How to Solve Sixth Grade Ratios

People use ratios every day to calculate such values as how much will gasoline cost.

Knowing how to solve sixth-grade ratios is not just going to help you get an "A+" in class, it is also going to help you get through life. People use ratios everyday. If you need know how how much 4.5 gallons of gas costs given a rate of $3.58 per gallon, then you will need to know how to solve ratios. As you can see, knowing how to solve ratios comes in handy.

Instructions

1. Setup some initial ratios with the data values you know. For clarification, a ratio is the relationship between two quantities expressed as a fraction. The numbers 1/2, 2/3 and 3/4 are all ratios. Let's use the example cited in the introduction to form some initial ratios. Given that gas costs $3.58 per gallon, you could setup the ratio 3.58 dollars/1 gallon, or 3.58/1.

2. Establish ratios for the data values you don't know. Given that you need to know how much it would cost to buy 4.5 gallons of gas, you could create the ratio 4.5 gallons / X dollars. We are using an 'X' to indicate that we don't yet know that specific value.

3. Compare the ratio you know with the ratio you don't and make certain that they are compatible. For two ratios to be compatible, they must be in the same form. For instance, if the first ratio's numerator is in dollars and denominator is in pennies, then the second ratio's numerator should be in dollars and denominator should be in pennies.

   In the example, the ratio you know is 3.58 dollars/1 gallon, and the ratio you don't know is 4.5 gallons / X dollars. These ratios aren't compatible because the first ratio's numerator and denominator are dollars and gallons, respectively, while the second ratio's numerator and denominator are gallons and dollars. To fix this, you need only reverse one of the ratios. So if you choose to reverse the unknown ratio, it would become X dollars / 4.5 gallons.

4. Cross-multiply both ratios. Cross-multiplying involves multiplying the first ratio's numerator by the second ratio's denominator, and then setting that to be equal to the product of the first ratio's numerator and the second ratio's numerator. Given the ratios 3.58 dollars / 1 gallon and X / 4.5 gallons, you would multiply 3.58 by 4.5 and set it to equal the product of 1 multiplied by X. So 3.58 x 4.5 = 1 x X. Since 1 times anything equals itself, you know that the unknown value (X) is just 3.58 x 4.5, or 16.11, which just happens to be the final answer.

References

• Home School Math: Teaching Ratios and Proportions