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Fractions

                                          1
                                              /8

55
     / 60



                  /12
                 11

                                       1 2/10
            1遜
                             1
                                 /12
What is a fraction?
 Loosely speaking, a fraction is a quantity that
 cannot be represented by a whole number.
           Why do we need fractions?
Consider the following scenario.
Can you finish the whole cake?

If not, how many cakes did you
eat?
1 is not the answer,
neither is 0.

This suggest that we need a
new kind of number.
Definition:
A fraction is an ordered pair of whole numbers, the 1st one
is usually written on top of the other, such as 遜 or 他 .

               a          numerator

               b          denominator


The denominator tells us how many congruent pieces
the whole is divided into, thus this number cannot be 0.

The numerator tells us how many such pieces are
being considered.
Examples:
How much of a pizza do we have below?
 we first need to know the size of the original pizza.

                              The blue circle is our whole.
                              - if we divide the whole into 8
                                congruent pieces,
                              - the denominator would be 8.

                                We can see that we have 7 of
                                these pieces.
                                Therefore the numerator is 7,
                                and we have
                                                 7
                                                     of a pizza.
                                                 8
DO NOW (not later):

   Compare the number of students
    sitting on left side and on the right
    side of the class.
   The number of students sitting at left side=

   The number of students sitting at right side =

   If we compare students sitting at left side to
    students sitting at right side we get

     ___ students sitting at left side to _____
    students sitting at right side.
What do we call a comparison between
two or more quantities?
                             We just found the
             RATIO           RATIO of students
                             sitting at left side
                             to right side.
                            Is the ratio of
                            students sitting at
                            left side to right
                            side the same ?

  No, when writing a ratio, ORDER matters.
AIM:


What is a ratio?
How many basketballs to footballs are
there?


   For every 4 basketballs
    there are 6 footballs.
   The ratio is 4 to 6.
What are some other ways we
    can write the ratio of basketball
    to footballs?
    Every ratio can be written in 3 ways:



    4 to 6      First quantity to Second quantity     Careful!!
                                                       Order matters in a ratio.
    4:6         First quantity : Second quantity
                                                       4 to 6
     4         First quantity divided by the second   Is NOT the same as
      6         quantity (as a fraction).              6 to 4
Equivalent Ratios
   Simplify the following ratios:
                                                4 = 4/4       =1      = 1 to 2
       4 to 8                                  8      8/4      2
       10 to 8
                                               GCF = 4
       8 to 10

    Step 1  Write the ratio as a fraction
    Step 2  Simplify the fraction (Find the greatest common factor (GCF) of
    both numbers and divide the numerator and denominator by the GCF).
    Step 3  Write the equivalent ratio in the same form as the question
Equivalent Ratios can be formed by
multiplying the ratio by any number.

   For example, the ratio 2 : 3 can also be
    written as
       4 : 6 (multiply original ratio by by 2)
       6 : 9 (multiply original ratio by by 3)
       8 : 12 (multiply original ratio by by 4)

        The ratio 2 : 3 can be expressed as
         2x to 3x (multiply the original ratio
        by any number x)
Compound Ratios

   A ratio that compares more than 2 quantities
    is called a compound ratio.
   Example:
       A cake recipe says the ratio of cups of milk, sugar,
        and butter are 1:2:4.
           This means that there is one cup of milk for every
            two cups of sugar and four cups of butter.
Home assignment:
   1)   You go to a party where the
        ratio of boys to girls is 28 to
        56. Express the ratio of boys
        to girls in simplest form.
   2)   Explain what this ratio tells
        us.

More Related Content

Manisha ratio

  • 1. Fractions 1 /8 55 / 60 /12 11 1 2/10 1遜 1 /12
  • 2. What is a fraction? Loosely speaking, a fraction is a quantity that cannot be represented by a whole number. Why do we need fractions? Consider the following scenario. Can you finish the whole cake? If not, how many cakes did you eat? 1 is not the answer, neither is 0. This suggest that we need a new kind of number.
  • 3. Definition: A fraction is an ordered pair of whole numbers, the 1st one is usually written on top of the other, such as 遜 or 他 . a numerator b denominator The denominator tells us how many congruent pieces the whole is divided into, thus this number cannot be 0. The numerator tells us how many such pieces are being considered.
  • 4. Examples: How much of a pizza do we have below? we first need to know the size of the original pizza. The blue circle is our whole. - if we divide the whole into 8 congruent pieces, - the denominator would be 8. We can see that we have 7 of these pieces. Therefore the numerator is 7, and we have 7 of a pizza. 8
  • 5. DO NOW (not later): Compare the number of students sitting on left side and on the right side of the class.
  • 6. The number of students sitting at left side= The number of students sitting at right side = If we compare students sitting at left side to students sitting at right side we get ___ students sitting at left side to _____ students sitting at right side.
  • 7. What do we call a comparison between two or more quantities? We just found the RATIO RATIO of students sitting at left side to right side. Is the ratio of students sitting at left side to right side the same ? No, when writing a ratio, ORDER matters.
  • 8. AIM: What is a ratio?
  • 9. How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs. The ratio is 4 to 6.
  • 10. What are some other ways we can write the ratio of basketball to footballs? Every ratio can be written in 3 ways: 4 to 6 First quantity to Second quantity Careful!! Order matters in a ratio. 4:6 First quantity : Second quantity 4 to 6 4 First quantity divided by the second Is NOT the same as 6 quantity (as a fraction). 6 to 4
  • 11. Equivalent Ratios Simplify the following ratios: 4 = 4/4 =1 = 1 to 2 4 to 8 8 8/4 2 10 to 8 GCF = 4 8 to 10 Step 1 Write the ratio as a fraction Step 2 Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF). Step 3 Write the equivalent ratio in the same form as the question
  • 12. Equivalent Ratios can be formed by multiplying the ratio by any number. For example, the ratio 2 : 3 can also be written as 4 : 6 (multiply original ratio by by 2) 6 : 9 (multiply original ratio by by 3) 8 : 12 (multiply original ratio by by 4) The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x)
  • 13. Compound Ratios A ratio that compares more than 2 quantities is called a compound ratio. Example: A cake recipe says the ratio of cups of milk, sugar, and butter are 1:2:4. This means that there is one cup of milk for every two cups of sugar and four cups of butter.
  • 14. Home assignment: 1) You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form. 2) Explain what this ratio tells us.