Ontario 09 Applied (MFM1P)
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Introduction to negatives with fractions
Lesson

Size of a Negative Fraction

Just like we saw in the positive and negative numbers chapters, like Is it positive or negative? we discovered that negative numbers lie to the left of $0$0 on the number line. All of those concepts also apply to fractions.

In this chapter you need to be able to identify which, from a selection of fractions, is closest to 0.  

Example

Question 1

Question: Consider $\frac{2}{12}$212 and $-\frac{3}{12}$312, which is closest to $0$0.

Think: Remember that the size of a number is the value it holds, we only need to identify which number has it's size closest to $0$0, the negative is simply an indication of direction, (where the number is on the number line).  

Do: $\frac{2}{12}$212 is smaller than $\frac{3}{12}$312, so $\frac{2}{12}$212 is closer to $0$0 than $-\frac{3}{12}$312 

 

Ascending or Descending

Arranging fractions in ascending or descending order is a similar process.  remember that 

Example

Question 2

Question: Arrange the following fractions $-\frac{1}{6}$16, $-\frac{6}{8}$68 and $-\frac{7}{48}$748 in ascending order

Think: To compare fractions we need them to have a common denominator, so we will have to do that first, and then we need to remember that ascending order means from smallest to largest, (how they would appear on the number line from left to right).

Do: Get a common denominator.  The lowest common multiple between $6$6, $8$8 and $48$48 is $48$48

$-\frac{1}{6}$16 becomes $-\frac{8}{48}$848

$-\frac{6}{8}$68 becomes $-\frac{36}{48}$3648

$-\frac{7}{48}$748 is already $-\frac{7}{48}$748

So now we are ordering $-\frac{8}{48}$848, $-\frac{36}{48}$3648 and $-\frac{7}{48}$748

Let's imagine a number line now and see where the numbers would appear,

Here is the number line from $-1$1 to $0$0 (i've also marked on the $48$48ths for $-1$1 and $-\frac{1}{2}$12 to get an idea)

Here is the number line with the fractions marked on,

Now we can order them!  In ascending order we have

$-\frac{36}{48}$3648, $-\frac{8}{48}$848 and $-\frac{7}{48}$748 (but remember we need to answer using the fractions I was given)

The final answer is

$-\frac{6}{8}$68, $-\frac{1}{6}$16 and $-\frac{7}{48}$748

Worked Examples

QUESTION 1

Consider $\frac{3}{5}$35 and $-\frac{4}{5}$45. Which of these fractions is closest to zero?

  1. $\frac{3}{5}$35

    A

    $-\frac{4}{5}$45

    B

    $\frac{3}{5}$35

    A

    $-\frac{4}{5}$45

    B

QUESTION 2

Arrange the following in ascending order: $-\frac{2}{10},-\frac{7}{10},-\frac{4}{10}$210,710,410

  1. $\editable{}$, $\editable{}$, $\editable{}$

QUESTION 3

Consider the following fractions:

$-1\frac{2}{7}$127, $-\frac{39}{14}$3914, $-\frac{19}{7}$197

  1. What is the lowest common denominator of the 3 fractions?

  2. Rewrite all three fractions as improper fractions with the lowest common denominator.

    $-1\frac{2}{7}$127 = $-\frac{\editable{}}{14}$14

    $-\frac{39}{14}$3914 = $-\frac{\editable{}}{14}$14

    $-\frac{19}{7}$197 = $-\frac{\editable{}}{14}$14

  3. Hence determine which of the following lists the fractions in descending order:

    $-\frac{39}{14},-\frac{19}{7},-1\frac{2}{7}$3914,197,127

    A

    $-1\frac{2}{7},-\frac{19}{7},-\frac{39}{14}$127,197,3914

    B

    $-1\frac{2}{7},-\frac{39}{14},-\frac{19}{7}$127,3914,197

    C

    $-\frac{19}{7},-1\frac{2}{7},-\frac{39}{14}$197,127,3914

    D

    $-\frac{39}{14},-\frac{19}{7},-1\frac{2}{7}$3914,197,127

    A

    $-1\frac{2}{7},-\frac{19}{7},-\frac{39}{14}$127,197,3914

    B

    $-1\frac{2}{7},-\frac{39}{14},-\frac{19}{7}$127,3914,197

    C

    $-\frac{19}{7},-1\frac{2}{7},-\frac{39}{14}$197,127,3914

    D

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