The character in our video multiplied the original value for black paint by 5 to get the new value for black paint. So, she also
multiplied the original value for green paint by 5 to get the new value for green paint. There are multiplicative relationships, relationships related to multiplication, in a ratio table. To get from values for green and black in one ratio to values for green and black in another ratio, we can multiply both the initial values by the same number. For example, to get from the ratio 3:2 to the ratio 6:4, we multiply both the 3 and 2 by 2. And to get from the ratio 3:2 to the ratio 15:10, we multiply both the 3 and 2 by 5. Sometimes, there are also relationships related to addition, called additive relationships, in a ratio table. To get from one value for green to another value for green, we can add 3. To get from one value for black to another value for black, we can add 2. When using the multiplicative relationship to find equivalent ratios, we can multiply both columns by the same number. But when using the additive relationship, we cannot add the same number to both columns.
A cookie mixture requires 3 teaspoons of sugar for every 4 teaspoons of salt. You want to triple the mixture. Which of these describes the ratio of teaspoons of sugar to salt you will use?
The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses.
