How to multiply fractions?
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Time to read 2 min
In mathematics, fractions are a way of representing a part of a whole or a number of equal parts. They are written as one integer or number, called the numerator, divided by another integer or number, called the denominator. The numerator represents the part of the whole or the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole.
For example, the fraction 3/5 represents three parts out of five equal parts, while the fraction 1/2 represents one part out of two equal parts. Fractions can be used to represent quantities, such as measurements, ratios, probabilities, and percentages. They are an important concept in many areas of mathematics, including arithmetic, algebra, and calculus.
Short version.
To multiply fractions, you can follow these steps:
- Multiply the numerators (top numbers) of the fractions together.
- Multiply the denominators (bottom numbers) of the fractions together.
- Write the product of the numerators over the product of the denominators, as a fraction in its simplest form (i.e., reduce the fraction to its lowest terms).
Here is an example:
2/3 * 3/4
- Multiply the numerators: 2 * 3 = 6
- Multiply the denominators: 3 * 4 = 12
- Write the product of the numerators over the product of the denominators: 6/12
- Simplify the fraction to its lowest terms: divide both the numerator and denominator by their greatest common factor (GCF), which is 6 in this case. 6/12 reduces to 1/2.
Therefore, 2/3 * 3/4 = 1/2.
Long version.
Multiplying fractions involves multiplying the numerators together and multiplying the denominators together. The resulting product is then simplified by canceling out any common factors between the numerator and denominator. If the product is an improper fraction, it can be converted to a mixed number by dividing the numerator by the denominator and writing the quotient as the whole number and the remainder as the new numerator over the original denominator.
For example, let's multiply 2/3 and 5/6:
Step 1: Multiply the numerators: 2 x 5 = 10 Step 2: Multiply the denominators: 3 x 6 = 18 Step 3: Simplify the product by canceling out any common factors: 10/18 = 5/9 Step 4: Convert the improper fraction to a mixed number: 5 ÷ 9 = 0 with a remainder of 5, so the final answer is 0 5/9.
To multiply fractions, you first need to make sure that both fractions have the same denominator. If the denominators are different, you need to find a common denominator. This can be done by finding the lowest common multiple (LCM) of the two denominators.
Once you have the same denominator, you can multiply the numerators of the fractions together and write the product over the common denominator. The resulting fraction may need to be simplified by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by that number.
It is important to note that when multiplying fractions, the product may need to be written in simplest form, which means that the numerator and denominator have no common factors other than 1. In some cases, the product may also be a mixed number, which means that the fraction can be expressed as a whole number and a proper fraction.
For example, to multiply 1/2 and 2/3, we first need to find a common denominator, which is 6. Then, we can multiply the numerators together to get 1 x 2 = 2 and write the product over the common denominator to get 2/6. Finally, we can simplify this fraction by dividing both the numerator and denominator by their GCF, which is 2, to get 1/3 as the final product.
