# Adding and Subtracting Fractions and Mixed Numbers

## Learning Objectives for all Adding and Subtracting Fractions lessons in Unit 16.

**Adding Fractions with Like Denominators**

The student will be able to:

- Define units, common denominator, simplify, and lowest terms
- Describe the procedure for adding fractions with like denominators.
- Determine the sum of two or more fractions with like denominators by applying the procedure above.
- Simplify the result when necessary.
- Recognize that only the numerators should be added, not the denominators.
- Apply addition procedures to complete five interactive exercises.

**Subtracting Fractions with Like Denominators**

The student will be able to:

- Define fraction bar.
- State the Multiplication Property of Zero.
- State the additive inverse property of zero.
- Describe the procedure for subtracting fractions with like denominators.
- Find the difference of two fractions with like denominators by applying the procedure above.
- Simplify the result when necessary.
- Recognize that a fraction bar indicates that a division of the numerator by the denominator will be performed
- Recognize that division by zero is undefined.
**Recognize that****any fraction with zero in the numerator and a nonzero number in the denominator equals zero.**- Apply subtraction procedures to complete five interactive exercises.

**Adding and Subtracting Fractions with Unlike Denominators**

The student will be able to:

- Define least common denominator (LCD), least common multiple, and equivalent fractions.
- Find a
**common denominator**by multiplying the denominators together. - Rename fractions using their least common denominator.
- Identify the LCD of two or more fractions.
- Add fractions with unlike denominators by converting to equivalent fractions with a LCD.
- Simplify the result when necessary.
- Recognize that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.
- Recognize that there are two methods for adding and subtracting fractions with unlike denominators: common denominators and LCD.
- Describe the procedure for each method of adding and subtracting fractions with unlike denominators.
- Add and subtract fractions with unlike denominators by applying one the procedures above.
- Apply procedures to complete five interactive exercises.

**Adding Mixed Numbers**

The student will be able to:

- Define mixed numbers.
- Describe the procedure for adding mixed numbers.
- Recognize that a mixed number consists of a whole-number part and a fractional part.
- Recognize that it is easier to arrange the work vertically in order to add mixed numbers.
- Find the sum of two mixed numbers by applying the procedure for adding mixed numbers.
- Find the sum of a mixed number and a whole number by applying the procedure for adding mixed numbers.
- Simplify the result when necessary.
- Apply the procedure to complete five interactive exercises.

**Subtracting Mixed Numbers**

The student will be able to:

- Identify the whole-number part and the fractional part of a mixed number.
- Describe the procedure for subtracting mixed numbers with like denominators.
- Borrow a mixed number by converting it to an improper fraction.
- Describe the procedure for subtracting mixed numbers with unlike denominators.
- Subtract mixed numbers with like and unlike denominators by following the procedures presented.
- Subtract a mixed number from a whole number by following the procedures presented.
- Subtract a whole number from a mixed number by following the procedures presented.
- Recognize that there is another way to subtract mixed numbers is to convert each mixed number into an improper fraction.
- Recognize subtract mixed numbers by convert each mixed number into an improper fraction can lead to careless errors.
- Solve a real-world problem by subtracting mixed numbers.
- Apply procedures to complete five interactive exercises.

**Solving Word Problems**

The student will be able to:

- Examine problems involving addition and subtraction 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 procedure 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 the instruction provided in this unit.

**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 answers to exercises 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.