Fraction Of Allowance Spent On Food A Math Problem Solved

In this article, we will delve into a common mathematical problem involving fractions and proportions. Many students find fraction problems challenging, but with a clear, step-by-step approach, these problems can be easily solved. We will break down the problem: Adrian spent 5/8 of his weekly allowance. Three-fifths of the amount was spent on food. What fraction of his weekly allowance did he spend on food? This question requires us to understand how to multiply fractions and apply this knowledge to a real-world scenario. By the end of this article, you will not only understand the solution to this specific problem but also grasp the general principles involved in solving similar fraction-related questions.

To effectively solve this problem, we need to break it down into smaller, manageable parts. The first key piece of information is that Adrian spent 5/8 of his weekly allowance. This means that if we divide Adrian's total allowance into eight equal parts, he spent five of those parts. The second crucial piece of information is that three-fifths of the amount he spent was used for food. This tells us that out of the 5/8 of his allowance that Adrian spent, we need to find what fraction represents the portion spent on food. Understanding these two fractions and how they relate to each other is the key to solving the problem. We are essentially looking for a fraction of a fraction, which involves multiplying the two fractions together. This step-by-step approach makes the problem less daunting and easier to understand. Before diving into the calculation, it's important to visualize what these fractions mean in the context of Adrian's allowance. This will help in ensuring that the final answer makes logical sense.

Now that we have a clear understanding of the problem, let's apply the mathematical approach to find the solution. The core concept here is multiplying fractions. When we want to find a fraction of another fraction, we multiply them. In this case, we need to find three-fifths (3/5) of five-eighths (5/8) of Adrian's allowance. Mathematically, this translates to multiplying 3/5 by 5/8. The rule for multiplying fractions is simple: multiply the numerators (the top numbers) together and multiply the denominators (the bottom numbers) together. So, we have (3/5) * (5/8) = (3 * 5) / (5 * 8). This gives us 15/40. However, this fraction is not in its simplest form. To simplify it, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it. The GCD of 15 and 40 is 5. Dividing both 15 and 40 by 5, we get 3/8. Therefore, Adrian spent 3/8 of his weekly allowance on food. This mathematical process provides a clear and concise way to arrive at the solution.

To ensure clarity, let's walk through the step-by-step solution again:

1. Identify the fractions: Adrian spent 5/8 of his allowance, and 3/5 of this amount was for food.
2. Set up the multiplication: We need to find 3/5 of 5/8, which means we multiply the two fractions: (3/5) * (5/8).
3. Multiply the numerators: 3 * 5 = 15.
4. Multiply the denominators: 5 * 8 = 40.
5. Write the resulting fraction: This gives us 15/40.
6. Simplify the fraction: Find the greatest common divisor (GCD) of 15 and 40, which is 5. Divide both the numerator and the denominator by 5.
7. Simplified fraction: 15 ÷ 5 = 3, and 40 ÷ 5 = 8. So, the simplified fraction is 3/8.
8. Final answer: Therefore, Adrian spent 3/8 of his weekly allowance on food. This step-by-step breakdown not only provides the answer but also ensures a clear understanding of the process involved. Each step is logical and builds upon the previous one, making it easier to follow and replicate for similar problems.

When dealing with fraction problems, several common mistakes can occur. One frequent error is adding or subtracting fractions without finding a common denominator first. This is incorrect because fractions must have the same denominator to be added or subtracted directly. In our problem, we are multiplying fractions, so a common denominator is not required, but it's a crucial point to remember for addition and subtraction. Another mistake is forgetting to simplify the final fraction. While 15/40 is technically correct, it is best practice to simplify it to 3/8 to represent the fraction in its simplest form. This makes the answer cleaner and easier to understand. A third common mistake is misinterpreting the problem and performing the wrong operation. For instance, students might mistakenly add the fractions instead of multiplying them. Carefully reading the problem and identifying the key words (such as "of," which often indicates multiplication) can help avoid this mistake. By being aware of these common pitfalls, students can approach fraction problems with greater confidence and accuracy.

Understanding fractions is not just about solving mathematical problems in textbooks; it has numerous real-world applications. Fractions are used in cooking, baking, measuring ingredients, calculating discounts, and even in understanding time. For example, when a recipe calls for 1/2 cup of flour, you need to understand what that fraction represents to measure the correct amount. In financial contexts, fractions are used to calculate percentages and proportions, such as understanding interest rates or calculating shares of a company. In construction and engineering, fractions are crucial for accurate measurements and cutting materials to the correct size. Even in everyday situations like splitting a pizza with friends, you are using fractions to divide the pizza into equal slices. The ability to work with fractions is a fundamental life skill that helps in making informed decisions and solving practical problems in various aspects of life. Therefore, mastering fractions is not just an academic exercise but a valuable tool for navigating the world around us.

To further reinforce your understanding of fraction problems, let's look at a few practice problems:

1. Problem 1: Sarah spent 2/3 of her savings on a new bicycle. If she had $150 in savings, how much did the bicycle cost?
2. Problem 2: A recipe calls for 3/4 cup of sugar. If you only want to make half of the recipe, how much sugar do you need?
3. Problem 3: John read 1/5 of a book on Monday and 2/5 of the book on Tuesday. What fraction of the book has he read in total?

Solutions:

1. Problem 1 Solution: To find 2/3 of $150, multiply (2/3) * 150 = $100. The bicycle cost $100.
2. Problem 2 Solution: To find half of 3/4, multiply (1/2) * (3/4) = 3/8. You need 3/8 cup of sugar.
3. Problem 3 Solution: To find the total fraction of the book read, add 1/5 + 2/5 = 3/5. John has read 3/5 of the book.

These practice problems illustrate how fraction concepts can be applied in various scenarios. By working through these examples, you can build confidence and improve your problem-solving skills. Remember to break down each problem into smaller steps and identify the key information needed to arrive at the solution.

In conclusion, solving fraction problems like the one about Adrian's allowance involves understanding the basic principles of fraction multiplication and simplification. By breaking the problem down into smaller steps, identifying the key information, and applying the correct mathematical operations, you can arrive at the solution with confidence. Remember, the key is to practice regularly and apply these concepts to real-world situations. Understanding fractions is not just about getting the right answer in a math problem; it's a fundamental skill that enhances your ability to solve a wide range of problems in everyday life. From cooking and baking to managing finances and making informed decisions, fractions play a crucial role. So, keep practicing, and you'll find that fractions become less daunting and more manageable over time. Mastering fractions is a valuable investment in your mathematical skills and your overall problem-solving abilities.