Writing an expression for the sequence of operations described below means converting a set of verbal instructions into a mathematical expression. The key is to preserve the order in which each operation is performed, especially when a later operation applies to an entire earlier result Not complicated — just consistent..
You'll probably want to bookmark this section Not complicated — just consistent..
Introduction
A sequence of operations may begin with a number or an unknown quantity, then ask you to add, subtract, multiply, divide, square, or take a square root. To represent that sequence algebraically, choose a variable for the starting value and translate each instruction from left to right.
There is no single correct expression without the actual sequence of operations. And for example, “add 5 to a number and then multiply by 3” produces 3(x + 5), while “multiply a number by 3 and then add 5” produces 3x + 5. The same words and numbers appear in both descriptions, but the different order changes the expression That's the part that actually makes a difference..
What Is a Mathematical Expression?
A mathematical expression is a combination of numbers, variables, operation symbols, and grouping symbols. It represents a value but does not contain an equals sign. An equation, by contrast, states that two expressions are equal Surprisingly effective..
Examples of expressions include:
- x + 8
- 4(n − 3)
- \frac{2x+7}{5}
- y² − 10
A variable, such as x, n, or y, represents an unknown or changing number. In practice, parentheses and fraction bars act as grouping symbols. They show which operations must be completed together before another operation is applied.
Steps for Writing an Expression
1. Identify the starting quantity
Determine what the sequence begins with. If the starting number is unknown, assign it a variable. Common choices include x, n, and y The details matter here..
Take this: if a problem says “a number,” write x. If it says “a number increased by 6,” begin with x + 6 Worth keeping that in mind. Surprisingly effective..
2. List the operations in order
Read the description carefully and record each action in the sequence in which it occurs. Do not rearrange operations merely because another order seems easier Small thing, real impact..
For instance:
- Start with x.
- Add 9.
- Multiply the result by 4.
- Subtract 2.
The order is essential because addition occurs before multiplication in this sequence Easy to understand, harder to ignore..
3. Translate words into mathematical symbols
Use the following common translations:
- “Add,” “increase by,” or “more than” indicates addition.
- “Subtract,” “decrease by,” or “less than” indicates subtraction.
- “Multiply by,” “times,” “double,” or “triple” indicates multiplication.
- “Divide by,” “split into equal groups,” or “the quotient of” indicates division.
- “Square” means raise to the power of 2.
- “Cube” means raise to the power of 3.
- “Square root” means apply the radical operation √.
Pay special attention
