Open Middle®
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
Finding Equivalent Ratios
Now do the same with the digits 0 through 8.
it can be the same
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.
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.
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
1:2 = 2:4
I noticed one of your pages have a 404 error.
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