# Multiplying and Dividing Fractions and Mixed Numbers

## Learning Objectives for all Multiplying and Dividing Fractions 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.