Divide the total length of the race by the number of athletes. Rewrite the whole number as a fraction. Then, multiply the first fraction by the reciprocal of the second fraction.
Equation: 110÷ 4= Solution: 140 kilometer
Practice makes perfect
A relay race is 110 kilometer long. We are told that 4 athletes will run an equal distance to complete the relay. We want to write an equation and solve it to determine how far each athlete will run. The distance will be the result of a division of the length of the race by the number of athletes. We can write the following equation to represent this situation.
1/10÷ 4=
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.
1/10÷ 4=1/10÷4/1
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 41 is 14, because 41* 14=1.
1/10 ÷ 4/1=1/10 * 1/4
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.
1/10÷ 4=1/40
This means that the each athlete will run 140 kilometer.
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.
