Equivalent Fractions and Ratios


Brush up the concept of Equivalent Ratios.

Julia is making goodie bags. She packs 1 candy and 4 cookies in each goodie bag.



  The table below shows the number of candies and the number of cookies that she will need.

Number of goodie bags12345
Number of candies12345
Number of cookies48121620
Number of candies as a fraction of the number of cookies1
4
2
8
 3 
12
 4 
16
 5 
20
Simplified fraction1
4
1
4
1
4
1
4
1
4
Ratio of the number of candies to the number of cookies1 : 42 : 83 : 124 : 165 : 20
Simplified ratio1 : 41 : 41 : 41 : 41 : 4


1
4
  =  2
8
  =   3 
12
  =   4 
16
  =   5 
20
When two or more fractions can be simplified to the same fraction, they are said to be equivalent fractions.

1 : 4  =  2 : 8  =  3 : 12  =  4 : 16  =  5 : 20
When two or more ratios can be simplified to the same ratio, they are said to be equivalent ratios.

The number of candies and cookies used for the goodie bags are in the same ratio.
  • If Julia uses 2 candies, she uses 8 cookies.

  • If Julia uses 6 candies, how many cookies does she use?
    Using fraction:   1
    4
      =  6
    ?
     1
    4
      =  1 × 6
    4 × 6
        =   6 
    24
     She uses 24 cookies.
     
    Using ratio:   1 : 4  =  6 : ?
     1 : 4  =  1 × 6 : 4 × 6
        =  6 : 24
     She uses 24 cookies.

  • If Julia uses 28 cookies, how many candies does she use?
    Using fraction:   1
    4
      =  ?
    28
     1
    4
      =  1 × 7
    4 × 7
        =   7 
    28
     She uses 7 candies.
     
    Using ratio:   1 : 4  =  ? : 28
     1 : 4  =  1 × 7 : 4 × 7
        =  7 : 28
     She uses 7 candies.

  • If Julia makes 9 goodie bags, how many cookies does she use?
    Using fraction:   1
    4
      =  1 × 9
    4 × 9
        =   9 
    36
     She uses 36 cookies.
     
    Using ratio:   1 : 4  =  1×9 : 4×9
        =  9 : 36
     She uses 36 cookies.

Word Problem 1

Leela adds fertilizer to her flower pots which are all of the same size. She uses 3 tablespoons of fertilizer for every 9 flower pots.
   a)
 
Express the number of tablepoons of fertilizer as a fraction of the number of flower pots in the simplest form.
   b)
 
If she has 6 flower pots, how many tablespoons of fertilizer does she need?
   c)How many flower pots are needed if 5 tablespoons of fertilizer is used?
a)    3
9
  =  3 ÷ 3
9 ÷ 3
  =  1
3
      
b)    1
3
  =  ?
6
 1
3
  =  1 × 2
3 × 2
    =  2
6
       She needs 2 tablespoons of fertilizer.

c)    1
3
  =  1 × 5
3 × 5
    =   5 
15
       15 flower pots are needed if 5 tablespoons of fertilizer is used.

Word Problem 2

Larry is making a pattern with 14 green tiles for every 70 blue tiles.
   a)
 
Find the ratio of the number of green tiles to the number of blue tiles in the simplest form.
   b)
 
Find the ratio of the number of blue tiles to the number of green tiles.
   c)If he uses 35 green tiles, how many blue tiles does he use?
   d)If he uses a total of 120 tiles, how many of them are blue?
   e)
 
 
He adds red tiles to the pattern so the ratio of the number of green tiles to the number of blue tiles to the number of red tiles is 1:5:2. If he uses 240 tiles altogether, how many of them are red?
a)    14 : 70 = 1471 : 70355 = 1 : 5
 The ratio of the number of green tiles to the number of blue
tiles is 1 : 5.

b)    70 : 14 = 70355 : 1471 = 5 : 1
 The ratio of the number of blue tiles to the number of green
tiles is 5 : 1.

c)    
 
The number of green tiles and blue tiles used are in the ratio
1 : 5.

      

      1 unit  =  35
      5 units  =  35 × 5
         =  175
 
      He uses 175 blue tiles.

d)    
 
Again, the ratio of the number of green tiles to the number
of blue tiles is 1 : 5.

      

      6 units  =  120
      1 unit  =  120 ÷ 6
         =  20
      5 units  =  20 × 5
         =  100
 
      There are 100 blue tiles.

e)    
 
The ratio of the number of green tiles to the blue
tiles to red tiles is 1 : 5 : 2.

      

      8 units  =  240
      1 unit  =  240 ÷ 8
         =  30
      2 units  =  30 × 2
         =  60
 
      There are 60 red tiles.