Welcome to our math problem-solving journey! In this article, we will delve into the intriguing question of what 3/4 of 4 is. Through step-by-step explanations and numerical computations, we will unlock the solution to this commonly asked problem. So, put on your math hats and let’s dive in!

### Key Takeaways:

- Understanding and solving fraction calculations is essential in
**math problem solving**. - Equations can be rewritten to represent word problems, facilitating solution determination.
- Addition, subtraction, division, and multiplication properties can be utilized to solve equations effectively.
- Applying equation-solving techniques equips us to tackle more complex mathematical problems.
- Fraction calculations are crucial in real-life scenarios, and our skills can be applied to solve practical problems.

## Understanding Fractions and Equations

To effectively solve the problem of finding 3/4 of 4, it’s crucial to have a solid grasp of fractions and equations. Understanding these concepts will enable us to break down word problems into mathematical equations and find solutions through substitution. Let’s take a closer look at how we can apply this knowledge to solve our **fraction calculation**.

### Breaking Down Word Problems

When faced with a word problem involving fractions, it’s essential to translate the problem into an equation. By doing so, we can easily identify the variables and formulate a step-by-step approach to finding the solution. Let’s consider an example:

“Samantha used 3/4 of her allowance to buy a book. If her total allowance is 4 dollars, how much money did she spend on the book?”

In this case, we can assign the variable “x” to represent the amount of money Samantha spent on the book. We also know that 3/4 of her allowance equals 4 dollars. This can be expressed as the equation:

x= (3/4) * 4

By rewriting the word problem as an equation, we have transformed it into a solvable mathematical problem. Now, let’s move on to solving the equation through substitution.

### Solving Equations Through Substitution

Substitution is a powerful technique that allows us to find the value of a variable in an equation. To solve our equation *x = (3/4) * 4*, we substitute the value of 4 for the fraction, resulting in:

x= (3/4) * 4 = 3

Having a visual representation of the **fraction calculation** can further enhance our understanding. The image above depicts the process of finding 3/4 of 4, reinforcing the concept and making it easier to follow along.

### Summary

Understanding fractions and equations is essential when solving complex math problems involving fraction calculations. By breaking down word problems into equations and applying substitution techniques, we can confidently find solutions. In the next sections, we will delve deeper into solving equations using different mathematical properties and explore various fraction operations. Stay tuned!

## Solving Equations Using Addition and Subtraction

When it comes to solving equations, the addition and subtraction properties play a crucial role. By adding or subtracting the same quantity from both sides of an equation, we can create equivalent equations with easily identifiable solutions. Let’s dive into the steps of using the **addition-subtraction property** to solve equations.

Step 1: Identify the equation and the variable you want to solve for. For example, consider the equation:

x + 7 = 15

Step 2: Determine whether you need to add or subtract to isolate the variable on one side of the equation. In the given equation, we need to subtract 7 from both sides to isolate the variable *x*.

x + 7 – 7 = 15 – 7

Step 3: Simplify both sides of the equation by performing the addition or subtraction. In this case:

x = 8

So, the solution to the equation *x + 7 = 15* is *x = 8*. We have successfully used the **addition-subtraction property** to find the value of *x*.

To further illustrate the **addition-subtraction property**, let’s consider another example:

2y – 5 = 11

In this case, we need to add 5 to both sides of the equation to isolate the variable *y*. After simplifying, we find:

2y = 16

Dividing both sides of the equation by 2, we find that *y = 8*. The addition-subtraction property allows us to solve equations efficiently by manipulating the equation to isolate the variable of interest.

### Example table:

Equation | Solution |
---|---|

x + 7 = 15 | x = 8 |

2y – 5 = 11 | y = 8 |

Now that we have mastered the addition-subtraction property, let’s move on to exploring other equation-solving techniques in the upcoming sections.

## Solving Equations Using Division

In mathematics, the **division property** is a valuable tool for solving equations. By dividing both sides of an equation by the same nonzero quantity, we can simplify the equation and find the solution. Let’s explore this method further.

When solving equations using the **division property**, the goal is to isolate the variable on one side of the equation. By dividing both sides of the equation by the same nonzero number, we create equivalent equations that maintain the equality.

Example:

Consider the equation 5x = 20. To solve for x, we can divide both sides of the equation by 5, as follows:

- 5x/5 = 20/5
- x = 4

The **division property** allows us to simplify the equation and find its solution efficiently. However, it’s important to note that division can only be performed when the divisor is nonzero. Dividing by zero is undefined and does not yield a valid solution.

### Applying the Division Property in Practice

Now that we understand the division property, let’s apply it to a real-life problem:

Problem: You have a cake that is divided into 8 equal slices. How many slices will each person receive if there are 24 people?

To solve this problem, we can set up the following equation: 8x = 24, where x represents the number of slices each person will receive.

By applying the division property, we can divide both sides of the equation by 8:

- 8x/8 = 24/8
- x = 3

Therefore, each person will receive 3 slices of cake.

The division property is a fundamental concept in **equation solving** and plays a crucial role in various mathematical applications. By understanding and applying this property, we can confidently solve equations involving division and find solutions efficiently.

## Solving Equations Using Multiplication

When it comes to solving equations, the **multiplication property** is a valuable tool in our arsenal. By multiplying both sides of an equation by the same nonzero quantity, we can generate equivalent equations that have the same solution.

Let’s take a look at an example:

x– 5 = 10

To solve this equation, we can use the **multiplication property** to isolate the variable *x*. We want to get rid of the constant term (-5) on the left side of the equation, so we can multiply both sides by a suitable number that will cancel it out. Let’s choose 2 as our multiplier:

2(

x– 5) = 2(10)

When we distribute the 2 on the left side, we get:

2

x– 10 = 20

Now, we can simplify the equation by combining like terms:

2

x= 30

Finally, to find the value of *x*, we divide both sides of the equation by 2:

x= 15

Thus, the solution to the equation *x* – 5 = 10 is *x* = 15.

Step | Equation | Explanation |
---|---|---|

1 | x – 5 = 10 | Original equation |

2 | 2(x – 5) = 2(10) | Multiply both sides by 2 |

3 | 2x – 10 = 20 | Distribute 2 on the left side |

4 | 2x = 30 | Combine like terms |

5 | x = 15 | Divide both sides by 2 |

By utilizing the **multiplication property**, we were able to solve the equation and find the value of *x*. Remember, when applying this property, it’s crucial to consider the entire equation and perform the same operation on both sides to maintain the equation’s equality.

## Further Solutions of Equations

Now that we have learned various equation-solving techniques, we can apply them to solve more complex equations. In this section, we will explore the order of operations, **simplification rules**, and steps for solving first-degree equations. Let’s dive in!

### Order of Operations

When solving equations, it’s crucial to follow the correct order of operations to ensure accurate results. The commonly remembered acronym *PEMDAS* can help us remember the correct sequence:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Let’s see an example:

Solve the equation: *3x + 6 = 15 – 2x*

Step | Equation | Simplified Equation |
---|---|---|

Step 1 | 3x + 6 = 15 – 2x | 3x + 2x + 6 = 15 |

Step 2 | 5x + 6 = 15 | 5x = 9 |

Step 3 | x = 9/5 |

### Simplification Rules

When solving equations, it’s important to simplify both sides of the equation by applying **simplification rules**. Here are some common **simplification rules**:

- Combine like terms by adding or subtracting them.
- Move terms to the opposite side of the equation by adding or subtracting them.
- Multiply or divide both sides of the equation by the same nonzero quantity.

Let’s apply these simplification rules to solve another equation:

Solve the equation: *2(3x – 4) = 10*

Step | Equation | Simplified Equation |
---|---|---|

Step 1 | 2(3x – 4) = 10 | 6x – 8 = 10 |

Step 2 | 6x = 18 | |

Step 3 | x = 3 |

By following these equation-solving techniques and simplification rules, we can confidently solve more complex equations. Practice applying these concepts to gain proficiency in solving a variety of mathematical problems.

## Applying the Techniques to Our Problem

Now that we have acquired a solid understanding of fractions, equations, and various solving techniques, it’s time to apply our newfound knowledge to the specific problem of **finding three quarters of a number**, in this case, 3/4 of 4.

In order to solve this problem, we will follow a step-by-step approach, using the equations and techniques we have learned throughout the previous sections. By applying these strategies, we will be able to find the solution efficiently and accurately.

Let’s start by writing the equation to represent the problem. We can rewrite “three quarters of a number” as “3/4 times the number.” So, the equation becomes:

3/4 * x = 4

Now, to solve for ‘x,’ we must isolate it on one side of the equation. We can do this by using the techniques discussed, such as addition, subtraction, multiplication, and division properties.

Let’s begin by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3. By doing so, we eliminate the fraction and simplify the equation:

4/3 * (3/4 * x) = 4/3 * 4

By simplifying, we get:

x = 16/3

Therefore, three quarters of 4 is equal to 16/3.

To provide further clarity, let’s visualize the step-by-step solution in a table:

Equation | Steps | Solution |
---|---|---|

3/4 * x = 4 | Multiply both sides by 4/3 | x = 16/3 |

By following the appropriate techniques and utilizing our problem-solving skills, we have successfully determined the solution to the problem of finding three quarters of 4.

Let’s continue our exploration of fraction calculations in the upcoming sections to enhance our mathematical abilities and problem-solving proficiency.

## Exploring Fraction Calculations

In order to solve our problem of finding 3/4 of 4, it is crucial to understand and master various **mathematical operations** involving fractions. Let’s delve into these operations and explore how they can help us find the solution we seek.

### Addition and Subtraction with Fractions

Adding and subtracting fractions is a fundamental skill when it comes to fraction calculations. By finding a common denominator and performing the necessary operations, we can efficiently solve fraction-based equations and problems.

### Multiplication with Fractions

Multiplication with fractions involves multiplying the numerators and denominators to obtain the desired result. Whether multiplying two fractions or multiplying a fraction with a whole number, knowing how to perform this operation is essential for accurate fraction calculations.

### Division with Fractions

Dividing fractions requires inverting the second fraction and multiplying it with the first. This operation is particularly useful when we need to divide a quantity or find a fraction of a number. Mastering division with fractions is crucial for solving our problem of finding 3/4 of 4.

### An Example of Fraction Calculation

To further understand how fraction calculations work, let’s consider an example:

Suppose we need to find 2/3 of 9. To do this, we can multiply the fraction (2/3) by the whole number (9) as follows:

Step | Calculation | Result |
---|---|---|

Step 1 | 2/3 * 9 | 18/3 |

Step 2 | Simplify 18/3 to lowest terms | 6 |

Therefore, 2/3 of 9 is equal to 6.

### Applying Fraction Calculations to Our Problem

By applying the knowledge and techniques learned in fraction calculations, we will be able to solve our problem of finding 3/4 of 4. Through a step-by-step process, we will demonstrate how these **mathematical operations** can help us arrive at the solution.

## Fraction Calculations in Word Problems

Fraction calculations are not just theoretical concepts; they play a crucial role in **solving real-life scenarios**. By understanding how to apply our problem-solving skills to **fraction word problems**, we can navigate through everyday situations with confidence.

Let’s explore some word problems that involve fractions and see how we can break them down to find the solutions:

**Problem:**John wants to share a pizza with his two friends. If he eats 3/8 of the pizza, what fraction of the pizza will each person get?

**Solution:**To find the fraction each person will get, we need to divide the remaining 5/8 (1 – 3/8) among three people. We can represent the problem as the equation:

5/8 ÷ 3 = x

where x represents the fraction each person will get. Solving this equation, we find that each person will get 5/24 of the pizza.

**Problem:**An aquarium contains 7/10 gallon of water. If 3/5 of the water is poured into a smaller container, how much water is transferred?

**Solution:**To find how much water is transferred, we can multiply the fraction 3/5 by the total amount of water in the aquarium (7/10 gallon). This can be represented as:

7/10 × 3/5 = x

where x represents the amount of water transferred. Solving this equation, we find that 21/50 gallon of water is transferred to the smaller container.

As you can see, understanding fraction calculations allows us to solve practical problems effectively. By converting real-life scenarios into equations and applying our problem-solving skills, we can find accurate solutions that help us make informed decisions and navigate through everyday challenges.

Remember, practice makes perfect when it comes to solving **fraction word problems**. The more familiar we become with different scenarios and the steps involved in solving them, the more confident and efficient we will be in handling real-life situations.

## Conclusion

After exploring various concepts and solving techniques, we have successfully tackled the math problem of finding 3/4 of 4. By understanding fractions, equations, and utilizing addition, subtraction, division, and multiplication properties, we have acquired the skills needed to navigate similar math challenges.

With the knowledge gained from this exploration, we can confidently approach fraction calculations and equation-solving tasks in the future. Whether it’s finding a fraction of a number or solving complex equations, we now have a solid foundation to rely on.

By following the step-by-step explanations and applying the techniques discussed in this article, we can confidently break down math problems into manageable steps. Solving equations and working with fractions is no longer a daunting task but an opportunity to apply our mathematical prowess.

## FAQ

### What is 3/4 of 4?

To find 3/4 of 4, you can multiply 4 by 3/4. The answer is 3.

### How do I solve equations using addition and subtraction?

You can add or subtract the same quantity from both sides of an equation to create equivalent equations with easily identifiable solutions.

### How do I solve equations using division?

You can divide both sides of an equation by the same nonzero quantity to simplify the equation and find the solution.

### How do I solve equations using multiplication?

You can multiply both sides of an equation by the same nonzero quantity to generate equivalent equations with the same solution.

### How can I apply equation-solving techniques to solve more complex equations?

By understanding the order of operations, simplification rules, and steps for solving first-degree equations, you can tackle more complex equations.

### How do I apply equation-solving techniques to find 3/4 of 4?

You can use the equations and techniques you’ve learned to find the solution step by step.

### How do I perform fraction calculations?

Fraction calculations involve addition, subtraction, multiplication, and division operations with fractions.

### How can I solve fraction word problems in real-life scenarios?

By applying your problem-solving skills and using fractions, you can find solutions to **fraction word problems** in real-life scenarios.

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