### Variables and Verbal Expressions Worksheets

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.

Verbal expressions are group of words that comprised a verbal problem or mathematical word problem. Since these would give meaning to the equation/inequality that would represent a problem, one needs to be extra careful in translating any verbal expression into its equivalent mathematical expression.

In this connection, listed below are some of the most commonly used key words to indicate an operation.

Operation Key Words
+
-
minus, subtract, subtracted from, less, less than, decreased by, reduced by, diminished by, difference between
$$\times$$
times, product, multiply, twice, thrice, doubled, tripled, quadrupled, of, as much as
$$\div$$
divide, ratio, quotient, divided by, divided into, partitioned into

After learning the key words for each fundamental operation, let’s try to translate some verbal expressions into its equivalent mathematical expression.
Operation Key Words
Twice a number $$2x$$
A number is subtracted from 10 $$10-x$$
The sum of 9 and a number $$9+x$$
The quotient of a number and 5 $$\displaystyle \frac{x}{5}$$
The ratio of two numbers x and y $$\frac{x}{y}$$
Twice a number decreased by 3 $$2x-3$$
Twenty percent of a number $$20\%x$$
8 more than 3 times a number $$3x+8$$
The sum of two numbers divided by 7 $$\displaystyle \frac{x+y}{7}$$
The quotient of twice a number and 5 $$\displaystyle \frac{2x}{5}$$
The product of a number and 5 decreased by 15 $$5x-15$$
Thrice a number less than 1 $$1-3x$$
Half a number $$\displaystyle \frac{1}{2}x$$
12 less than thrice a number $$3x-12$$
Four times a number more than 20 $$20+4x$$

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