Fraction operations

Fraction operations are a type of math that involve manipulating two or more fractions. For example, an operation might involve adding or subtracting fractions, or multiplying or dividing them. This can be done using the four basic mathematical operations: addition, subtraction, multiplication, and division. Many calculations involving fraction operations require factoring, which is the process of breaking down fractions into their parts, such as numerator and denominator.

Here is an example of a fraction operation.
$$
1 \frac{5}{6} + \frac{1}{2}
$$

addition and subtraction of fractions

To add and subtract fractions, they must first be written in equivalent form, meaning they have the same denominator. To do this, the numerators and denominators must be multiplied or divided until the fractions have the same denominators. Once the fractions are in equivalent form, the numerators of the fractions can be added or subtracted but the denominator remains the same.

multiplication of fractions

To multiply fractions, you need to multiply the numerators and denominators separately. When multiplying two fractions, one fraction is multiplied by the numerator of the other and the denominators are multiplied together. Then the result must be simplified. To divide fractions, you must first invert the second fraction, meaning you must flip it and take its reciprocal, and then apply the multiplication rule mentioned previously.

division of fractions

Dividing fractions can be a bit more difficult than adding, subtracting, or multiplying fractions.

Keep, Change, Flip

For this, we will learn a technique called KCF - Keep Change Flip.
Here is an example of KCF

Before;
$$
\frac{1}{2} \div \frac{2}{4}
$$
After;
$$
\frac{1}{2} \cdot \frac{4}{2}
$$

As you can see we simply multiply the first fraction by the reciprocal of the second.
And then we can solve it easily like this.
$$
\frac{1\cdot4}{2\cdot2} = \frac{4}{4} = 1
$$

Fraction operations are an important part of mathematics and can be used to solve many types of problems. Many real-world situations require the use of fractions such as measurements, recipes, and calculations of discounts on prices. Learning how to complete fraction operations can help make solving these types of problems easier, and give a better understanding of math.