Fractions: Step by Step

Table of Contents

UNIT 1: FACTORS & MULTIPLES

Lesson 1.1 - Factors, Prime, & Composite Numbers

  • Factors
  • Multiplying factors
  • Prime numbers
  • Composite numbers

Lesson 1.2 - Factors – Word Problems

  • Word problems using factors

Lesson 1.3 - Greatest Common Factor

  • Common factors
  • Greatest common factor
  • Finding the greatest common factor

Lesson 1.4 - Multiples and Least Common Multiple

  • Multiples
  • Skip counting
  • Common multiples
  • Least common multiple
  • Finding the least common multiple

Lesson 1.5 - Least Common Multiple – Word Problems

  • Word problems using the least common multiple

UNIT 2: FRACTION CONCEPTS

Lesson 2.1 - Fractions and Mixed Numbers

  • The concept of a fraction
  • Numerator and denominator
  • Fractions in measurement
  • Fraction of a set
  • Fractions larger than one
  • Mixed numbers

Lesson 2.2 - Equivalent Fractions and Lowest Terms

  • Equivalent fractions
  • Using common multiples to create equivalent fractions
  • Reducing fractions to lowest terms
  • Using common factors to reduce fractions

Lesson 2.3 - Least Common Denominator

  • Common denominator
  • Making common denominators
  • Least common denominator
  • Using least common multiple to find equivalent fractions with common denominators

Lesson 2.4 - Comparison Symbols

  • Less than symbol
  • Greater than symbol

Lesson 2.5 - Comparing Fractions

  • Comparing fractions with the same denominators
  • Comparing fractions with different denominators by making equivalent fractions
    with common denominators

Lesson 2.6 - Mixed Numbers and Improper Fractions

  • Mixed numbers and improper fractions
  • Converting a mixed number to an improper fraction
  • Converting an improper fraction to a mixed number

UNIT 3: ESTIMATION OF FRACTIONS

Lesson 3.1 - Benchmarks

  • Benchmark numbers
  • Benchmark fractions
  • Converting mixed numbers to benchmarks

Lesson 3.2 - Estimating with Benchmarks

  • Replacing fractions with benchmarks
  • Estimating fractions calculations using benchmarks

Lesson 3.3 - Adding & Subtracting Fractions with Benchmarks

  • Adding amounts using benchmarks
  • Subtracting amounts using benchmarks

Lesson 3.4 - Multiplying & Dividing Fractions with Benchmarks

  • Using benchmarks to estimate multiplication of amounts
  • Using benchmarks to estimate division of amounts

UNIT 4: ADDITION & SUBTRACTION OF FRACTIONS

Lesson 4.1 - Adding & Subtracting Like Fractions

  • Like fractions with common denominators
  • Adding like fractions
  • Subtracting like fractions
  • Reducing to lowest terms in fractions calculations

Lesson 4.2 - Adding & Subtracting Unlike Fractions

  • Adding unlike fractions by creating equivalent fractions with common denominators
  • Subtracting unlike fractions by creating equivalent fractions with common
    denominators
  • Using least common denominator in fractions calculations
  • Reducing to lowest terms in fractions calculations

Lesson 4.3 - Adding Mixed Numbers

  • Regrouping mixed numbers for addition
  • Converting mixed numbers to improper fractions for addition
  • Recording sum of mixed numbers as a mixed number

Lesson 4.4 - Subtracting Mixed Numbers

  • Regrouping mixed numbers for subtraction
  • Converting mixed numbers to improper fractions for subtraction
  • Recording the remainder of subtraction mixed numbers as a mixed number

Lesson 4.5 - Adding & Subtracting Fractions – Word Problems

  • Using addition where word problems combine or increase quantities
  • Using subtraction where word problems reduce or remove quantities

UNIT 5: MULTIPLICATION WITH FRACTIONS

Lesson 5.1 - Multiplying Whole Numbers by Fractions

  • Converting whole numbers to fractions to multiply by another fraction
  • Multiplying numerators and denominators of fraction numbers

Lesson 5.2 - Multiplying Fractions by Fractions

  • Multiplying numerators and denominators of fraction numbers
  • Reducing the product of multiplied fractions to lowest terms

Lesson 5.3 - Multiplying Mixed Numbers by Fractions

  • Converting mixed numbers to improper fractions for multiplication
  • Recording the product of multiplied mixed numbers as a mixed number

Lesson 5.4 - Multiplying by Fractions – Word Problems

  • Using multiplication where word problems combine or increase quantities many times

UNIT 6: DIVISION WITH FRACTIONS

Lesson 6.1 - Dividing Whole Numbers by Fractions

  • Divide by a fraction by multiplying the reciprocal of the fraction divisor – flip and multiply
  • Reducing the quotient in fraction form to lowest terms

Lesson 6.2 - Dividing Fractions by Fractions

  • Divide a fraction by another fraction by multiplying the reciprocal of the fraction divisor
  • Reducing the quotient in fraction form to lowest terms

Lesson 6.3 - Dividing Mixed Numbers

  • Converting mixed numbers to improper fractions for arithmetic operations
  • Divide an improper fraction by multiplying the reciprocal of the fraction divisor
  • Reducing the quotient in fraction form to lowest terms

Lesson 6.4 - Dividing with Fractions

  • Using division to separate something many times

UNIT 7: WORKING WITH FRACTIONS

Lesson 7.1 - Performing Fraction Arithmetic Operations

  • Rules for mixed operations
  • Adding and subtracting operations are done from left to right
  • Multiplying and dividing operations are done from left to right
  • If mixing operations, do multiplication and division before addition and subtraction
  • If brackets are used, do the operations in brackets first

Lesson 7.2 - Solving Fraction Word Problems

  • Standard steps for solving word problems: plan, model, calculate, check, answer
  • Reading word problems carefully

APPENDICIES

  • Appendix A - Glossary
  • Appendix B - Multiplication Table