Problem 40 - Elementary and Intermediate Algebra

Question

Translate to an algebraic expression. \(t\) subtracted from \(p\)

Step-by-Step Solution

Answer

p - t

Step 1 - Identify the terms

Determine the terms involved in the expression. Here, the terms are given as 't' and 'p'.

Step 2 - Understand the operation

The phrase 'subtracted from' indicates a subtraction operation where the first term comes second in the expression.

Step 3 - Construct the expression

Arrange the terms according to the operation identified. Since 't' is subtracted from 'p', the algebraic expression is constructed as 'p - t'.

Key Concepts

Subtraction in Algebra

Subtraction in algebra might feel a bit different from basic arithmetic subtraction, because now we are dealing with variables alongside numbers. The concept remains the same: subtracting one quantity from another means taking the first quantity and removing the second one from it.

When you see the phrase 'subtracted from', remember that it's a clue. It tells you to reverse the order of the terms—what comes after 'subtracted from' is the starting point. For instance, 't subtracted from p' translates into the algebraic expression:

\(p - t\).

It can be a bit tricky, but with practice, you will get comfortable with spotting these clues in algebraic problems.

So, always read the phrase carefully and place the terms in the correct order for subtraction.

Algebraic Terms

When learning about algebra, it's crucial to understand what algebraic terms are. An algebraic term can be a constant (a fixed number), a variable (a symbol representing a number we don't know yet), or the product of constants and variables.

In the exercise, our terms are 'p' and 't'. Both are variables, representing unknown quantities.

Algebraic terms can also have coefficients, which are numbers multiplied by the variables (e.g., in \(3x\), 3 is the coefficient). They might also have exponents (e.g., \(x^2\), where 2 is the exponent), although in our case, the terms do not include coefficients or exponents.

Always note the type of terms you’re working with, as this helps in correctly understanding and forming algebraic expressions._

Translating Phrases to Expressions

One key skill in algebra is translating verbal phrases into algebraic expressions. This skill requires careful reading and understanding of the language used.

Here are some general steps to help with this:

• Identify the terms: Determine what variables or numbers are involved. In the example given, our terms are 't' and 'p'.
• Understand the operations: Look for words like 'sum', 'difference', 'product', or 'quotient' to identify the mathematical operations needed. In our case, 'subtracted from' points to a subtraction operation.
• Construct the expression: Arrange the terms according to the operation identified. For 't subtracted from p', we write: \(p - t\).

Small practice can boost your confidence. Soon, you’ll be translating phrases to algebraic expressions with ease!