S k i l l   i n   A r i t h m e t i c

Home

To view these pages as intended, it is best to view them with Internet Explorer 6 or Firefox 3, and with Garamond as the font.

---

Introduction

Prologue 1     Elementary Addition

Sums less than 10.  Composing 10 itself.
Sums between 10 and 20.  Zero.

Prologue 2     The Multiplication Table

The classes: Ones, thousands, millions, billions, and so on.
What is a unit?
Place value.  Positional numeration.
Expanded form.
How to round off a whole number.
How to multiply a whole number by a power of 10.

Lesson 2    The Meaning of Decimals

Cardinal and ordinal numbers.
Division into equal parts. The decimal units.
How to write and how to read a decimal.
Trailing 0's. Leading 0's.
How to compare decimals.

How to multiply a decimal by a power of 10.
How to divide a decimal by a power of 10.
Per centum -- For each 100.
How to take 1% of a number.
How to take 10%.
Scientific notation.
Conversions within the metric system.

Regrouping to form a multiple of 10.
Adding by endings.
Adding from left to right by place value.
Rounding off.

Written calculations.

What number must we add?
Completing 100.  Rounding off.

Written calculation by compensating.
Written calculation by regrouping.

The multiplier, the multiplicand, the product.
Factors and the order property.
Multiplying whole numbers that end in 0's.
Decomposing the multiplier.
Decomposing the multiplicand:
   The "distributive" property.
Rounding off.

Written calculation.
How to find a percent of a number.
The area of a rectangle.

Lesson 10    The Meaning of Division

The divisor, the dividend, and the quotient.
Rates.  Exact versus inexact division.
The division bar.
Mental calculation: Decomposing the  dividend.
The divisor a decimal.

Lesson 11    Short Division

What is short division?
The dividend a decimal.
How to round off a decimal.
How to express the quotient as a decimal.
The dividend less than the divisor.
Calculator problems.

Lesson 12    Dividing Decimals  

The divisor a decimal.

Lesson 13    Percent with a Calculator  

Lesson 14    Parts of Natural Numbers 1  

The natural numbers.
The definition of a part of a number.
Percent -- parts of 100%.

Lesson 15    Parts of Natural Numbers 2  

Increase or decrease by a given part.
A mixed number of times.
The percent that means a third.
Half of any number.
A fourth or 25% of a number.
5% of a number -- 15%.

Lesson 16    Ratio and Proportion  1  

The definition of the ratio of two natural numbers.
Percents are ratios.
The definition of a proportion.
Lowest terms.
The theorem of the common divisor.

Lesson 17    Ratio and Proportion  2  

How to solve proportions by the theorem of the same multiple.
How to find a percent by the method of proportions.

Lesson 18    Proportionality  

"Directly" proportional.
"Inversely" proportional.

Fractions are numbers that we need for measuring.
How to place a fraction on the number line.
How to change an improper fraction to a mixed number.
How to change a mixed number to an improper fraction.
The relative sizes of fractions.
"Out of."

Lesson 20    Unit Fractions  

How to express a whole number as a fraction.  
The complement of a proper fraction.
How to subtract a proper fraction from a whole number.

Lesson 21    Equivalent Fractions  

How to change denominators.
How to simplify or reduce a fraction.
How to clear a fraction of decimals.

Lesson 22    Lowest Common Multiple  

How to find the LCM of two numbers.
How to compare fractions with different denominators.
The ratio of two fractions.
Comparing fractions to ½.

Lesson 23    Fractions into Decimals  

What is a "decimal fraction"?
Frequent decimals and frequent percents:     Half, quarters, eighths, thirds, fifths.
Exact versus inexact decimals.

How to multiply a fraction by a whole number.
How to multiply a fraction by a fraction.
Dividing fractions compared to adding them.

The meaning of multiplying a number by
a fraction.
How to express a fraction as a percent.
How to take a part of a fraction.

Lesson 27    Percents are Ratios  

The ratio to 100%.
Percent increase or decrease. Estimations.

Lesson 28    Percent of a Number  

Finding the Amount.
The meaning of ½%.
Finding the Base.

Finding the Percent.

Lesson 30    Percent Increase or Decrease  

"Out of" problems versus "difference"
 problems.
Banking problems.

Lesson 31    Prime Numbers  

The definition.  Prime factorization.
Is there a last prime?

How to find the GCD and the LCM of two numbers from their prime factorizations.