Adding and Subtracting Fractions with Unlike Denominators

Adding and Subtracting Fractions with Unlike Denominators

Before delving into the world of adding and subtracting fractions with unlike denominators, let's first recall the basics. Fractions are represented by a numerator (the top number) divided by a denominator (the bottom number). When both fractions have the same denominator, you can simply add or subtract by adding or subtracting their numerators.

However, when dealing with unlike denominators, the situation becomes more complex due to the need to find a common denominator. Here's what you should know about adding and subtracting fractions with unlike denominators.

Finding a Common Denominator

To add or subtract unlike fractions, you first need to find a common denominator. The common denominator is the lowest number that can divide both denominators evenly. The procedure involves finding the greatest common divisor (gcd) of the two denominators and selecting the least common multiple (LCM) of the gcd and each denominator.

For example:

To add [\frac{3}{4}] and [\frac{5}{8}], first find the gcd of 4 and 8, which is 4. The LCM of 4 and 4, and 4 and 8 is 8 and 16, respectively. Since 8 is the smaller number, use it as the common denominator.

Adding Unlike Fractions

Once you have a common denominator, you can add or subtract the original fractions as if they had the same denominator. To add unlike fractions, simply find the equivalent fraction for each using the common denominator, and then add the numerators.

For example:

[\frac{3}{4} + \frac{5}{8} = \frac{3 \times 2}{4 \times 2} + \frac{5}{8} = \frac{6}{8} + \frac{5}{8} = \frac{11}{8}]

Subtracting Unlike Fractions

Subtracting unlike fractions is similar to adding them, just with a different sign. To subtract unlike fractions, follow the same steps as adding, but with a negative sign between the two fractions.

For example:

[\frac{5}{6} - \frac{3}{8} = \frac{5 \times 4}{6 \times 4} - \frac{3}{8} = \frac{20}{24} - \frac{3}{8} = \frac{16}{24} - \frac{3 \times 3}{8} = \frac{16 - 9}{24} = \frac{7}{24}]

Simplifying Fractions

After finding the equivalent fraction using the common denominator, you can simplify the fraction by finding the greatest common divisor of the numerator and denominator.

For example:

If you've found [\frac{11}{8}] after adding unlike fractions, simplify it by finding the gcd of 11 and 8, which is 1. So, the simplified fraction is [\frac{11 \div 1}{8 \div 1} = \frac{11}{8}].

Important Notes

• The order of the fractions in a subtraction problem is important. Switching the order of the fractions will result in a negative answer, which should be considered a different problem.
• Beware of negative fractions in subtraction problems. If the result is negative, it will require a different interpretation than an addition problem.
• Fractions with unlike denominators are commonly found in real-world applications, so learning how to handle them is essential.

Eagerly master these skills, and you'll be able to add and subtract fractions with unlike denominators with confidence and ease.

Learn how to add and subtract fractions that have different denominators by finding a common denominator and applying the necessary operations on the numerators. Understand the steps to simplify fractions after addition or subtraction. Mastering these skills will enhance your ability to work with fractions effectively.