Question

Dan mows 1/4 of his grandmother's lawn and uses 1/2 gallon of gas. What fraction of the lawn can Dan mow per gallon?

Answer 1

$\frac{1}{2}$ of the grandmother's lawn Dan can mow per gallon.

Option C

Solution:

Given that, mowing $\frac{1}{4}$ uses $\frac{1}{2}$ gallon of gas.

To find: The fraction of the lawn can Dan mow per gallon

According to unitary method,

$\frac{1}{2}$ gallon of gas is required to mow $\frac{1}{4}$ of lawn that is $\frac{1}{2}\rightarrow \frac{1}{4}$

Therefore, 1 gallon of gas will be required to mow $\frac{1}{2}\times2\rightarrow \frac{1}{4}\frac2$

$\Rightarrow1 \text{ gallon }\rightarrow \frac{1}{2} \text{ of lawn}$

Therefore, one gallon will be enough to mow $\frac{1}{2}$ of lawn.

Unitary method:

The unitary method is a technique to solve a problem by finding the value of a single unit first, and then finding the required value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.