Divide the total length of the licorice by the number of pieces. Rewrite the whole number as a fraction. Then, multiply the first fraction by the reciprocal of the second fraction.
Equation: 23÷ 10= Solution: 115 yard
Practice makes perfect
We are told that a piece of licorice is to be cut into 10 equal-size pieces. We want to find the length of each piece of licorice if the length of the whole piece is 23 yard. To do so, we will write and solve an equation. The length of a single piece will be the result of a division of the length of the licorice by the number of pieces it will be cut into. We can write the following equation to represent this situation.
2/3÷ 10=
Now, to find the solution of this equation, we need to divide a fraction by a whole number. Before we do so, we will write the whole number as a fraction.
2/3÷ 10=2/3÷10/1
Next, 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 101 is 110, because 101* 110=1.
2/3 ÷ 10/1=2/3 * 1/10
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.
2/3÷ 10=1/15
This means that the length of each piece of licorice will be 115 yard.
Checking Our Answer
We can check our answer by substituting the obtained result for the first fraction and multiplying it by the second fraction from the transformed equation. The product we get should be the dividend of the written expression.
