A painter has $\frac{2}{3}$ gallon of paint. Each section of fence requires $\frac{2}{9}$ gallon of paint. How many sections can the painter paint with the amount he has?
Answer (1)
Divide the total amount of paint by the amount of paint required per section: 3 2 ÷ 9 2 .
Multiply by the reciprocal: 3 2 × 2 9 .
Simplify the fraction: 6 18 = 3 .
The painter can paint 3 sections.
Explanation
Understanding the Problem We are given that a painter has 3 2 gallon of paint, and each section of fence requires 9 2 gallon of paint. We need to find out how many sections of fence the painter can paint with the available amount of paint.
Setting up the Calculation To find the number of sections the painter can paint, we need to divide the total amount of paint the painter has by the amount of paint required for each section. This can be written as: Number of sections = Amount of paint per section Total amount of paint \text{Number of sections} = \frac{\frac{2}{3}}{\frac{2}{9}}$ 3. Performing the Division To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction: \frac{\frac{2}{3}}{\frac{2}{9}} = \frac{2}{3} \div \frac{2}{9} = \frac{2}{3} \times \frac{9}{2} N o w , w e m u lt i pl y t h e n u m er a t ors an d t h e d e n o mina t ors : \frac{2 \times 9}{3 \times 2} = \frac{18}{6} F ina ll y , w es im pl i f y t h e f r a c t i o n : \frac{18}{6} = 3
Final Answer Therefore, the painter can paint 3 sections of fence with the amount of paint he has.
Examples
Imagine you're baking a cake and have 2/3 of a cup of sugar. If each cake requires 2/9 of a cup of sugar, this problem helps you determine how many cakes you can bake. Understanding division with fractions is crucial in various real-life scenarios, such as cooking, construction, and resource allocation. This skill enables you to efficiently manage and distribute resources according to specific requirements.
