# Posts Tagged: "arithmetic"

## Variables and Verbal Expressions

- -

Some real-life situations involving numbers can directly be solved using the four fundamental operations: addition, subtraction, multiplication and division. For instance, if 1 apple cost 5 pesos, how much do 15 apples cost? To solve this problem simply multiply 15 by 5. However, there are other practical applications which can best be solved by looking for a general pattern, relationship or formula before arriving at the answers.

An example would be, study the sequence: 2, 4, 8, 16, 32 and so on, what is the sum of the first 12 numbers in this sequence? This problem entails a formula to shorten the procedure. It is on this context, that the core of Algebra lies on representing quantities, patterns or relationships by symbols other than numbers. These symbols, which can be any letter in the English alphabet, are called variables that can take on more than one value. These symbols can further be grouped using the four fundamental operations, which in turn give meaning to equations or inequalities. These groups of symbols are called mathematical expressions which are used to represent verbal expressions or phrases.

## Evaluating Variable Expressions

- -

A variable is a letter which is used to represent a number or a set of numbers. It is usually denoted by a letter of the English alphabet. Greek letters too can denote a variable. Examples of variables are x, y, r, s, t, and n.

Greek letters such as $\alpha$, and $\beta$ can be used also to denote a variable.

## Order of Operations (PEMDAS)

- -

The order of operations in mathematics, also known as PEMDAS which stands for (Parentheses, Exponents), (Multiplication, Division), and (Addition, Subtraction), is generally use to perform indicated operations in algebra or arithmetic. The calculator itself is performing operations based on PEMDAS rules.

## Multiplying Decimals

- -

Multiplying decimals is similar with multiplying whole numbers. To multiply decimals, we may disregard the decimal points and just treat the decimal number as whole number. Following the rule for multiplying whole numbers, multiply the last digit in the multiplier with every digit in the multiplicand. Then multiply the second digit (from the right) of the multiplier to every digit of the multiplicand but place the first product or the unit digit of the first product one positional value below from the first digit of the first line of products obtained from multiplying the first digit in the multiplier and the digits in the multiplicand. Follow the same rule until all the digits in the multiplier have been multiplied to all the digits in the multiplicand. Add all the partial products by following addition rule for whole numbers. Count the total number of places to the right of the decimal point in the multiplier and in the multiplicand. The number of digits to the right of the decimal point of the product is equal to the number of places in these factors.

## Multiplying Integers

- - Pre-Algebra

Recall that the set of counting numbers is closed over multiplication. Thus, the set of positive integers, also known as counting numbers is closed over multiplication. This implies that if two positive integers are multiplied then their product is also a positive. It has been previously known that multiplication is a repeated addition.

## Dividing Integers

- - Pre-Algebra

The rules for dividing integers follow from the rules for multiplying integers since these two operations are reversed operations. After teaching these rules, dividing integers worksheets are essential tools to evaluate learning of students.

## Adding and Subtracting Fractions and Mixed Numbers

- - Pre-Algebra

Before learning how to add and subtract fractions and mixed numbers, let us recall some terminologies like similar fractions, dissimilar fractions, proper fraction, improper fraction and mixed number. Similar fractions are fractions with like or the same denominator while dissimilar fractions are those with unlike or different denominators.

A proper fraction is a fraction whose numerator is less than its denominator while an improper fraction is a fraction whose numerator is greater than its denominator. Lastly, a mixed number contains a whole number and a proper fraction. The rules for adding and subtracting fractions would greatly depend on the kind of fractions to be added or subtracted.

## Addition and Subtraction of Decimals

- - Pre-Algebra

If one knows how to add and subtract whole numbers, then he must for sure know how to add and subtract decimals. Adding and subtracting decimal numbers is very similar to adding and subtracting whole numbers. In adding and subtracting decimals, see to it that the decimal points are aligned so the digits with the same place value must properly be aligned.

## Adding and Subtracting Integers or Whole Numbers

- - Pre-Algebra

Adding and subtracting integers or whole numbers need the understanding of positive and negative integers. From your previous experience in arithmetic you are aware of the necessity for a system of numbers which will denote direction as well as amount. Thus, if +3 indicates 3 units to the right on a number scale, -3 indicates 3 units to the left.

## Converting between Fractions, Decimals, and Percents

- - Pre-Algebra

Percents are widely used in business and everyday life. Business professionals use percent to calculate percent of loss or profit, and percent of increase or decrease in transactions such as sales, cost and expenses. Retailers and dealers use percent to give discount to their customers. Consumers are concerned with the percent of change of prices while employees are worried with the percent of their salaries paid in taxes.