Category: Basic Mathematics

  • Adding and Subtracting Fractions
    • How do we add or subtract fractions? What number should we choose as the common denominator? How do we add mixed numbers? How do we subtract a mixed number from a whole number?
  • Adding Whole Numbers and Decimals
    • How do we add whole numbers? How do we add decimals?
  • Addition 3
    • Practice carrying digits to add multiple digit numbers. (Arithmetic and pre-algebra; Addition and subtraction; Addition with carrying)
  • Addition 4
    • More practice carrying with multiple digit numbers. (Arithmetic and pre-algebra; Addition and subtraction; Addition with carrying)
  • Arithmetic
    • Contains a series of 33 lessons in basic math skills.
  • Arithmetical Problems
    • from 100 Great Problems of Elementary Mathematics
  • Basic Addition
    • Introduction to addition, and multiple visual ways to represent addition. (Arithmetic and pre-algebra; Intro to addition and subtraction)
  • Basic Arithmetic
    • Arithmetic is the result of adding two or more numbers together.
  • Comparing Fractions
    • How can we compare fractions with the same numerator? How can we compare fractions with the same denominator? How can we find the lowest common multiple of two numbers? How can we compare fractions when the numerators and denominators are different? How can we know whether a fraction is more than or less than ?
  • Decimals
    • Which numbers are the decimal units? What is the function of the decimal point? How do we read a decimal? How do we compare decimals?
  • Dividing Decimals
    • When the divisor is a decimal, what must we do?
  • Elementary Addition
    • Covers sums less than 10, composing 10 itself, and up to 20.
  • Equivalent Fractions
    • What are equivalent fractions? How can we know when fractions are equivalent? How can we reduce a fraction to its lowest terms? How can we reduce a fraction in which the numerator or denominator is a decimal?
  • Farmers' Market - Weigh Cool
    • A short game to play which will help you practice adding fractions. This game requires Flash Player to be installed on your computer.
  • Fractions into Decimals
    • What is a "decimal"? How can we change a fraction to a decimal? Frequent decimals and frequent percents: Half, thirds, quarters, fifths, eighths. Complete versus incomplete decimals.
  • Greatest Common Divisor, Lowest Common Multiple
    • We will now see how to find the greatest common divisor and the lowest common multiple of two numbers from their prime factorizations.
  • Guided Tour to Teaching and Learning about Decimals
    • Lessons, games and discussion points targeted at choosing and using concrete models, diagnosing misconceptions, connecting decimals, whole numbers, and fractions, and more.
  • Introduction To Carrying When Adding
    • Adding 2-digit numbers. (Arithmetic and pre-algebra; Addition and subtraction; Addition with carrying)
  • Lessons in Numbers and Arithmetic
    • Lessons in Numbers and Arithmetic
  • MacTutor History of Mathematics Archive
    • Biographies, Historical Mathematical Topics, Famous Curves, and more.
  • Math Refresher
    • Review of fundamental math concepts in a straight-forward, accessible way.
  • Mathematics
    • Basic math worksheets for kids.
  • MathTrax: The Intelligent Math Tutor
    • MathTrax is a graphing tool for middle school and high school students to graph equations, physics simulations or plot data files; for approximately 6-12th grade levels.
  • Max/Min Problems
    • from 100 Great Problems of Elementary Mathematics
  • Meaning of Division
    • The divisor, the dividend, and the quotient. What is the problem in division? What is a rate? Exact versus inexact division. The divisor a decimal. How do we divide by decomposing the dividend?
  • Mental Calculation
    • The emphasis will be on problems that do not require a calculator -- problems that you should not even have to write down! Mental calculation is now arithmetic of the most practical kind.
  • Mental Calculation: Multiplication
    • What is "multiplication"? Covers basic multiplication skills and practices.
  • Mental Calculation: Subtraction
    • First, the meaning of subtraction. Then, methods for achieving it.
  • Method of Proportions
    • How can we find the Percent by the method of Proportions? What is a general method for finding the Percent?
  • Multiplication of Sums
    • Learn how to prove the binomial theorem by first considering the multiplication of any sums.
  • Multiply and Divide by 10
    • In this Lesson we will learn to multiply and divide by a power of 10 -- simply by moving the decimal point. Having done that, we can then understand scientific notation.
  • Multiplying and Dividing Fractions
    • How do we multiply a fraction by a whole number? How do we multiply a fraction by a fraction? How do we divide fractions?
  • Multiplying Whole Numbers and Decimals
    • In writing, how do we multiply whole numbers? How do we multiply decimals? How can we find a percent of a number? How can we find the area of a rectangle?
  • Parts of Fractions
    • What does it mean to multiply a number by a fraction? How can we express a fraction as a percent? How can we take a part of a fraction?
  • Parts of Natural Numbers: Part 1
    • In this chapter we will learn to speak the language of arithmetic. This will allow us to relate any two numbers. We will be able to say, for example, that 12 is half of 24, or that 18 is three fourths of 24. We are not concerned here with How do you do it? but, rather, What does that mean?
  • Parts of Natural Numbers: Part 2
    • What do we mean by a mixed number of times? How can we find a part by dividing? How can we find a fifth or 20% of a number? How can we take half of any number? How can we take a fourth or 25% of a number? How can we multiply by 5 or 15? Increase or decrease by a part.
  • Percent Increase or Decrease
    • "Out of" problems and "difference" problems.
  • Percent of a Number
    • In this lesson we will learn how to find the Amount and the Base. Here, we will present examples that require a minimum amount of writing.
  • Percents Are Ratios
    • How do percents express ratios? Percent increase or decrease. Estimations.
  • Powers of 10
    • Which numbers are the powers of 10? How do we read a whole number? What do we mean by the place value of a digit? How do we write a whole number in expanded form? How do we round off a whole number to a given place?
  • Prime Numbers
    • Skills in arithmetic; all about prime numbers.
  • Proper Fractions, Mixed Numbers, Improper Fractions
    • We will see that everything we have learned about ratios will apply to fractions, because, as we will see, each numerator has a ratio to its denominator. And the fraction itself is a number that has a ratio to 1.
  • Proportionality
    • What does it mean to say that two quantities are directly proportional? How do we solve problems of proportionality? What does it mean to say that two quantities are inversely proportional?
  • Ratio and Proportion 1
    • A ratio is a relationship between two quantities of the same kind: A number of people to a number of people; an amount of money to an amount of money; a distance to a distance.
  • Ratio and Proportion 2
    • What is the Theorem of the Alternate Proportion? What is the Theorem of the Same Multiple? What percent of 100 is any number?
  • Short Division
    • Division means finding what number times the divisor will equal the dividend. Ways to practice short division.
  • Subtracting Whole Numbers and Decimals
    • How do we subtract by compensating? How do we subtract by regrouping?
  • The Multiplication Table
    • The importance of knowing the multiplication table cannot be overstated. "Multiplication" of a number is its repeated addition.
  • Unit Fractions
    • What is a unit fraction? How can we express a whole number as a fraction? What do we mean by the complement of a proper fraction?