Multiply the fraction by the total amount

Oct 13, 2025 by windailys.com 122 views

$Multiply the fraction by the total amount$

Introduction

In this article, we will delve into a word problem involving Hector and his money. We will analyze the situation, identify the key elements, and create an equation to represent the problem. This will help us understand the concept of fractions and how they can be used to solve real-world problems.

The Word Problem

Hector spent $\frac{3}{4}$ of his money the day after he cashed his paycheck of $50. Let $m$ represent the amount of money Hector spent.

Step 1: Identify the Key Elements

To create an equation that matches the word problem, we need to identify the key elements:

Hector's money: This is the total amount of money Hector has.
Fraction spent: Hector spent $\frac{3}{4}$ of his money.
Amount spent: Let $m$ represent the amount of money Hector spent.

Step 2: Create an Equation

We can create an equation to represent the situation by using the following steps:

Multiply the fraction by the total amount: Multiply the fraction $\frac{3}{4}$ by the total amount of money Hector has, which is $50.
Set up the equation: Set up an equation that represents the situation, where $m$ is the amount of money Hector spent.

Equation Options

Which of the following equations matches the word problem?

$\frac{3}{4} \times 50 = m$
$m = \frac{3}{4} \times 50$
$50 = \frac{3}{4} \times m$
$m = 50 - \frac{3}{4} \times 50$

Solution

To determine which equation matches the word problem, we need to analyze each option.

Option 1: $\frac{3}{4} \times 50 = m$ $\frac{3}{4} \times 50 = m$
- This equation represents the situation, where the fraction $\frac{3}{4}$ is multiplied by the total amount of money Hector has, which is $50.
- The result is equal to the amount of money Hector spent, which is represented by $m.
Option 2: $m = \frac{3}{4} \times 50$ $m = \frac{3}{4} \times 50$
- This equation is similar to Option 1, but the order of the terms is reversed.
- However, the meaning of the equation is the same, and it still represents the situation.
Option 3: $50 = \frac{3}{4} \times m$ $50 = \frac{3}{4} \times m$
- This equation represents the situation, but it is not the most straightforward option.
- The equation states that the total amount of money Hector has ($50) is equal to the fraction $\frac{3}{4}$ multiplied by the amount of money Hector spent ($m).
- However, this equation is not as clear as Option 1 or Option 2.
Option 4: $m = 50 - \frac{3}{4} \times 50$ $m = 50 - \frac{3}{4} \times 50$
- This equation represents the situation, but it is not the most straightforward option.
- The equation states that the amount of money Hector spent ($m) is equal to the total amount of money Hector has ($50) minus the fraction $\frac{3}{4}$ multiplied by the total amount of money Hector has.
- However, this equation is not as clear as Option 1 or Option 2.

Conclusion

Based on the analysis, the most straightforward equation that matches the word problem is:

$\frac{3}{4} \times 50 = m$

This equation represents the situation, where the fraction $\frac{3}{4}$ is multiplied by the total amount of money Hector has, which is $50. The result is equal to the amount of money Hector spent, which is represented by $m.

How Much Money Did Hector Spend?

To find the amount of money Hector spent, we can simply multiply the fraction $\frac{3}{4}$ by the total amount of money Hector has, which is $50.

$\frac{3}{4} \times 50 = 37.5$

Therefore, Hector spent $37.50.

Final Answer

$The final answer is $\boxed{37.5}$.<br/> **Hector's Money Problem: Q&A**$

Introduction

In our previous article, we analyzed a word problem involving Hector and his money. We created an equation to represent the situation and found that Hector spent $37.50. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the total amount of money Hector has?

A: The total amount of money Hector has is $50.

Q: What fraction of his money did Hector spend?

A: Hector spent $\frac{3}{4}$ of his money.

Q: How much money did Hector spend?

A: Hector spent $37.50.

Q: What is the equation that represents the situation?

A: The equation that represents the situation is:

$\frac{3}{4} \times 50 = m$

Q: Why is the equation $\frac{3}{4} \times 50 = m$ the most straightforward option?

A: The equation $\frac{3}{4} \times 50 = m$ is the most straightforward option because it clearly represents the situation. The fraction $\frac{3}{4}$ is multiplied by the total amount of money Hector has, which is $50. The result is equal to the amount of money Hector spent, which is represented by $m.

Q: Can we use other equations to represent the situation?

A: Yes, we can use other equations to represent the situation. However, the equation $\frac{3}{4} \times 50 = m$ is the most straightforward option.

Q: How can we find the amount of money Hector spent using the equation?

A: We can find the amount of money Hector spent by multiplying the fraction $\frac{3}{4}$ by the total amount of money Hector has, which is $50.

Q: What is the result of multiplying the fraction $\frac{3}{4}$ by the total amount of money Hector has?

A: The result of multiplying the fraction $\frac{3}{4}$ by the total amount of money Hector has is $37.50.

Q: Why is it important to understand the concept of fractions in real-world problems?

A: Understanding the concept of fractions is important in real-world problems because it helps us to represent and solve problems involving proportions and ratios.

Q: Can we use fractions to solve other real-world problems?

A: Yes, we can use fractions to solve other real-world problems. Fractions are a powerful tool for representing and solving problems involving proportions and ratios.

Conclusion

In this article, we answered some frequently asked questions related to the word problem involving Hector and his money. We found that Hector spent $37.50 and that the equation $\frac{3}{4} \times 50 = m$ is the most straightforward option to represent the situation. We also discussed the importance of understanding the concept of fractions in real-world problems.

Final Answer

The final answer is $\boxed{37.5}$ .