Multiplying and Dividing Fractions and Mixed Numbers

Multiplying and Dividing Fractions and Mixed Numbers

This page lists the Learning Objectives for all lessons in Unit 17.


Multiplying Fractions

The student will be able to:

  • Define greatest common denominator (GCF), simplify, and lowest terms.
  • Recognize that the word OF means multiply.
  • Describe the procedure for multiplying fractions.
  • Determine the product of two or more fractions by applying the procedure above.
  • Determine the product of a whole number and a fraction by applying the above procedure.
  • Recognize that the result can be simplified by dividing the numerator and the denominator by their GCF, or by cancelling common factors.
  • Simplify the result of each problem when necessary by using the GCF method.
  • Apply the procedure above to solve word problems, and simplify the result.
  • Apply multiplication procedures to complete five interactive exercises.

Multiplying Fractions By Cancelling Common Factors

The student will be able to:

  • Define common factors, cancel.
  • Describe the procedure for multiplying two or more fractions by dividing out common factors.
  • Determine the product of two or more fractions by applying the procedure above.
  • Determine the product of a whole number and a fraction by applying the procedure above.
  • Recognize that the factor being divided out can appear in any numerator and any denominator.
  • Recognize that dividing out common factors alleviates the need to simplify the result (unless that result is an improper fraction).
  • Recognize that dividing out common factors is more efficient when working with large numbers in the numerator and the denominator.
  • Apply procedures to complete five interactive exercises.

Multiplying Mixed Numbers

The student will be able to:

  • Describe the procedure for multiplying mixed numbers.
  • Recognize that each mixed number must be converted to an improper fraction before multiplying
  • Determine the product of two or more mixed numbers by applying the procedure above.
  • Simplify the result when necessary.
  • Connect finding the area of real-world objects to multiplying mixed numbers.
  • Recognize that in some cases, there are no common factors to divide out.
  • Apply procedures to complete five interactive exercises.

Reciprocals

The student will be able to:

  • Define reciprocals, inverting.
  • Describe the relationship between a fraction and its reciprocal.
  • Recognize that reciprocals come in pairs.
  • Determine the reciprocal of a given fraction.
  • Recognize that to find the reciprocal of a mixed number, you must convert it to an improper fraction first.
  • Determine the reciprocal of a mixed number by converting it to an improper fraction first.
  • Apply procedures to complete five interactive exercises.

Dividing Fractions

The student will be able to:

  • Define divisor, and invert.
  • Recognize that division indicates how many times one quantity is contained in another quantity.
  • Recognize that dividing a first fraction by a second, nonzero fraction, is the same as multiplying the first fraction by the reciprocal of the second fraction.
  • Describe the procedure for dividing one fraction by another.
  • Recognize that the second fraction must be a nonzero number.
  • Describe the process of inverting and multiplying.
  • Apply reciprocal relationships to convert division of fractions into a multiplication problem.
  • Apply procedures to divide fractions and simplify the result when necessary.
  • Apply procedures to cancel common divisors.
  • Connect real-world problems to dividing fractions.
  • Apply procedures to complete five interactive exercises.

Dividing Mixed Numbers

The student will be able to:

  • Describe the procedure for dividing mixed numbers.
  • Recognize that each mixed number must be converted to an improper fraction before dividing.
  • Apply the procedure for dividing mixed numbers, cancelling out common divisors when necessary.
  • Simplify the result when necessary.
  • Recognize that some problems will have no common divisors.
  • Connect real-world problems to dividing mixed numbers.
  • Apply procedures to complete five interactive exercises.

Solving Word Problems

The student will be able to:

  • Examine real world problems involving multiplication and division of fractions and mixed numbers.
  • Identify strategies for solving each problem.
  • Apply strategies for solving each problem.
  • Connect addition and subtraction of fractions and mixed numbers with the real word.
  • Apply all concepts and procedures to complete five interactive exercises with real-world problems.

Practice Exercises

The student will be able to:

  • Examine ten interactive exercises for all topics in this unit.
  • Identify the concepts and procedures needed to complete each practice exercise.
  • Compute all answers and solve all problems by applying appropriate concepts and procedures.
  • Self-assess knowledge and skills acquired from this unit of instruction.

Challenge Exercises

The student will be able to:

  • Evaluate ten challenging exercises for all topics in this unit.
  • Analyze each problem to identify the given information.
  • Formulate a strategy for solving each problem.
  • Apply strategies to solve problems and write answers.
  • Synthesize all information presented in this unit.
  • Develop strong problem-solving skills and the ability to handle challenging problems.

Solutions

The student will be able to:

  • Examine the solution for each exercise presented in this unit.
  • Compare solutions to completed exercises.
  • Identify which solutions need to be reviewed.
  • Identify and evaluate incorrect exercise answers from this unit.
  • Amend and label original answers.
  • Identify areas of strength and weakness.
  • Decide which concepts and procedures need to be reviewed from this unit.

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