Divide the total amount of dye by the amount needed to tie-dye 1 T-shirt. To do so, multiply the first fraction by the reciprocal of the second fraction.
Equation: 34÷ 38= Solution: 2 T-shirts
Practice makes perfect
We are told that to tie-dye 1 T-shirt, 38 cup of dye is needed. We are given a table showing the number of cups of dye in Mr. Galvez's art class. We want to write and solve an equation to find how many T-shirts can be made using only orange dye. First, consider the given table.
Amount of Dye
Color
Number of Cups
red
12
orange
3/4
To find the number of T-shirts that can be made using orange dye, we will divide the total amount of orange dye, by the amount needed to tie-dye 1 T-shirt. We can write the following equation to represent this situation.
3/4÷ 3/8=
Recall that dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. In our case, the reciprocal of 38 is 83, because 38* 83=1.
3/4 ÷ 3/8=3/4 * 8/3
When multiplying fractions, remember that the product of two fractions is equal to the product of the numerators over the product of the denominators.
Finally, we can write the solution of the previously written equation.
3/4÷ 3/8=2
This means that using only orange dye, 2 T-shirts can be made.
Checking Our Answer
We can check our answer by substituting the obtained result for the first expression and multiplying it by the second fraction from the equation. The product we get should be the dividend of the written expression.
