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ARITHMETIC LESSONS

At Mr. X, we practice arithmetic. Then we practice some more. The benefits of knowing and understanding basic arithmetic relationships are priceless. Mastering arithmetic is essential to understanding algebra and all higher mathematics. We have a library of sample arithmetic problems with examples of solved problems for each arithmetic lesson. Check out our free samples below, as well as the arithmetic curriculum. Arithmetic lessons and problems are included with a subscription to Mr. X.

Arithmetic Sample Lesson 1

Arithmetic Sample Lesson 2

Arithmetic Sample Lesson 3

ARITHMETIC CURRICULUM

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Title	Description
Master Percent-Decimal-Fraction Chart 1	Let's take a look at the "official" Mr. X PDF chart.
Master Percent-Decimal-Fraction Chart 2	You have to learn a few fractions in this life. Just a few. Learn them.
Master Percent-Decimal-Fraction Chart 3	We all know that 50 percent is the same as one-half. Learn just a few more fractions. You'll be glad you did!
Master Percent-Decimal-Fraction Chart 4	Here is a nice, long look at the "official" Mr. X master PDF Chart.
New Primary 001 - Numbers and Figures	Counting and recognizing digits comes early.
New Primary 002 - Counting 11 though 30	We continue counting through thirty.
New Primary 003 - Counting 31 though 60	We continue counting through sixty.
New Primary 004 - Counting 61 though 100	We continue counting, reading number names, through one hundred.
New Primary 005 - Numbers to be Read	You should be able to read any of the numbers in this lesson.
New Primary 006 - Numbers to be Written	Learn your digits, how to read them, how to write them, how to recognize them. We focus on two-digit numbers in this lesson.
New Primary 007 - Oral Exercises for Objects	Associate a number made from digits to represent a set of objects. You should be able to answer all of the questions in this lesson.
New Primary 008 - Oral Exercises	We begin arithmetic with no operators or operational symbols. Instead, we rely on "and" for sums and "times" for products. How many are two and six? This is the beginning of arithmetic.
New Primary 009 - Oral Exercises	More questions with "and" and "times" for addition and multiplication, with no operators. "One from nine leaves how many?" This is the beginning of subtraction.
New Primary 010 - Addition	How many birds are two birds and five birds? We sum objects with the conjunction "and."
New Primary 011 - Addition of One	We practice the facts of addition that include adding a single unit to another (integer) value.
New Primary 012 - Addition of Two	We practice sums that add two to a value.
New Primary 013 - Addition of Three	We practice sums that include addition of three to a value.
New Primary 014 - Addition of Four	Addition with four. This lesson practices adding 4.
New Primary 015 - Addition of Five	We practice addition facts with addends of fives.
New Primary 016 - Addition of Six	Addition of six is practiced with a list of facts.
New Primary 017 - Addition of Seven	We practice the facts of basic addition with sevens.
New Primary 018 - Addition of Eight	We practice the facts of adding eight to other one-digit integers.
New Primary 019 - Addition of Nine	Addition of nine includes facts to be learned, to be able to be recalled without effort.
New Primary 020 - Addition of Ten	In our Base-Ten system, addition of ten is especially convenient.
New Primary 021 - Review of Simple Addition	We answer many questions quickly, such as, "How many are two and nine?" We practice the facts and reinforce that the order in which we sum terms does not matter. We sum three terms.
New Primary 022 - Addition with Triple Sets of Integers	We sum three terms. We reduce the work by combining terms to reduce the number of terms. We review basic addition.
New Primary 023 - Reading Review of Simple Addition	We read word problems to reinforce the basic facts of addition for small positive integers.
New Primary 024 - Subtraction	The words "leaves" and "less" and "left" are key to learning the basic concept of subtraction. We still have no operational symbol.
New Primary 025 - Subtraction of One	We practice the facts of subtraction with a subtrahend or difference of one.
New Primary 026 - Subtraction of Two	We practice the facts of subtraction with a subtrahend or difference of two.
New Primary 027 - Subtraction of Three	We practice the facts of subtraction with a subtrahend or difference of three.
New Primary 028 - Subtraction of Four	We practice the facts of subtraction with a subtrahend or difference of four.
New Primary 029 - Subtraction of Five	We practice the facts of subtraction with a subtrahend or difference of five.
New Primary 030 - Subtraction of Six	We practice the facts of subtraction with a subtrahend or difference of six.
New Primary 031 - Subtraction of Seven	We practice the facts of subtraction with a subtrahend or difference of seven.
New Primary 032 - Subtraction of Eight	We practice the facts of subtraction with a subtrahend or difference of eight.
New Primary 033 - Subtraction of Nine	We practice the facts of subtraction with a subtrahend or difference of nine.
New Primary 034 - Subtraction of Ten	We practice the facts of subtraction with a subtrahend or difference of ten.
New Primary 035 - Review Subtraction	You need to recall quickly and easily the basic facts of subtraction.
New Primary 036 - Review Addition and Subtraction	Singular or plural state-of-being verbs do not matter in the language of arithmetic. We may correctly say that "seven less three are four," or "seven less three is four."
New Primary 037 - Review with Sequential Subtraction	We count by numbers other than one, and we count toward lesser values with subtraction. Multiplication is implied in some of the word problems in this lesson.
New Primary 038 - Multiplication	Don't be too quick to enter the world of multiplication before mastering the basic facts of addition and subtraction. Plural versus singular forms of state-of-being verbs do not matter in equating the factors to the product.
New Primary 039 - Multiplicative Identity	When we multiply by one, we employ the multiplicative identity.
New Primary 040 - Multiplication Doubling	Multiplication by two effectively doubles the first (or other) factor or factors.
New Primary 041 - Multiplication Tripling	When we triple a number we multiply that number by three.
New Primary 042 - Multiplication by Four	We practice the basic products that include a factor of four.
New Primary 043 - Multiplication by Five	We practice the basic facts of multiplication with a factor of five.
New Primary 044 - Multiplication by Six	We practice the basic facts of multiplication with a factor of six.
New Primary 045 - Multiplication by Seven	We practice the basic facts of multiplication with a factor of seven.
New Primary 046 - Multiplication by Eight	We practice the basic facts of multiplication with a factor of eight.
New Primary 047 - Multiplication by Nine	We practice the basic facts of multiplication with a factor of nine.
New Primary 048 - Multiplication by Ten	We practice the basic facts of multiplication with a factor of ten. We multiply an integer by ten by writing a following zero.
New Primary 049 - Multiplication Review with Two and Three Simple Factors	We reinforce the basic facts of multiplication. Again, plural versus singular forms of verbs do no matter within the language of arithmetic. We also multiple three factors.
New Primary 050 - Multiplication Around Subtraction	We deal with more complicated forms of math statements in English. We read left-to-right.
New Primary 051 - Promiscuous Questions	Diverse, casual, and random questions related to addition, subtraction, and multiplication.
New Primary 052 - Division	We learn that division is actually a form of multiplication. So we focus on multiplication to learn division.
New Primary 053 - Division with Two	When we divide by two we take half. Two divides evenly into even numbers.
New Primary 054 - Division with Three	We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three.
New Primary 055 - Division with Four	We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four.
New Primary 056 - Division with Five	We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five.
New Primary 057 - Division with Six	We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six.
New Primary 058 - Division with Seven	We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven.
New Primary 059 - Division with Eight	We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight.
New Primary 060 - Division with Nine	We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine.
New Primary 061 - Division with Ten	Because we use a base-ten system, dividing by ten means to move the decimal point. We practice the facts of division with tens by practicing the facts of multiplication that have a factor of ten.
New Primary 062 - Cognitive Division	If you learn your times tables you can answer these questions quickly and easily.
New Primary 063 - Review Situational Division	Simple and straightforward word problems give us a glimpse into the nature of both division and multiplication.
New Primary 064 - Arithmetic Operators	We introduce the operators of arithmetic, the signs (or symbols) for addition, subtraction, multiplication, and division. These are generally read "plus," "minus," "times," and "divided by," respectively. We also officially introduce the equal sign.
New Primary 065 - Addition with Operators	The familiar facts of addition are now presented with the plus-sign operator for taking sums.
New Primary 066 - Practice with Addition Operator	Technically, we transposed lessons LXV and LXVI from Ray's New Primary Arithmetic from 1877. It really does not matter, because Lesson 66 and Lesson 65 both practice with the addition operator, the plus sign.
New Primary 067 - Simple Additional Situations	Word problems allow us to practice basic addition with the powerful symbolism of the language of mathematics.
New Primary 068 - Practice with Situational Operations	Basic statements in mathematics derive from simple situations.
New Primary 069 - Statements with Addition and Subtraction	Read math statements left-to-right, just as we do in English. However, there is no one way to combine terms in a math statement. That is, there is no single or unique way to correctly think about arithmetic.
New Primary 070 - Situations with Addition and Subtraction	Basic word problems allow us to write basic math statements. Generally, there is no single way to do this correctly.
New Primary 071 - Statements with Addition, Subtraction and Multiplication	We look at mathematical statements to begin thinking of numbers a little more abstractly, as entities unto themselves.
New Primary 072A - Cognitive Grouping	The difference between writing a decimal point and writing a multiplication dot for the operation to multiply factors can be a very small distance on the page.
New Primary 072B - Build a Multiplication Table	We design a multiplication table using a standard spreadsheet. The facts are universal, but your design for its look should be your own.
New Primary 072C - Counting with Different Values	With the assistance of the multiplication table, we count by various small integers.
New Primary 072D - Counting with Different Values	With the multiplication table, we count by different values.
New Primary 072E - Uncover Ten Covers	Ten little black "manhole covers" are revealed atop the multiplication table.
New Primary 073 - More Cognitive Grouping	Multiplication, addition, and subtraction commingle in various forms, so that division appears naturally as a consequence of understanding numbers.
New Primary 074 - Promiscuous Questions	Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality.
New Primary 075 - Promiscuous Questions	Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality.
New Primary 076 - Promiscuous Questions	Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality.
New Primary 077 - Promiscuous Questions	Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality.
Percent-Decimal-Fraction Lesson in 11ths	You should know your elevenths. When you see the patterns, 11ths are extremely easy to understand in terms of decimals or percents.
Percent-Decimal-Fraction Lesson in 12ths	You should learn your twelfths. This little lesson reinforces basic twelfths in terms of both decimals and percentages.
Percent-Decimal-Fraction Lesson in 20ths	If you can count by fives, you can quickly understand decimal and percent equivalence for 20ths.
Percent-Decimal-Fraction Lesson in 8ths	Instead of using a calculator every time you encounter a multiple of one eighth, just remember a few facts about them.
Percent-Decimal-Fraction Lesson in 9ths	You should know your ninths, which are exceptionally easy to convert to decimals or percents.
Percent-Decimal-Fraction Lesson in eighths	It is important to know eighths. There is no substitute for practice with fractions, decimals, and percents.
Percent-Decimal-Fraction Lesson in ninths	Know the facts, know the truth about ninths and how they convert to decimals. Learn these and you will have them forever. Just learn them.
Percent-Decimal-Fraction Lesson in twelfths	Look for patterns in basic fractions. Converting twelfths to decimals or percents is actually pretty easy once you catch onto them.
Prime Factorization Lesson 20	Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers. These problems are also part of a Problem Set: Prime Factorization Problem Set 20.
Prime or Composite?	If an integer is prime its only factors (or divisors) are itself and one. This lesson is, essentially, a lesson in the facts of multiplication, which you should know.
Ray Intellectual Arithmetic 007 - Subtraction Table	You need to know these facts. They are basic facts of subtraction and they are essential to understanding what comes later. Learn these facts. They need to reside between your ears, in the circuits of your brain.
Ray's Intellectual Arithmetic 001 - Cognitive Addition	An initial review of counting and simple addition from Ray's New Intellectual Arithmetic ,from 1877.
Ray's Intellectual Arithmetic 002 - More Cognitive Addition	Make sure you understand that the order we take terms to sum does not matter at all. The Commutative Law of Addition is emphasized.
Ray's Intellectual Arithmetic 003 - Addition Table	You need to know all of these facts for simple addition. You need to infuse these facts to the gray matter between your ears. You need to know every single one of these facts.
Ray's Intellectual Arithmetic 004 - Addition of Pairs of One- and Two-Digit Integers	These questions should be automatic. You need to be able to answer all of the questions in this lesson quickly and effortlessly.
Ray's Intellectual Arithmetic 005 - Addition of Multiple Integers	Just as we add two integers together, we may add any number of integers almost as easily, and in any order we choose. A sum of terms does not rely on the order or sequence in which we take the terms; order of the terms does not matter.
Ray's Intellectual Arithmetic 006 - Subtraction	We hope you can answer all of these questions. Your previous practice of arithmetic should make this lesson exceptionally easy and straightforward. Subtraction provides the difference between two values.
Ray's Intellectual Arithmetic 008 - Cognitive Subtraction	Simple word problems provide a glimpse into the meaning of subtraction as a difference between two values.
Ray's Intellectual Arithmetic 009 - Review	Word problems provide a fundamental understanding to the meaning of subtraction and taking the difference between two values.
Ray's Intellectual Arithmetic 010 - Addition and Subtraction with Operators	This is some really good practice with simple integers with both plus and minus signs. You need to get used to working with these symbols. You should do every single one of these problems on your own. Have a knowledgeable person check your answers. Don't use a calculator. Learn these facts to understand the basics of the language of arithmetic.
Ray's Intellectual Arithmetic 011 - Cognitive Addition and Subtraction	Word problems illustrate the concepts of both addition and subtraction. Basic addition facts and basic subtraction facts are reinforced. We express in English and in mathematics the same ideas.
Ray's Intellectual Arithmetic 012 - Multiplication	Basic arithmetic includes our facts from the multiplication table. Simple word problems emphasize these facts, which need to be memorized.
Ray's Intellectual Arithmetic 013 - Multiplication Table with Exercises	What used to be termed "multiplicand" and "multiplier" are now called, simply, factors. The basic facts of multiplication must be memorized. There is no substitute for this knowledge. Learn these facts.
Ray's Intellectual Arithmetic 014 - Cognitive Multiplication	Simple word problems reinforce the basic facts of multiplication.
Ray's Intellectual Arithmetic 015 - More Cognitive Multiplication	This lesson continues the application of your knowledge of the basic facts of multiplication. It is important to build a good foundation in arithmetic.
Ray's Intellectual Arithmetic 016 - Division	Division is just another way to look at multiplication. If you know your facts of multiplication, then division is very straightforward. We define "dividend," "divisor," and "quotient."
Ray's Intellectual Arithmetic 017 - Division Table	This is a systematic review of basic multiplication, as division facts. We recommend learning these facts as multiplication facts. If you memorize the facts of multiplication, then this lesson is a piece of cake.
Ray's Intellectual Arithmetic 018 - Practice in Division	You have to know how many times a smaller number is contained in a larger number.
Ray's Intellectual Arithmetic 019 - Operative Arithmetic Practice	From word problems we practice the basic facts of multiplication, addition, subtraction, and division.
Ray's Intellectual Arithmetic 020 - Fractions	One entire object is called a "unit" or a "whole." We introduce fractions as parts of a whole (unit).
Ray's Intellectual Arithmetic 021 - Reading and Writing Fractions	Fractions need to be understood in several different ways. We do not like the terms "proper fraction" and "improper fraction." Fractions are easy as pie.
Ray's Intellectual Arithmetic 022 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 023 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 024 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 025 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 026 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 027 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 028 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 029 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 030 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 031 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 032 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 033 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 034 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 035 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 036 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 037 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 038 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 039 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 040 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 041 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 042 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Ray's Intellectual Arithmetic 043 - Practice with Fractions	We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and second-nature to you.
Rounding Integers Lesson 17	A lesson in rounding, accompanied by a Problem Set. This basic skill of rounding is important for almost everyone.