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The following lessons provide some basic understanding of Integers.

MATH MILESTONE #B2: INTEGERS

Mathematics of integers appears to be quite troublesome to most students. But when we look at it as arithmetic with increase and decrease from zero, it becomes easy to grasp.

Confusion takes place because “plus” and “minus,” which represent operations between two numbers, are also used to show a number as “positive” or ‘”negative.” This becomes clear when integers are defined as being referenced from zero.

–1   =    0 – 1

+1   =    0 + 1

This allows us to convert “positive” or ‘”negative” signs into “plus” and “minus” operations, and vice versa.

Furthermore, confusion arises when “plus” and “minus” operate on “positive” and “negative” numbers, giving consecutive signs. However, once we understand that LIKE consecutive signs produce a positive number…

– (–1)      =     +1

+ (+1)      =     +1

…and UNLIKE consecutive signs produce a negative number, the operations are greatly simplified.

– (+1)      =     –1

+ (–1)      =     –1

Here are some videos from Khan Academy on the subject of Integers.

Negative Numbers Introduction

Adding/Subtracting negative numbers

Multiplying and dividing negative numbers

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To practice Mixed Operations, go to the link

MATH MILESTONE # B1: MIXED OPERATIONS

When the various operations of addition, subtraction, multiplication and division are present together in an arithmetic expression we have mixed operations.

Counting is the beginning of computation.

Addition is “counting together,” and therefore, it is an operation of first order. Subtraction, being opposite, or inverse, of addition, is also an operation of first order.

When addition and subtraction are present together they may be carried out from left to right in that sequence. An operation on the right may be carried out first only when there is addition to its left.

Multiplication consists of repeated additions. Therefore, multiplication is an operation of second order. Division, being opposite, or inverse, of multiplication is also an operation of second order.

When multiplication and division are present together they may be carried out from left to right in that sequence.

In mixed operations, second order operations always take priority over first order operations.

Multiplication, division, and parentheses (which group operations) make up the individual terms. “Plus” and “minus” separate the individual terms from each other in an arithmetic expression.

Always compute the individual terms first before you compute the arithmetic expression completely.

Thus, the concept of terms automatically enforces the precedence of second order operations over first order operations.

Understanding this logic involved in reducing mixed operations is very important. Only when you understand this logic, do the various “formulas” about the precedence of operations make sense.

Here are some videos on this subject from Khan Academy.

Introduction to Order of Operations

More Complicated Order of Operations Example

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