Finding Equivalent Ratios

Directions: Use the digits 1-9 to create 3 equivalent ratios.
Each digit can only be used once.

__:__ = __ __ : __ = __ __ : __ __

Hint

Think halves

Answer

6:3 = 18:9 = 54:27

Source: Graham Fletcher

Print Friendly, PDF & Email

Check Also

Greatest Common Factor

Directions: Using the digits 0 to 9 at most one time each, place a digit …

13 comments

  1. Now do the same with the digits 0 through 8.

  2. A second solution is: 6:3 = 14:7 = 58:29. Perhaps a secondary hint could be: given the series of numbers think where to place the “5” digit. It narrows the possibility for third ratio to be either: 27/54, 28/56, 29/58. I ended up writing up a solution for teachers working our Title 1 after school program. https://teacherleaders.files.wordpress.com/2016/02/finding-equivalent-ratios-open-middle1.pdf

    • But how did you get 14? There is no way 6 can get 14.
      1*6 =6
      2*6 =12
      3*6 =18
      4*6 =24
      5*6 =30
      6*6 =36
      7*6 =42
      8*6 =48
      9*6 =54

      • Equivalent ratios are equivalent when they have the same value of the ratio. Meaning when you turn a ratio into a fraction and simplify, the answers should equal if they are equivalent.

        x:y = x/y
        6:3 = 6/3 = 2
        14:7 = 14/7 = 2
        58:29 = 58/29 = 2

        These are all equivalent and would be found on the same graph.

    • THANK YOU SO MUCH THE MATH TEACHER made us do digest with 1 to 9 and you can’t repeat it thank you so much I wish you the best in life.

  3. 6:3 = 18:9 = 54:27

    • Nina, 6 times 2 and 1/3 is 14, 3 times 2 and 1/3 is 7, so 6:3 is equivalent to 14:7 because both numbers have been multiplied by 2 1/3.

  4. A florist uses 225 branches of winterberry to make 75 wreaths based on this ratio how many branches of winterberry does the floris use for 25 wreaths

  5. I noticed one of your pages have a 404 error.

  6. Rudolf Österreicher

    6/3 = 14/7 = 58/29 and 6/3 = 18/9 = 54/27 are the only possible solutions.

    With (non-leading) zero added as a digit, we also get:
    4/2 = 10/5 = 76/38
    4/2 = 10/5 = 78/39
    4/2 = 16/8 = 70/35
    4/2 = 18/9 = 70/35
    8/4 = 10/5 = 72/36
    8/4 = 12/6 = 70/35
    9/2 = 36/8 = 45/10
    9/6 = 12/8 = 45/30

    With leading zeros allowed, we additionally get:
    2/3 = 06/9 = 54/81
    2/6 = 03/9 = 18/54
    3/2 = 09/6 = 81/54
    3/9 = 02/6 = 18/54
    4/1 = 28/7 = 36/09
    4/1 = 36/9 = 28/07
    6/2 = 09/3 = 54/18
    6/9 = 02/3 = 54/81
    7/1 = 28/4 = 63/09
    7/1 = 63/9 = 28/04
    8/1 = 24/3 = 56/07
    8/1 = 32/4 = 56/07
    8/1 = 56/7 = 24/03
    8/1 = 56/7 = 32/04
    9/1 = 27/3 = 54/06
    9/1 = 36/4 = 72/08
    9/1 = 54/6 = 27/03
    9/1 = 54/6 = 72/08
    9/1 = 72/8 = 36/04
    9/1 = 72/8 = 54/06
    9/3 = 06/2 = 54/18
    9/6 = 03/2 = 81/54

Leave a Reply to Mila Cancel reply

Your email address will not be published. Required fields are marked *