Adding and Subtracting Fractions and Mixed Numbers

Adding and Subtracting Fractions and Mixed Numbers

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.

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