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52 West Main Street
Washingtonville, NY 10992

Phone: 845.497.4000
Fax: 845.497.4030

How do you get to Carnegie Hall? Practice. Practice. Practice.

How do you get to Carnegie Hall?  Practice. Practice. Practice.


Topic of the Week: 

Understanding Ratios
and
Equivalent Ratios 
Mr.Chin's Class: Module 1, Lesson 4 - Read the Lesson Summary and complet the Problem Set. Finish Finding Equivalent Fractions 1.
Mr. Andersen's Class.Module 1, Lesson 4 - Read the Lesson Summary and complet the Problem Set. Finish Finding Equivalent Fractions 1
Skeleton Notes
A.  Ratios are comparisons. They show how two amounts compare to each other. Ratios are expressed as a fraction, with a colon (:) or with the word "to".
     Example:  For every 2 red candies there are 5 blue candies. The ratio here can be expressed in three ways:  2/5, 2:5 or 2 to 5 
Two ways to use your words to describe a ratio can be seen below. These two ways describe a group of fruit that is made up of 3 apples and 7 oranges.
    a.  The ratio of the number of apples to the the number of oranges is 3 to 7.
    b.  For every 3 apples there are 7 oranges.
 
B.  Expressing a ratio in a sentence form is easily accomplished if you use these two sentence starters:
            1.  Using 3:2 - For every 3 bananas, there are 2 apples.
            2.  Using 3:2 - The ratio of the number of bananas to the number of apples is 3:2
 
C. Using the Tape Diagram with Problem Solving
      1. Construct the tape diagram.
      2.  Use division to solve for the value of nonzero number c.
      3.  Use multiplication and the value of nonzero number c to help you find the value of the second tape.  
      4.  State your answer by using the words in the question. 
 
D. Discovering Equivalent Ratios
If you can list multiples of a number, then you can find equivalent ratios for most given ratios. Multiples are numbers that we can county by.
For example, the multiples of 2 are 2, 4, 6, 8, 10, etc... 
The multiples of 3 are 3, 6, 9, 12, 15, etc...
The multiples of 4 are  4, 8, 12, 16, 20, etc...
If I start with the ratio 4:3, I can use multiples to find equivalent ratios (ratios that are equal to 4:3).
Looking at the multiples of 4, I can see that the next three numbers are 8, 12, and 16.
Looking at the multiples of 3, I can see that the next three numbers are 6, 9, and 12.
If I match the multiples in order, I get the following ratios that are equal to 4 to 3:
            8:6, 12:9, and 16:12
There are an infinite number of equivalent ratios.
 
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52 West Main Street Washingtonville, NY 10992  |  Phone: 845.497.4000  |  Fax: 845.497.4030
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