Multiplying and Dividing Fractions: Step-by-Step Guide

Study Notes

Fractions: Multiplying and Dividing

Fractions are a way to represent parts of a whole, and they can be combined through various operations. In this article, we will focus on the subtopics of multiplying and dividing fractions.

Multiplying Fractions

To multiply two fractions, follow these steps:

Multiply the numerators (top numbers) of the fractions.
Multiply the denominators (bottom numbers) of the fractions.
Reduce the resulting fraction to its simplest form.

For example, let's multiply the fractions 3/4 and 5/6:

Multiply the numerators: 3 * 5 = 15
Multiply the denominators: 4 * 6 = 24
Reduce the resulting fraction: 15/24

So, the product of 3/4 and 5/6 is 15/24.

Multiplying Mixed Numbers

When multiplying mixed numbers, first convert the mixed number to an improper fraction, then multiply the fractions as usual. For example, to multiply 2 1/2 and 3 1/4, first convert them to improper fractions:

2 1/2 = 9/4 3 1/4 = 12/4

Now, multiply the fractions:

9/4 * 12/4 = 108/16

So, the product of 2 1/2 and 3 1/4 is 108/16.

Multiplying Fractions with Unlike Denominators

To multiply fractions with unlike denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator.

For example, let's multiply the fractions 3/4 and 2/5:

Find the LCM of the denominators: The LCM of 4 and 5 is 20.
Convert both fractions to have the same denominator: 3/4 * (5/5) and 2/5 * (4/4).
Multiply the fractions: 3/4 * (5/5) * (2/4) = 3 * 2 / (4 * 5) = 6/20.

So, the product of 3/4 and 2/5 is 6/20.

Dividing Fractions

To divide two fractions, you need to invert the divisor (the second fraction) and multiply the dividend (the first fraction) by the inverted divisor. For example, to divide 3/4 by 2/5:

Invert the divisor: 5/2
Multiply the dividend by the inverted divisor: 3/4 * (5/2) = 15/8.

So, the quotient of 3/4 and 2/5 is 15/8.

Dividing Mixed Numbers

When dividing mixed numbers, first convert the mixed number to an improper fraction, then divide the improper fractions as usual. For example, to divide 3 1/2 by 2 1/4:

Convert both mixed numbers to improper fractions: 3 1/2 = 7/2 and 2 1/4 = 6/4.
Divide the improper fractions: 7/2 / 6/4 = 7/2 * (4/6) = 7/6.

So, the quotient of 3 1/2 and 2 1/4 is 7/6.

Dividing Fractions with Unique Denominators

To divide two fractions with unique denominators, simply invert the divisor and multiply the dividend by the inverted divisor. For example, to divide 3/4 by 2/3:

Invert the divisor: 3/2
Multiply the dividend by the inverted divisor: 3/4 * (3/2) = 9/8.

So, the quotient of 3/4 and 2/3 is 9/8.

In conclusion, multiplying and dividing fractions involve different steps depending on the type of fractions involved. By following these steps, you can successfully perform these operations and obtain the correct results.

Description

Learn the step-by-step process for multiplying and dividing fractions, including mixed numbers and those with unique denominators. This guide provides clear examples and methods for obtaining accurate results in fraction operations.