Math Problem Statement

George is building a fence. He builds his fence at a constant rate of 1/3 section of fence every 1/2 hour. At this rate, what fraction represents the section of fence George can build per hour?

Solution

Let's break down the problem in the image step by step:

Problem:

  • George builds 13\frac{1}{3} section of fence in 12\frac{1}{2} hour.
  • We are asked to find what fraction of the fence George can build per hour.

Solution Approach:

To find the amount of fence George builds per hour, we need to divide the section of fence built (13\frac{1}{3}) by the time it takes (12\frac{1}{2} hour). This can be expressed as:

13÷12\frac{1}{3} \div \frac{1}{2}

When dividing fractions, we multiply by the reciprocal of the divisor. So:

13×21=1×23×1=23\frac{1}{3} \times \frac{2}{1} = \frac{1 \times 2}{3 \times 1} = \frac{2}{3}

Final Answer:

George builds 23\frac{2}{3} of a section of the fence per hour.

Would you like further details on this process, or any clarifications?

Follow-up Questions:

  1. What is the general rule for dividing fractions?
  2. Can you apply this method to different values of fence sections and time?
  3. How would this change if George built 14\frac{1}{4} of the fence in 12\frac{1}{2} hour?
  4. What if George built 13\frac{1}{3} of the fence in 34\frac{3}{4} of an hour?
  5. How would you calculate the time needed if George built an entire fence at the same rate?

Tip:

When dividing fractions, remember to multiply by the reciprocal of the second fraction!

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Multiplication of Fractions
Unit Rate

Formulas

Division of fractions: a ÷ b = a × (1/b)
Multiplication of fractions: a/b × c/d = (a × c)/(b × d)

Theorems

Reciprocal Theorem: Division by a fraction is equivalent to multiplying by its reciprocal

Suitable Grade Level

Grade 5-7