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Adding and Subtracting Fractions and Mixed Numbers

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Operations with Rational Numbers

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Adding and Subtracting Fractions and Mixed Numbers


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You will add and subtract proper fractions and mixed numbers with unlike denominators.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Use models to add or subtract proper fractions or mixed numbers.
  • Add or subtract proper fractions with unlike denominators.
  • Add or subtract mixed numbers with unlike denominators.

Everything You'll Have Covered

Fractions can be added by using models.

Therefore, the correct response is 1 whole; because all of the shape is shaded once the two fractions are added together.

Estimations can be used to judge the reasonableness of an answer.

It can be assumed that if two positive fractions are being added the value will always be greater than 0. However, to estimate a difference, you must look at the fraction models and determine whether the difference will be a negative number, thus giving an estimation of less than 0.

In order to find the sum or difference each fraction must be a new fraction and must be written using the common denominator.

Once there is a common denominator, only the numerators should be added or subtracted.

Always simplify your answers if possible.

To subtract fractions, some of the same principles of addition apply.

Sometimes fractions need to be regrouped in order to subtract.

Some of the operations in this Activity Object may result in negative numbers or integers.

The following key vocabulary terms will be used throughout this Activity Object:

addition - the arithmetic operation of finding the sum of two or more values

common denominator - denominators that are the same number, usually found by finding the least common multiple of previous denominators

denominator - the number written below the line of a fraction.

estimation - to calculate approximately

fraction - A number of the form a/b , where b ? 0, that represents part of a whole.

fraction model - a visual representation of a fraction

...-1, 0, 1, ...

least common multiple (LCM) - the smallest multiple two or more numbers have in common; the LCM can be determined by listing the multiples in order for each number or by using prime factorization

negative - less than zero

numerator - the number written above the line of a fraction

simplify - the fraction that is in simplest form, where the numerator and denominator have a greatest common factor of 1; it also means to change an improper fraction into a mixed number

subtraction - the arithmetic operation of finding the difference between two quantities or numbers

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should be familiar with addition of fractions, common denominators, equivalent fractions, integers, least common multiple, negative numbers, simplifying fractions, and subtracting fractions.
Course Pre-Algebra
Type of Tutorial Skills Application
Key Vocabulary addition of fractions, fractions, subtraction of fractions