How to Add Fractions


How to Add Fractions
Add fractions by making the denominators the same and then adding the numerators.

Adding fractions is a fundamental skill in mathematics that plays a crucial role in various aspects of everyday life and advanced mathematical concepts. Understanding how to add fractions helps in dealing with situations involving parts of a whole, such as cooking, budgeting, and even time management.

Why Learning How to Add Fractions Is Important

Maybe math isn’t your favorite subject, but learning how to add fractions is important:

  1. Practical Applications: In cooking, fractions measure ingredients. In budgeting, fractions help in understanding portions of money spent or saved.
  2. Foundation for Advanced Mathematics: Knowledge of fractions is essential for understanding more complex mathematical concepts like algebra, calculus, and statistics.
  3. Developing Problem-Solving Skills: Learning how to add fractions enhances logical thinking and problem-solving abilities.

Steps for Adding Fractions

Probably the first step is understanding the parts of a fraction. The top portion (above the line) is the numerator. This is the part of the fraction where the actual addition occurs. The bottom portion of the fraction (below the line) is the denominator. You make the denominator the same (if it isn’t already) and then add up the numerators. After you have an answer, simplify the fraction.

  1. Same Denominator:
    1. Just add the numerators while keeping the denominator the same.
    2. Simplify the fraction if possible.
  2. Different Denominators:
    1. Find a common denominator by finding the least common multiple (LCM) of the denominators. The easiest way of doing this is multiplying both the numerator and denominator of each fraction by the denominator of the other fraction.
    2. Once both fractions have the same denominator, add the numerators of these equivalent fractions.
    3. Simplify the resulting fraction if possible.

Examples of How to Add Fractions

Adding Fractions With the Same Denominator

This is the easiest case, since all you do is add up the numerators.

 \frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1

The process is the same when working with negative numbers, but pay attention to the signs.

 \frac{1}{4} + \left(-\frac{3}{4}\right) = -\frac{2}{4} = -\frac{1}{2}

Adding Fractions With Different Denominators

Remember, make the denominators the same and then add the numerators. In this example, the denominators are 3 and 5. Multiplying both the numerator and denominator of each fraction by the denominator of the other fraction yields the LCM, which is 15 in this case.

 \frac{1}{2} + \frac{2}{5} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}

Here is an example of adding fraction with different denominators involving negative numbers:

 \frac{3}{4} + \left(-\frac{1}{2}\right) = \frac{3}{4} + \left(-\frac{2}{4}\right) = \frac{3 - 2}{4} = \frac{1}{4}

Adding Improper Fractions

Improper fractions are fractions where the numerator is larger than or equal to the denominator. The process of adding improper fractions is the same as adding proper fractions. After adding, if the result is an improper fraction, convert it into a mixed fraction. A mixed fraction is one which has a whole number together with a fraction. For example, 7/3 is an improper fraction, while 2⅓ is the equivalent mixed fraction.

Adding Mixed Fractions

Adding mixed fractions involves a few more steps compared to adding simple fractions. A mixed fraction is a combination of a whole number and a fraction. To add mixed fractions, you either convert them to improper fractions first and then add, or add the whole numbers and fractions separately.

  1. Convert to Improper Fractions:
    • Multiply the whole number by the denominator of the fraction.
    • Add this to the numerator of the fraction.
    • Place this over the original denominator.
  2. Add the Improper Fractions:
    • Find a common denominator if necessary.
    • Add the numerators, keeping the denominator the same.
    • Simplify the resulting fraction if possible.
  3. Convert Back to a Mixed Number (if needed):
    • Divide the numerator by the denominator to get the whole number part.
    • The remainder becomes the numerator of the fractional part.

Example

Add 2⅓ and 1⅔​.

  1. Convert to improper fractions.
  2. Add the improper fractions.
  3. Simplify the result.
 2 \frac{1}{3} + 1 \frac{2}{3} = \frac{2 \times 3 + 1}{3} + \frac{1 \times 3 + 2}{3} = \frac{7}{3} + \frac{5}{3} = \frac{12}{3} = 4

If the denominators are different, find the LCM and make them the same before the addition step.

References