When it comes to mathematical operations, division can sometimes feel daunting, especially when fractions are involved. In this article, we will dissect the operation of dividing a whole number by a fraction, specifically focusing on the question: What is 4 divided by 3/5?
What Does 4 Divided by 3/5 Mean?
To understand what dividing by a fraction entails, it's essential to grasp that division by a fraction is the same as multiplying by its reciprocal.
Reciprocal of a Fraction: The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of 3/5 is 5/3.
The StepbyStep Calculation
Here’s how we can solve 4 ÷ (3/5):

Convert the Division into Multiplication: [ 4 \div \frac{3}{5} = 4 \times \frac{5}{3} ]

Rewrite the Whole Number as a Fraction: To make multiplication easier, we can express the whole number 4 as a fraction: [ 4 = \frac{4}{1} ]

Multiply the Two Fractions: [ \frac{4}{1} \times \frac{5}{3} = \frac{4 \times 5}{1 \times 3} = \frac{20}{3} ]

Convert the Improper Fraction to a Mixed Number (optional): To express (\frac20}{3}) as a mixed number, we divide 20 by 3. The result is 6 with a remainder of 2{3} = 6 \frac{2}{3} ]
Practical Examples
To further cement this concept, let’s consider practical scenarios where this kind of calculation might apply.
Example 1: Baking Recipe
Suppose you have a recipe that requires (\frac{3}{5}) of a cup of sugar for one batch of cookies. If you want to make 4 batches, you need to calculate how much sugar in total you need.
Using the division we calculated:
 Total Sugar: 4 ÷ (3/5) = (\frac{20}{3}) or approximately 6.67 cups of sugar.
Example 2: Painting a Fence
If a section of a fence requires (\frac{3}{5}) of a gallon of paint, and you want to paint 4 sections, you again use the same calculation to find out how many gallons are needed:
 Total Paint Needed: 4 ÷ (3/5) = (\frac{20}{3}) gallons or 6.67 gallons.
Conclusion
Dividing whole numbers by fractions may initially seem complicated, but understanding the operation of multiplying by the reciprocal simplifies the process significantly. As demonstrated, when you calculate 4 divided by 3/5, you arrive at a result of (\frac{20}{3}) or 6⅔.
This operation is not just theoretical; it has practical applications in everyday situations, from cooking to home improvement projects. Mastering how to divide by fractions will surely enhance your math skills and confidence in tackling realworld problems.
Attributions
 Questions and Answers from BrainlY: This article builds upon common inquiries found on educational platforms like BrainlY, which encourages deeper understanding through practical examples and clear explanations.
By breaking down mathematical concepts into relatable scenarios, we can make learning not just effective but enjoyable. Whether you're a student trying to grasp the fundamentals or someone looking to brush up on your math skills, understanding division with fractions is a valuable tool.