5is a mixed number.

  • How do you convert a mixed number into a top heavy fraction?

    To convert from a mixed number into a top heavy fraction, multiply the whole number by the denominator. Add that value to the numerator. This becomes the new numerator.

    The denominator stays the same.

    E.g. 4 5 over 8 equals fraction numerator 4 cross times 8 plus 5 over denominator 8 end fraction equals 37 over 8

  • How do you convert a top heavy fraction into a mixed number?

    To convert from a top heavy fraction to a mixed number, divide the numerator by the denominator.

    The number of times that the denominator goes into the numerator is the whole number for the mixed number.

    The remainder is the numerator for the mixed number.

    The denominator stays the same.

    E.g. 22 over 7 equals 21 over 7 plus 1 over 7 equals 3 1 over 7

  • True of False?

    Improper fractions is another name for mixed numbers.

    False.

    Improper fractions is another name for top heavy fractions.

  • What is the lowest common denominator of two fractions.

    E.g. 2 over 5 and 1 third.

    The lowest common denominator of two fractions is the smallest whole number that each denominator divides into. I.e. the lowest common multiple of the denominators.

    E.g. The fractions 2 over 5 and 1 third have denominators of 3 and 5.

    Therefore, the lowest common denominator of these two fractions is 15.

  • True or False?

    To work out 1 fourth plus 5 over 7, you add the numerators and add the denominators to get 6 over 11.

    False.

    It is a common error to add together the numerators and add together the denominators when adding fractions.

    Instead, you need to first convert both fractions so that they have a common denominator and just add the numerators.

    E.g. 1 fourth plus 5 over 7 equals 7 over 28 plus 20 over 28 equals 27 over 28.

  • True or False?

    When adding or subtracting fractions, sometimes you only need to change one of the denominators.

    True.

    When adding or subtracting fractions, if one denominator is a multiple of the other then you only need to change the smaller one.

    E.g. 2 over 5 plus 4 over 15 equals 6 over 15 plus 4 over 15.

  • How do you add or subtract two mixed numbers?

    E.g. 5 2 over 3 minus 4 1 over 6.

    It is easiest to convert the mixed numbers into improper fractions first and then complete the addition or subtraction.

    E.g. 5 2 over 3 minus 4 1 over 6

    table row cell fraction numerator 5 cross times 3 plus 2 over denominator 3 end fraction minus fraction numerator 4 cross times 6 plus 1 over denominator 6 end fraction end cell equals cell 17 over 3 minus 25 over 6 end cell row blank equals cell 34 over 6 minus 25 over 6 equals 9 over 6 equals 3 over 2 equals 1 1 half end cell row blank blank blank end table

  • True or False?

    When multiplying two fractions, you first must write them with a common denominator.

    False.

    You can multiply fractions without writing them with common denominators.

    It is only necessary to find a common denominator when adding or subtracting fractions.

  • Dividing a number by a fraction is the same as multiplying the original number by what?

    Dividing a number by a fraction is the same as multiplying the original number by the reciprocal of the fraction.

    For example, 9 divided by 2 over 3 equals 9 cross times 3 over 2.

  • How do you multiply two fractions?

    E.g. 5 over 8 cross times 3 over 7.

    To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

    E.g. 5 over 8 cross times 3 over 7 equals fraction numerator 5 cross times 3 over denominator 8 cross times 7 end fraction equals 15 over 56

  • How do you divide one fraction by another fraction?

    E.g. 3 over 9 divided by 4 over 5.

    To divide one fraction by another fraction, flip the second fraction and change the division to multiplication.

    Then multiply the fractions as normal.

    E.g. 3 over 9 divided by 4 over 5 equals 3 over 9 cross times 5 over 4 equals 15 over 36 equals 5 over 12

  • True or False?

    When multiplying two fractions together, you can cancel out a common factor between the numerator of one fraction and the denominator of the other fraction.

    E.g. 4 over 15 cross times 25 over 11 equals fraction numerator 4 over denominator stack down diagonal strike 15 with 3 below end fraction cross times fraction numerator stack down diagonal strike 25 with 5 on top over denominator 11 end fraction.

    True.

    When multiplying two fractions together, you can cancel out a common factor between the numerator of one fraction and the denominator of the other fraction.

    This is called cross-cancelling.

  • True or False?

    The first step when multiplying together two mixed numbers is to convert the numbers to improper fractions.

    True.

    When multiplying together two mixed numbers, the first step is to write both as top heavy (improper) fractions.

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    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

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      Simple & Compound Interest, Growth & Decay

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      Surds

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      Working with FDP

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      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

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    13. Topic 13

      Rounding, Estimation & Bounds

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      Using a Calculator

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      Algebraic Fractions

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      Functions

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      Sequences

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      Proportion

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