How Do I Add subtract Multiply And Divide Fractions?

How Do I Add, Subtract, Multiply, and Divide Fractions?

Fractions are a part of everyday life. We use them to describe how much of something we have, such as a half of a pizza or a third of a pie. Fractions can also be used to compare two quantities, such as the speed of two cars or the height of two buildings.

In this article, we will learn how to add, subtract, multiply, and divide fractions. We will also learn some tips and tricks that will help us to make calculations with fractions easier.

So if you’re ever faced with a fraction problem, don’t be afraid – just follow the steps in this article and you’ll be sure to get the right answer!

Operation Symbol Example
Addition + 3/4 + 2/5 = 17/20
Subtraction 5/6 – 2/3 = 1/6
Multiplication * 3/4 * 2/5 = 6/20
Division / 5/6 / 2/3 = 15/4

What is a Fraction?

A fraction is a mathematical expression that represents a part of a whole. It is written in the form of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of parts of the whole that are being considered, and the denominator represents the total number of parts in the whole.

For example, the fraction 1/2 represents one part of a whole that is divided into two parts. The fraction 3/4 represents three parts of a whole that is divided into four parts.

Fractions can be used to represent a variety of different things, such as:

  • The number of people in a group
  • The amount of money in a budget
  • The percentage of a population that has a certain characteristic

Fractions can also be used to perform mathematical operations, such as addition, subtraction, multiplication, and division.

Types of Fractions

There are three main types of fractions:

  • Proper fractions have a numerator that is less than the denominator. For example, 1/2, 3/4, and 7/8 are all proper fractions.
  • Improper fractions have a numerator that is greater than or equal to the denominator. For example, 5/4, 8/5, and 13/12 are all improper fractions.
  • Mixed numbers are a combination of a whole number and a fraction. For example, 2 1/2, 5 3/4, and 8 7/8 are all mixed numbers.

Equivalent Fractions

Two fractions are equivalent if they represent the same part of a whole. For example, the fractions 1/2 and 2/4 are equivalent because they both represent one-half of a whole.

To find equivalent fractions, you can multiply the numerator and denominator of a fraction by the same number. For example, the fraction 1/2 is equivalent to the fractions 2/4, 3/6, 4/8, and so on.

Reducing Fractions to Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. For example, the fraction 10/20 is not in lowest terms because the numerator and denominator share the common factor 10. The fraction 1/2 is in lowest terms because the numerator and denominator have no common factors.

To reduce a fraction to lowest terms, you can divide the numerator and denominator by their greatest common factor (GCF). The GCF of two numbers is the largest number that divides both numbers evenly.

For example, the GCF of 10 and 20 is 10. So, to reduce the fraction 10/20 to lowest terms, we would divide the numerator and denominator by 10. This gives us the fraction 1/2, which is in lowest terms.

How to Add and Subtract Fractions?

Adding and subtracting fractions is a relatively simple process. However, there are a few things to keep in mind when performing these operations.

First, you need to make sure that the fractions have the same denominator. If the denominators are different, you will need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

Once you have a common denominator, you can add or subtract the fractions by adding or subtracting the numerators and keeping the denominator the same.

For example, to add the fractions 1/2 and 1/3, you would first find the common denominator, which is 6. Then, you would add the numerators, 1 + 1 = 2, and keep the denominator the same, 2/6.

To subtract the fractions 3/4 and 1/2, you would first find the common denominator, which is 4. Then, you would subtract the numerators, 3 – 1 = 2, and keep the denominator the same, 2/4.

Here are the steps for adding and subtracting fractions:

1. Find the common denominator. The common denominator is the least common multiple (LCM) of the two denominators.
2. Add or subtract the numerators. Add or subtract the numerators and keep the denominator the same.
3. Simplify the fraction, if possible. If the numerator and denominator have any common factors other than 1, you can divide them out to simplify the fraction.

How to Multiply and Divide Fractions?

Multiplying and dividing fractions is also a relatively simple process. However, there are a few things to keep in mind when performing these operations.

First, you need to multiply or divide the

How to Multiply Fractions?

Multiplying fractions is a simple process that involves multiplying the numerators and denominators of the two fractions. The resulting fraction will have the same value as the original two fractions, but it will be expressed in a different way.

To multiply fractions, follow these steps:

1. Multiply the numerators of the two fractions.
2. Multiply the denominators of the two fractions.
3. Simplify the resulting fraction, if possible.

Here is an example of multiplying two fractions:

“`
$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$
“`

In this example, we first multiply the numerators of the two fractions, which gives us 1 x 3 = 3. We then multiply the denominators of the two fractions, which gives us 2 x 4 = 8. Finally, we simplify the resulting fraction, which gives us 3 / 8.

Here are some additional examples of multiplying fractions:

“`
$\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$
$\frac{3}{4} \times \frac{5}{6} = \frac{15}{24}$
$\frac{7}{8} \times \frac{9}{10} = \frac{63}{80}$
“`

Multiplying Fractions with the Same Denominator

When multiplying fractions with the same denominator, the steps are the same as above, except that the denominators will be the same in both fractions.

For example, to multiply $\frac{1}{2}$ by $\frac{3}{2}$, we would first multiply the numerators, which gives us 1 x 3 = 3. We would then multiply the denominators, which gives us 2 x 2 = 4. Finally, we would simplify the resulting fraction, which gives us 3 / 4.

Here are some additional examples of multiplying fractions with the same denominator:

“`
$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$
$\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$
$\frac{7}{8} \times \frac{7}{8} = \frac{49}{64}$
“`

Multiplying Fractions with Different Denominators

When multiplying fractions with different denominators, the first step is to find the least common denominator (LCD) of the two fractions. The LCD is the smallest number that is evenly divisible by both denominators.

Once you have found the LCD, you can multiply each fraction by the appropriate number to get a new fraction with the LCD as its denominator.

For example, to multiply $\frac{1}{2}$ by $\frac{3}{4}$, we would first find the LCD, which is 4. We would then multiply $\frac{1}{2}$ by $\frac{2}{2}$ to get $\frac{2}{4}$. We would then multiply $\frac{3}{4}$ by $\frac{1}{1}$ to get $\frac{3}{4}$. Finally, we would add the two fractions to get $\frac{5}{4}$.

Here are some additional examples of multiplying fractions with different denominators:

“`
$\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}$
$\frac{3}{4} \times \frac{5}{6} = \frac{15}{24}$
$\frac{7}{8} \times \frac{9}{10} = \frac{63}{80}$
“`

Multiplying a Fraction by a Whole Number

To multiply a fraction by a whole number, you simply multiply the numerator of the fraction by the whole number. The denominator of the fraction remains the same.

For example, to multiply $\frac{1}{2}$ by 3, we would multiply the numerator, 1, by 3 to get 3. The denominator, 2, would remain the same. The resulting fraction would be $\frac{3}{2}$.

Here are some additional examples of multiplying a fraction by a whole number:

“`
$\frac{1}{2} \times 4 = \frac{4}{2} = 2$
$\frac{3}{4} \times 5 = \frac{15}{4}$
$\frac{7}{8} \times 6 =

How do I add fractions?

To add fractions, you need to find a common denominator. This is the least common multiple of the denominators of the two fractions. Once you have found a common denominator, you can multiply each fraction by the appropriate number to get equivalent fractions with the same denominator. Then, you can add the numerators of the two fractions and put the answer over the common denominator.

For example, to add 2/3 and 1/4, you would first find the least common multiple of 3 and 4, which is 12. Then, you would multiply 2/3 by 4/4 to get 8/12, and multiply 1/4 by 3/3 to get 3/12. Finally, you would add the numerators to get 11/12.

How do I subtract fractions?

To subtract fractions, you first need to find a common denominator. Once you have found a common denominator, you can multiply each fraction by the appropriate number to get equivalent fractions with the same denominator. Then, you can subtract the numerators of the two fractions and put the answer over the common denominator.

For example, to subtract 5/6 from 3/4, you would first find the least common multiple of 6 and 4, which is 12. Then, you would multiply 5/6 by 2/2 to get 10/12, and multiply 3/4 by 3/3 to get 9/12. Finally, you would subtract the numerators to get 1/12.

How do I multiply fractions?

To multiply fractions, you simply multiply the numerators together and the denominators together.

For example, to multiply 2/3 by 4/5, you would multiply the numerators together to get 8 and the denominators together to get 15. The answer is 8/15.

How do I divide fractions?

To divide fractions, you first need to invert the second fraction (flip it upside down). Then, you multiply the two fractions together.

For example, to divide 2/3 by 4/5, you would first invert the second fraction to get 5/4. Then, you would multiply the two fractions together to get 10/12. The answer is 5/6.

What are some common mistakes people make when adding, subtracting, multiplying, and dividing fractions?

Some common mistakes people make when adding, subtracting, multiplying, and dividing fractions include:

  • Not finding a common denominator. This is the most common mistake, and it can lead to incorrect answers.
  • Multiplying or dividing the numerators and denominators by the wrong numbers. This can also lead to incorrect answers.
  • Adding or subtracting fractions with different denominators. This is not possible, and it will result in an incorrect answer.
  • Dividing by zero. This is , and it will result in an error.

How can I avoid these mistakes?

To avoid these mistakes, you should:

  • Always find a common denominator before adding, subtracting, multiplying, or dividing fractions.
  • Carefully multiply or divide the numerators and denominators by the correct numbers.
  • Only add or subtract fractions with the same denominators.
  • Never divide by zero.

By following these tips, you can avoid common mistakes and calculate fractions correctly.

In this blog post, we have discussed the basics of adding, subtracting, multiplying, and dividing fractions. We have seen how to find the common denominator, how to add and subtract fractions with like denominators, and how to multiply and divide fractions. We have also seen how to simplify fractions.

We hope that this blog post has been helpful. If you have any questions, please feel free to leave them in the comments below.

Author Profile

Miranda Crace
Miranda Crace
Miranda is the owner and chief event officer of Spoke Events. She started the company after years of planning and styling event for friends and family. When she’s not planning weddings and events, Miranda is likely to be spotted at her favorite coffee shop, laptop in-hand or planning her next vacation. Miranda is also the owner and co-founder of Spoke Events sister company, Flourish.

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