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# Finding Equivalent Ratios

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

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

### Hint

Think halves

6:3 = 18:9 = 54:27

Source: Graham Fletcher

## Ordering Rational Numbers

Directions: Using the digits 1 to 9 at most once each, fill in the boxes …

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.

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