How Do You Determine Whether Values in a Table are Proportional?

If the ratio of veggie plants to flowers is the same for each column, then the values in the table are proportional
Translate the two rows in the table to ratios by writing them as fractions
Reduce ratios by dividing the top and bottom of each fraction by the GCF of the two numbers
GCF stands for Greatest Common Factor
All ratios reduce to 2/3, so they are all equivalent
This means the values in the table are proportional!

1. One way we can write ratios is as fractions, so we'll create five fractions from our table
2. Then we can reduce our fractions to see if our ratios are equivalent
3. The numbers of veggie plants are in the numerators
4. The numbers of flowers are in the denominators
1. GCF stands for Greatest Common Factor
2. The GCF of 4 and 6 is 2
3. The GCF of 6 and 9 is 3
4. The GCF of 8 and 12 is 4
5. The GCF of 10 and 15 is 5
6. The GCF of 14 and 21 is 7
7. GCF/GCF is just a fancy form of 1
1. Using each ratio's GCF, we reduced each one down to 2/3!
2. Since all the ratios reduce to the same thing, that means they are all equivalent
3. Since all the ratios are equivalent, that means the values in our table are proportional!

The 8th grade students are planting gardens for a science project. Determine whether the number of vegetable plants is proportional to the number of flowers in all the gardens.