Navigating Word Problems: Stating Mathematical Equations Clearly

Mathematical word problems can often be intimidating, especially when it comes to formulating and solving them. However, by understanding and identifying key words and phrases, you can easily translate these problems into mathematical equations. In this article, we will explore how to identify and use these key words to write and solve mathematical equations accurately.

Understanding Key Words for Addition

Addition is one of the fundamental operations in mathematics. Key words that signify addition include:

Increased by More than Combined together Added to Plus

For example, a word problem might state, 'A number increased by 5 is 12.' This can be translated into the equation: x 5 12.

Identifying Key Words for Subtraction

Subtraction is the inverse of addition, and key words that signify subtraction include:

Decreased by Minus Less Difference between/of Leftover

Consider the problem, 'A number decreased by 3 is 7.' This translates to the equation: x - 3 7.

Multiplication in Word Problems

Multiplication is used to find the total when the same number is added to itself multiple times. Key words that indicate multiplication are:

Of Times Multiplication Product of

For example, 'Three times a number is 21.' This can be written as: 3x 21.

Division Key Words in Problem-Solving

Division is used to find out how many times one number is contained within another. Key words that denote division are:

Per A Out of Ratio of Quotient of

Consider the problem, 'There are 16 books equally divided among 4 shelves.' This translates to: 16 / 4 x.

Key Words for Equality

Understanding key words related to equality is crucial to correctly formulating equations. Common equality-related key words include:

Is Are Was Were Will be Gives Yields Sold for Cost

An example might be, 'If you are selling oranges for $2 each, how much will 10 oranges cost?' This translates to: 2x 20.

Variables and Unknowns

A variable is a symbol, usually a letter, used to represent an unknown quantity. It is essential to identify the unknown and assign it a variable in your equation. For instance, if a problem states, 'Twice a number less 5 equals 11,' you can write:

2x - 5 11, where x is the unknown number.

By following these steps and understanding the key words and phrases associated with each operation, you can confidently tackle mathematical word problems and accurately translate them into equations. This skill is invaluable not only for academic success but also for real-world problem-solving scenarios that involve mathematics.

Keywords: word problems, mathematical equations, key words