Solving Math Problems Involving Fractions: A Comprehensive Guide

In this article, we will provide a step-by-step breakdown of how to solve math problems involving fractions. Specifically, we will address a common type of problem where a person distributes food: how much food is left after certain actions. We will explore different scenarios and show how to solve them accurately.

Introduction to Fractions and Problem Context

Fractions are an essential part of mathematics, and understanding them is crucial for solving various practical problems. A common real-life scenario involves distributing food or other items, as each fraction represents a portion of the total. For instance, consider the problem: Geo went to the store to pick up food and paid 37. He then ate 1/4 of the food and gave 1/6 to his mom. How much food did he have left?

Scenario #1: Eating and Giving Away Food

Let's first consider the original scenario where Geo ate 1/4 of the food and gave 1/6 to his mom. To find out how much food Geo has left, we need to determine the total amount of food that was consumed or given away and then subtract it from the initial amount.

Step-by-Step Solution

Total fraction consumed: Geo ate 1/4 of the food. He gave 1/6 to his mom.

To add these fractions, we need a common denominator. The least common denominator of 4 and 6 is 12. Converting the fractions: 1/4 3/12 1/6 2/12

Now, we add these fractions:
3/12 2/12 5/12

So, Geo consumed or gave away 5/12 of the food. The remaining food is: 1 - 5/12 7/12

Verifying the Solution

The cost of the food (37) is not relevant to the amount of food left. However, to verify the fraction, we can calculate the actual amount of food left: 7/12 of 37 37 * (7/12) 21.17 (approximately)

Scenario #2: Complex Distribution

Now, let's consider the scenario where the question states Geo ate 1/8 of the food and gave 1/2 to his mom. This scenario introduces an additional layer of complexity.

Step-by-Step Solution

Total fraction consumed: Geo ate 1/8 of the food. He gave 1/2 to his mom.

To add these fractions, we need a common denominator. The least common denominator of 8 and 2 is 8. Converting the fractions: 1/2 4/8

Now, we add these fractions:
1/8 4/8 5/8

So, Geo consumed or gave away 5/8 of the food. The remaining food is: 1 - 5/8 3/8

Verifying the Solution

Again, the cost of the food (37) is not relevant. However, to verify the fraction, we can calculate the actual amount of food left: 3/8 of 37 37 * (3/8) 13.88 (approximately)

Scenario #3: Mixed Fractions

Finally, let's consider the scenario where Geo initially ate 1/6 and then gave 2/10. This scenario combines different fractions that need to be adjusted for a common denominator.

Step-by-Step Solution

Adjusting Fractions for a Common Denominator: 1/6 5/30 2/10 6/30

Now, we add these fractions:
5/30 6/30 11/30

So, Geo consumed or gave away 11/30 of the food. The remaining food is: 1 - 11/30 19/30

Verifying the Solution

Again, the cost of the food (37) is not relevant. However, to verify the fraction, we can calculate the actual amount of food left: 19/30 of 37 37 * (19/30) 23.23 (approximately)

Conclusion

Understanding fractions is crucial for solving a wide range of math problems, especially those involving the distribution of items like food. By carefully following the steps of finding a common denominator, converting fractions, and then solving, you can accurately determine the remaining amount of food or any other item distributed in fractional parts.

Remember, the cost of the food (37 in this case) is not relevant to the problem of finding the remaining quantity of food. Always focus on the fractions and the operations involved in the distribution.