Solving a Real-World Math Problem: Batches of Biscuits with Fractions
When dealing with recipes and factory operations, understanding fractions is crucial. In this article, we will tackle a practical problem involving a factory's biscuit production. The challenge is to determine how many batches of biscuits a factory can produce with a given amount of flour. Specifically, we will explore the question: A factory takes 1 1/3 bags of flour to make a batch of biscuits. How many batches can it make with 1 2/3 bags of flour?
Understanding the Problem
The problem at hand requires us to divide the total amount of flour available by the amount needed per batch. Here's the problem in mathematical terms:
Problem Statement:
1 2/3 / 1 1/3
Step-by-Step Solution
Let's break down the steps to solve this problem with clarity and detail.
Simplifying the Problem
First, we need to convert the mixed numbers into improper fractions.
Convert 1 1/3 to an improper fraction: 1 1/3 (1 * 3 1) / 3 4/3 Convert 1 2/3 to an improper fraction: 1 2/3 (1 * 3 2) / 3 5/3Now, our problem looks like this:
5/3 / 4/3
Multiplying by the Reciprocal
To divide by a fraction, we multiply by its reciprocal. Therefore, we have:
5/3 * 3/4
When multiplying fractions, we multiply the numerators and denominators separately.
(5 * 3) / (3 * 4)
This simplifies to:
15/12
Next, we simplify the fraction 15/12.
15/12 5/4
Finally, we convert the improper fraction 5/4 back into a mixed number:
5/4 1 1/4
Therefore, the factory can make 1 1/4 batches of biscuits with 1 2/3 bags of flour.
Conclusion
By carefully breaking down the problem and performing the necessary calculations, we determined that a factory can produce 1 1/4 batches of biscuits with the provided amount of flour. Understanding these steps is not only beneficial for solving similar problems but also for managing resources in real-world factory settings. Fractions play a vital role in various industries, from baking and manufacturing to science and engineering. So, the next time you encounter a similar problem, you'll be well-equipped to solve it efficiently.