# How to Successfully Subtract Fractions

Table Contents:

## Introduction

Asensio, we understand that fractions can be quite tricky and confusing, especially when it comes to subtraction. However, we are here to give you a detailed explanation of how to subtract fractions and make the process easier for you. In this article, we will provide you with easy-to-follow steps, clear examples, and frequently asked questions. By the end of this article, you will be able to solve fraction subtraction problems with confidence.

We will begin by reviewing the basics of fractions.

### What Are Fractions?

Fractions are numbers expressed as a ratio of two integers (numbers without decimal points). They are generally written in the form a/b, where a is the numerator and b is the denominator. The numerator represents the number of parts taken, and the denominator represents the total number of parts. Fractions can be used to represent part of a whole or a specific quantity.

For example, consider the fraction 3/5. In this fraction, 3 is the numerator, and 5 is the denominator. This fraction can represent three parts out of five parts, or three-fifths of a whole.

### What Is Subtraction?

Subtraction is a mathematical operation that involves finding the difference between two numbers. To subtract fractions, we need to find a common denominator to make the fractions equivalent. Once these fractions are equivalent, the numerators can be subtracted. It is essential to simplify the answer by reducing the fraction to its lowest terms.

### Why Is Subtraction Important?

Subtraction is an essential mathematical operation that is used in various aspects of life, including finances, cooking, and construction. For example, when preparing a recipe that requires fractions, you will need to subtract fractions to find the right proportions of ingredients. Additionally, in construction, builders use fractions to measure and cut materials accurately.

### When Should You Subtract Fractions?

Subtraction of fractions is required when one part of a quantity is taken away from another part of a quantity. For instance, when you have two fractional quantities and you want to find the difference between them, you will need to subtract the fractions.

### What Is the Method to Subtract Fractions?

To subtract fractions:

1. Find a common denominator
2. Make the fractions equivalent
3. Subtract the numerators
4. Simplify the fraction to its lowest term

Let’s take a closer look at each step:

### Step 1: Find a Common Denominator

The first step is to find a common denominator for the fractions. A common denominator is a number that both denominators can divide into evenly. Finding a common denominator makes the fractions equivalent and easier to subtract.

For example, let’s subtract 1/8 from 2/5.

 2/5 = 16/40 1/8 = 5/40

### Step 2: Make the Fractions Equivalent

The next step is to make the fractions equivalent by multiplying both the numerator and denominator by the same number. In this case, we need to multiply 1/8 by 5 and 2/5 by 8.

 2/5 = 16/40 1/8 x 5/5 = 5/40 1/8 = 5/40

### Step 3: Subtract the Numerators

Now that the fractions are equivalent, we can subtract the numerators. To subtract the numerators, we simply need to subtract 16 from 5.

 16/40 – 5/40 = 11/40

### Step 4: Simplify the Fraction to Its Lowest Term

Finally, we need to simplify the fraction to its lowest term. In this case, 11/40 is already in its lowest term.

## How to Subtract Fractions

Now that we have reviewed the basics, let’s dive into the step-by-step process of subtracting fractions.

### Step 1: Find a Common Denominator

The first step is to find a common denominator for the fractions. A common denominator is a number that both denominators can divide into evenly. Finding a common denominator makes the fractions equivalent and easier to subtract.

For example, consider the fractions 2/3 and 1/6. To find the common denominator:

1. List the multiples of each denominator until a common multiple is found.
2. Select the smallest common multiple as the common denominator.

The multiples of 3 are: 3, 6, 9, 12, 15, 18…

The multiples of 6 are: 6, 12, 18, 24…

We can see that 6 is the smallest common multiple, so we will use 6 as the common denominator.

2/3 x 2/2 = 4/6

1/6 x 1/1 = 1/6

### Step 2: Make the Fractions Equivalent

The next step is to make the fractions equivalent by multiplying both the numerator and denominator by the same number. In this case, we need to multiply 1/6 by 6 and 4/6 by 1.

4/6 = 4/6 x 1/1 = 4/6

1/6 = 1/6 x 6/6 = 6/36

### Step 3: Subtract the Numerators

Now that the fractions are equivalent, we can subtract the numerators. To subtract the numerators, we simply need to subtract 4 from 6.

6/36 – 4/6 = 6/36 – 24/36 = -18/36

### Step 4: Simplify the Fraction to Its Lowest Term

Finally, we need to simplify the fraction to its lowest term. In this case, -18/36 can be simplified by dividing both the numerator and denominator by the greatest common factor (GCF) which is 18.

-18/36 ÷ 18/18 = -1/2

## FAQs

### 1. What is the difference between addition and subtraction of fractions?

Addition is a mathematical operation that combines two or more numbers to get a sum. In contrast, subtraction is a mathematical operation that involves finding the difference between two numbers.

### 2. What is the difference between proper and improper fractions?

Proper fractions are fractions where the numerator is smaller than the denominator. Improper fractions, on the other hand, are fractions where the numerator is larger than or equal to the denominator.

### 3. Can I subtract fractions with different denominators?

No. To subtract fractions, you need to have a common denominator.

### 4. What is the best way to simplify the answer?

The best way to simplify the answer is by reducing the fraction to its lowest term using the greatest common factor (GCF).

### 5. Can I add and subtract fractions in the same problem?

Yes. If you are adding and subtracting fractions in the same problem, you need to simplify each fraction to have the same denominator before performing the addition or subtraction.

### 6. Can I subtract mixed numbers?

Yes. To subtract mixed numbers, you need to convert them to improper fractions before finding the common denominator and subtracting.

### 7. Does the order of the fractions matter when subtracting?

Yes. The order of the fractions matters when subtracting. To get the correct answer, you need to subtract the second fraction from the first fraction.

### 8. What if my answer is a negative fraction?

A negative answer means that the second fraction is larger than the first fraction. You can either leave the answer as a negative fraction or convert it to a mixed number.

### 9. Can I use a calculator to subtract fractions?

Yes, you can use a calculator to subtract fractions. However, it is still important to understand the process of subtracting fractions.

### 10. Can I subtract a fraction from a whole number?

Yes. To subtract a fraction from a whole number, you need to convert the whole number to a fraction with the same denominator as the fraction.

### 11. Can I subtract more than two fractions?

Yes. To subtract more than two fractions, you need to find a common denominator and subtract the numerators.

### 12. Can I subtract fractions with negative values?

Yes. You can subtract fractions with negative values, but it is important to ensure that both fractions have the same sign before performing the subtraction.

### 13. What if the fractions have different signs?

If the fractions have different signs, you need to find the absolute value of both fractions before subtracting. The answer will have the sign of the larger fraction.

## Conclusion

In conclusion, Asensio, we hope that this article has simplified the process of subtracting fractions for you. We have provided a detailed explanation of the steps involved and easy-to-follow examples. Remember, when subtracting fractions, it is important to find the common denominator, make the fractions equivalent, subtract the numerators, and simplify the answer. Do not hesitate to practice more and attempt different examples to enhance your skills. We believe that with this knowledge, you can now confidently solve fraction subtraction problems.

Take action today and apply what you have learned. You will be impressed with your newfound understanding of how to subtract fractions.

## Closing Statement with Disclaimer

The content of this article is for educational purposes only. The information provided is not a substitute for professional advice or guidance. We are not responsible for any loss or damages resulting from the use or misuse of this article.

Please consult with a qualified expert before taking any actions or making any decisions based on the information provided in this article.