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4. Verbal statement vs algebraic statements

Objective:

To learn about the verbal statement and algebraic statements.

Verbal statement and Algebraic statements:

Do you know the difference between the verbal statement and algebraic statements?

Let's see an example to understand this clearly.

Example:

Arun is twice taller than Kumar. That is Arun height is two times larger than Kumar's height. Now, this is known as a verbal statement.

If you write the above verbal statement in an algebraic statement we get,

Let the height of the Kumar is $x$.

Therefore Arun height $=$

2 \times Height of Kumar = 2 \times x = 2 x

In the above example, we understood that normally we use the verbal statement to mention any mathematical operation, then we translate this verbal statement to an algebraic statement to find the unknown value.

Now let's see a few examples of how we are using the verbal and algebraic statement in the mathematical operation.

[Note: In a verbal statement the unknown value $x$ is represented as some number or a number].

Addition keywords: Sum, total, added, increased, more than, etc.

Operation	Phrase	Example -Verbal statement	Algebraic statements
Addition $(+)$	The sum of	The sum of a number and two	$x + 2$
	Plus	A number plus two	$x + 2$
	Increased by	two increased by some number.	$2 + x$

Subtraction keywords: Minus, Decreased by, less than, the difference of, subtracted, etc.

Operation	Phrase	Phrase example - Verbal statement	Algebraic statements
Subtraction $(-)$	Subtracted from	Six subtracted from a number.	$x - 6$
	Decreased by	Six decreased by some number.	$x - 6$
	The difference of	The difference between Six and some number.	$6 - x$

Multiplication keywords: Multiplied by, The product of, Times, Thrice, Twice etc.

Operation	Phrase	Phrase example - Verbal statement	Algebraic statements
Multiplication	Multiplied by	Some number multiplied by eight.	$8 x$
	The product of	The product of negative eight.	$- 8 x$
	Times	Eight times a number.	$8 x$

Division keywords:Divided by, The ratio of, The quotient of, etc.

Operation	Phrase	Phrase example - Verbal statement	Algebraic statements
Division	Divided by	Four divided by some number.	$\frac{x}{12}$
	The ratio of	The ratio of Four to a number.	$\frac{4}{x}$

Using these above, we can also make another operation that is,

Equals keywords: Equals, Is the same as, yields.

Operation	Phrase	Phrase example - Verbal statement	Algebraic statements
Equals	Equals	Six equals to less than two number.	$6 = 2 - x$
		Six is the same as thrice the number.	$6 = 3 x$

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4. Verbal statement vs algebraic statements

Theory: