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# Creating expressions and equations | Lesson

## What are expressions and equations?

On the test, we will be asked to create
expressions
and
equations
based on verbal descriptions. These expressions and equations will involve the
four basic operations
, but will not use more advanced operations such as exponents.
Some questions will ask for expressions or equations based on their verbal description or a real-world context. To create these expressions and equations, we need to familiarize ourselves with the relationship between key words, real-life scenarios, and mathematical operations.

### What skills are tested?

• Translating sentences to mathematical expressions
• Translating sentences to equations

## How do we translate sentences to expressions and equations?

plus
,
minus
,
multiply
,
divide
, and
equal
, we are often presented with other phrases that describe these same mathematical operations. Some of the most common ones are listed in the table below.
EnglishMath
The sum of a and ba, plus, b
The difference between a and b, b is subtracted from aa, minus, b
The product of a and ba, times, b
b times, b of...b, times
The quotient of a and ba, divided by, b or start fraction, a, divided by, b, end fraction
(The result) isequals
A certain number, an unknown quantityx, y, etc.
To translate verbal descriptions of mathematical operations:
1. Identify any key words or phrases that indicate an operation.
2. Combine the individual operations into an expression or equation. Make sure to preserve the order of operations.

## How do we translate real-world contexts to expressions and equations?

In questions with real-world contexts, the mathematical operations are often described by action verbs and comparative phrases. Some more ways we convey mathematical information are listed in the table below.
EnglishMath
b more than aa, plus, b
Increased by bplus, b
b less than aa, minus, b
Decreased by b, reduced by bminus, b
b times (as many)b, times
Double, twice2, times
Triple3, times
To translate verbal descriptions of mathematical operations:
1. Identify any key words or phrases that indicate an operation.
2. Combine the individual operations into an expression or equation. Make sure to preserve the order of operations.

## Practice

TRY: TRANSLATING SENTENCE TO EQUATION
If the product of a certain number and 4 is 64, which of the following equations, when solved, would give us the value of the number?

TRY: TRANSLATING SENTENCE TO EQUATION

When the sum of a certain number and 1 is multiplied by 3, the result is 6.
Which of the following equations matches the description above?

TRY: TRANSLATING REAL-WORLD CONTEXT TO EXPRESSION
At a craft fair, Tony bought 3 items, Isabella bought 1 item, and Tanisha bought 5 times as many items as Tony and Isabella did combined. Which of the following represents the number of items Tanisha bought?

TRY: TRANSLATING REAL-WORLD CONTEXT TO EXPRESSION
At a concert, Anton bought 3 bottles of water for x dollars each and a T-shirt for 25 dollars. Which of the following represents the total amount Anton spent in dollars?

## Things to remember

To translate verbal descriptions of mathematical operations:
1. Identify any key words or phrases that indicate an operation.
2. Combine the individual operations into an expression or equation. Make sure to preserve the order of operations.
EnglishMath
The sum of a and ba, plus, b
b more than aa, plus, b
Increased by b, b is added to...plus, b
The difference between a and b, b is subtracted from a, b less than aa, minus, b
Decreased by b, reduced by bminus, b
The product of a and ba, times, b
b times (as many), b of...b, times
Double, twice2, times
Triple3, times
The quotient of a and ba, divided by, b or start fraction, a, divided by, b, end fraction
(The result) isequals
A certain number, an unknown quantityx, y, etc.