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Creating expressions and equations | Lesson

What are expressions and equations?

On the test, we will be asked to create

and

based on verbal descriptions. These expressions and equations will involve the

, 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?

In addition to the words

, and

, 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.

English	Math
The sum of $a$ ‍ and $b$ ‍	$a + b$ ‍
$b$ ‍ is added to...	$+ b$ ‍
The difference between $a$ ‍ and $b$ ‍, $b$ ‍ is subtracted from $a$ ‍	$a - b$ ‍
The product of $a$ ‍ and $b$ ‍	$a \times b$ ‍
$b$ ‍ times, $b$ ‍ of...	$b \times$ ‍
The quotient of $a$ ‍ and $b$ ‍	$a \div b$ ‍ or $\frac{a}{b}$ ‍
(The result) is	$=$ ‍
A certain number, an unknown quantity	$x$ ‍, $y$ ‍, etc.

To translate verbal descriptions of mathematical operations:

Identify any key words or phrases that indicate an operation.
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.

English	Math
$b$ ‍ more than $a$ ‍	$a + b$ ‍
Increased by $b$ ‍	$+ b$ ‍
$b$ ‍ less than $a$ ‍	$a - b$ ‍
Decreased by $b$ ‍, reduced by $b$ ‍	$- b$ ‍
$b$ ‍ times (as many)	$b \times$ ‍
Double, twice	$2 \times$ ‍
Triple	$3 \times$ ‍

To translate verbal descriptions of mathematical operations:

Identify any key words or phrases that indicate an operation.
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

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:

Identify any key words or phrases that indicate an operation.
Combine the individual operations into an expression or equation. Make sure to preserve the order of operations.

English	Math
The sum of $a$ ‍ and $b$ ‍	$a + b$ ‍
$b$ ‍ more than $a$ ‍	$a + b$ ‍
Increased by $b$ ‍, $b$ ‍ is added to...	$+ b$ ‍
The difference between $a$ ‍ and $b$ ‍, $b$ ‍ is subtracted from $a$ ‍, $b$ ‍ less than $a$ ‍	$a - b$ ‍
Decreased by $b$ ‍, reduced by $b$ ‍	$- b$ ‍
The product of $a$ ‍ and $b$ ‍	$a \times b$ ‍
$b$ ‍ times (as many), $b$ ‍ of...	$b \times$ ‍
Double, twice	$2 \times$ ‍
Triple	$3 \times$ ‍
The quotient of $a$ ‍ and $b$ ‍	$a \div b$ ‍ or $\frac{a}{b}$ ‍
(The result) is	$=$ ‍
A certain number, an unknown quantity	$x$ ‍, $y$ ‍, etc.

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Praxis Core Math

Course: Praxis Core Math > Unit 1

What are expressions and equations?

What skills are tested?

How do we translate sentences to expressions and equations?

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

Practice

Things to remember

Want to join the conversation?