Adding Fractions with Different Denominators

Adding Fractions with Different Denominators

Adding fractions involves combining two or more fractions into one fraction with a common denominator. This process is crucial when dealing with measurements and ratios. Let's explore how this works by looking closely at three different scenarios: simplifying fractions, adding fractions with mixed numbers, and adding improper fractions.

Simplifying Fractions

Simplifying a fraction means eliminating any factors of the numerator and denominator other than 1. One method is to divide both the top and bottom of the fraction by an even number. For example, if we have the fraction (9) / (18), we can simplify it by dividing both parts by 6, resulting in (3) / (3). Since the top and bottom are now equal, this fraction is already simplified to its lowest terms.

Mixed Numbers

A mixed number is formed when a whole number is combined with a proper fraction. To add two mixed numbers, first find the sum of their whole numbers. Then, convert each mixed number back into an improper fraction. Finally, add the fractions together using the previously mentioned methods for adding fractions. For instance, if we want to add \frac{7}{10} and \frac{2}{3}, which can be written as \frac{7}{10} + \frac{2}{3}, we need to add the numerators while keeping the same denominators. In this case, (\frac{7+2}{10}), which equals (9/10).

Improper Fractions

An improper fraction is one where the denominator is larger than the numerator. Alternatively, it can also be expressed as a mixed number consisting of a whole number followed by an addition operation involving a proper fraction. To properly handle an improper fraction, you must rewrite it as a mixed number before proceeding with the rules of adding fractions. For instance, if we want to add \frac{9}{10} and \frac{2}{3}, which can be written as \frac{9}{10} + \frac{2}{3}, we first convert \frac{9}{10} to the mixed number (9\frac{1}{10}). Now, we can follow the steps outlined in the previous sections.

In summary, adding fractions requires identifying a common denominator and using the appropriate methods based on the form of the fractions being combined. By carefully analyzing the given examples, you can grasp the fundamental principles involved in adding fractions.