1. Multiply the numerators (the top numbers) of the fractions together.
2. Multiply the denominators (the bottom numbers) of the fractions together.
3. Write the product of the numerators over the product of the denominators.
4. Simplify the resulting fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor.
Here is an example:
Let's say you want to multiply 2/3 and 3/4.
2 * 3 = 6.
3 * 4 = 12.
Both 6 and 12 can be divided by 6, so the simplified fraction is 1/2.
Therefore, 2/3 multiplied by 3/4 equals 1/2.
Multiplying fractions is a fundamental operation in mathematics that involves multiplying the numerators and denominators of two or more fractions to obtain a new fraction. This process is relatively straightforward once you understand the basic principles and rules governing fraction multiplication.
To multiply fractions, you need to follow a few simple steps:
Step 1: Simplify the fractions (if necessary)
Before multiplying fractions, it is often helpful to simplify them. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by this common factor. Simplifying fractions makes the subsequent calculations easier and helps to obtain the most reduced form of the product.
Step 2: Multiply the numerators
To multiply fractions, you multiply the numerators of the fractions together. The numerator is the top number of the fraction that represents the quantity being considered. For example, if you have the fractions 2/3 and 4/5, you would multiply the numerators 2 and 4 together, resulting in 2 * 4 = 8.
Step 3: Multiply the denominators
Similarly, you multiply the denominators of the fractions together. The denominator is the bottom number of the fraction that represents the total number of equal parts into which the whole is divided. Continuing with the previous example, you would multiply the denominators 3 and 5 together, resulting in 3 * 5 = 15.
Step 4: Combine the results
After multiplying the numerators and denominators, you combine the results to form the product fraction. The product fraction is obtained by placing the product of the numerators over the product of the denominators. In our example, the product fraction would be 8/15.
Step 5: Simplify the product fraction (if necessary)
Finally, you should simplify the product fraction to its most reduced form. To do this, you need to find the GCD of the numerator and denominator of the product fraction and divide both by this common factor. In our example, the fraction 8/15 is already in its simplest form, so no further simplification is needed.
It is important to note that when multiplying fractions, the order in which you multiply them does not matter. For example, multiplying 2/3 by 4/5 will yield the same result as multiplying 4/5 by 2/3. This property is known as the commutative property of multiplication.
Additionally, if you are multiplying more than two fractions, you can follow the same steps outlined above. Simply multiply the numerators together, multiply the denominators together, and then combine the results to form the product fraction.
In summary, to multiply fractions, you need to multiply the numerators together, multiply the denominators together, and then combine the results to form the product fraction. Simplifying the fractions before and after multiplication can help obtain the most reduced form of the product. With practice, multiplying fractions will become second nature, and you will be able to confidently solve more complex mathematical problems involving fractions.
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