A 20-acre piece of land is subdivided into $\frac{5}{6}$ acre lots. How many lots are there?
Answer (2)
Divide the total land area (20 acres) by the area of each lot ( 6 5 acres).
Multiply 20 by the reciprocal of 6 5 , which is 5 6 .
Calculate 20 × 5 6 = 5 120 .
Simplify to find the number of lots: 24 .
Explanation
Understanding the Problem We are given a 20-acre piece of land that is subdivided into smaller lots, each with an area of 6 5 acres. Our goal is to determine the number of these smaller lots that can be created from the 20-acre piece of land.
Setting up the Calculation To find the number of lots, we need to divide the total area of the land by the area of each lot. This can be expressed as: Number of lots = Area of each lot Total area of land Number of lots = 6 5 20
Performing the Calculation To divide by a fraction, we multiply by its reciprocal. The reciprocal of 6 5 is 5 6 . Therefore, we have: Number of lots = 20 × 5 6 Number of lots = 5 20 × 6 Number of lots = 5 120 Number of lots = 24
Stating the Answer Therefore, the 20-acre piece of land can be subdivided into 24 lots, each with an area of 6 5 acres.
Examples
Imagine you're planning a community garden on a 20-acre plot, and you want to divide it into individual garden plots of 6 5 acre each. Knowing how many plots you can create helps you plan the layout, allocate resources, and manage the garden effectively. This division problem is also applicable in urban planning, where large areas are subdivided into smaller parcels for housing or commercial development. Understanding how to divide land efficiently ensures optimal use of space and resources.
A 20-acre piece of land can be subdivided into 24 lots of 6 5 acres each. This is found by dividing the total area by the area of each lot. The division involves multiplying by the reciprocal of the fraction.
;
