ORN - Add and Subtract Fractions Lesson

Add and Subtract Fractions

In this lesson, you will extend your experience with addition and subtraction of fractions by adding and subtracting mixed numbers, and by incorporating negative and positive fractions and mixed numbers into your expertise. Remember, the rules for addition and subtraction of fractions and mixed numbers are the same as integer rules.

Rules

Adding or Subtracting Fractions with Like Denominators

Add the numerators and keep the denominator. (Simplify)

Example: $LaTeX: \frac{5}{8}+\frac{1}{8}=\frac{5+1}{8}=\frac{6}{8}=\frac{3}{4}$ $\frac{5}{8}+\frac{1}{8}=\frac{5+1}{8}=\frac{6}{8}=\frac{3}{4}$
Example: $LaTeX: \frac{9}{11}-\frac{4}{11}=\frac{9-4}{11}=\frac{5}{11}$ $\frac{9}{11}-\frac{4}{11}=\frac{9-4}{11}=\frac{5}{11}$
Example: $LaTeX: \frac{4}{11}+-\frac{9}{11}=\frac{\left|9-4\right|}{11}=\frac{5}{11}=-\frac{5}{11}$ $\frac{4}{11}+-\frac{9}{11}=\frac{\left|9-4\right|}{11}=\frac{5}{11}=-\frac{5}{11}$

Investigate

Mr. Gordy walked ¼ mile to the library and then ¾ mile to the post office. What is the total distance he walked?

- - - - Solution: $LaTeX: \frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1=1\:mile$ $\frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1=1\:mile$

Adding or Subtracting Fractions with Different Denominators

It is important to remember that fractions must have the same denominator before they can be added or subtracted. If they do not, then you will need to find a common denominator by finding the LCM. (Least common multiple) The LCM of two denominators is the lowest common denominator (LCD) of the fractions.

You can either find the LCM of the denominators or simply multiply the denominators.

Once fractions are converted, you can add and subtract the numerators and keep the new common denominator.

Example: $LaTeX: \frac{5}{6}+\frac{7}{8}=\frac{5\times4}{6\times4}+\frac{7\times3}{8\times3}=\frac{20}{24}+\frac{21}{24}=\frac{41}{24}=1\frac{17}{24}$ $\frac{5}{6}+\frac{7}{8}=\frac{5\times4}{6\times4}+\frac{7\times3}{8\times3}=\frac{20}{24}+\frac{21}{24}=\frac{41}{24}=1\frac{17}{24}$
Example: $LaTeX: \frac{2}{3}-\frac{3}{4}=\frac{2\times4}{3\times4}-\frac{3\times3}{4\times3}=\frac{8}{12}-\frac{9}{12}=-\frac{1}{12}$ $\frac{2}{3}-\frac{3}{4}=\frac{2\times4}{3\times4}-\frac{3\times3}{4\times3}=\frac{8}{12}-\frac{9}{12}=-\frac{1}{12}$

When you add or subtract mixed numbers, simply keep the whole numbers separate from the fractions. When you subtract, you may want to regroup. Here is an activity that will help you do this. The problem in the activity is shown below.

Click here to see a clear version of the video. Links to an external site.

Add and Subtract Fractions Homework

Now that you have spent some time learning about the number properties, you are ready to complete your Integers and Rational Numbers: Add and Subtract Fractions Homework. Download your homework by CLICKING HERE Links to an external site..

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key Links to an external site..

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