Adding and Subtracting Fractions and Mixed Numbers

Learning Topics: 

Add and subtract fractions with like denominators, LCD, add and subtract with unlike denominators, add and subtract mixed numbers, solving real-world problems.

This page lists the Learning Objectives for all 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.