Adding and Subtracting Fractions and Mixed Numbers with Common Denominator

Study Notes

Adding and Subtracting Fractions and Mixed Numbers with the Same Denominator

When adding or subtracting fractions, having the same denominator makes the process incredibly simple. Here's how you can handle fraction addition, fraction subtraction, mixed number addition, and mixed number subtraction when they share a common denominator.

Fraction Addition

To add two fractions with the same denominator, simply perform standard arithmetic on the numerators and keep the shared denominator. For example:

3/5 + 1/5 = 4/5

This method works because both fractions have a common denominator of 5 in this case. The sum of their numerators forms the new numerator for the combined fraction.

Fraction Subtraction

Similarly, to subtract one fraction from another with the same denominator, follow the same basic procedure but use negative signs if necessary. For instance:

3/5 - 1/5 = 2/5

Here, the difference between the numerators gives us 2 as the new numerator, while the common denominator remains unchanged.

Mixed Number Addition

When dealing with mixed numbers, first convert both to improper fractions by multiplying the whole number part by the common denominator. Then add their numerators and keep the common denominator. For example:

3 + (1/5) = 15/5 = 3

In this case, the mixed number 3 is equivalent to 15/5 when expressed as an improper fraction. Adding another 1/5 gives us 16/5, which simplifies to 3 when reduced to lowest terms.

Mixed Number Subtraction

Subtracting mixed numbers follows the same pattern as addition. Convert each to an improper fraction, subtract the numerators, and keep the common denominator. For example:

3 - (1/5) = 12/5 = 2 1/5

Here, the mixed number 3 is equivalent to 12/5 as an improper fraction. Subtracting 1/5 gives us 11/5, which simplifies to 2 1/5 when reduced to lowest terms.

In summary, adding and subtracting fractions or mixed numbers with the same denominator is straightforward and involves simple arithmetic on the numerators while keeping the common denominator intact.

Description

Learn how to add and subtract fractions and mixed numbers efficiently when they share the same denominator. Understand the step-by-step process for fraction addition, fraction subtraction, mixed number addition, and mixed number subtraction.