Multiplication and division table pdf

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Terms of Use Terms of Use Agreement  The worksheets are in PDF format. You need the FREE Acrobat Reader to view and print PDF files. This article needs additional citations for verification. Multiplication can also be thought of as scaling.

Here we see 2 being multiplied by 3 using scaling, giving 6 as a result. The large rectangle is composed of 20 squares, each having dimensions of 1 by 1. Here 3 and 4 are the “factors” and 12 is the “product”. Thus the designation of multiplier and multiplicand does not affect the result of the multiplication. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property. The inverse operation of multiplication is division.

For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter. United States, the United Kingdom, and other countries where the period is used as a decimal point. In matrix multiplication, there is a distinction between the cross and the dot symbols. The numbers to be multiplied are generally called the “factors”. The number to be multiplied is called the “multiplicand”, while the number of times the multiplicand is to be multiplied comes from the “multiplier”.

The result of a multiplication is called a product. A product of integers is a multiple of each factor. For example, 15 is the product of 3 and 5, and is both a multiple of 3 and a multiple of 5. Multiplying numbers to more than a couple of decimal places by hand is tedious and error prone. Common logarithms were invented to simplify such calculations. The slide rule allowed numbers to be quickly multiplied to about three places of accuracy.

Methods of multiplication were documented in the Egyptian, Greek, Indian and Chinese civilizations. The Ishango bone, dated to about 18,000 to 20,000 BC, hints at a knowledge of multiplication in the Upper Paleolithic era in Central Africa. The Egyptian method of multiplication of integers and fractions, documented in the Ahmes Papyrus, was by successive additions and doubling. The Babylonians used a sexagesimal positional number system, analogous to the modern day decimal system.