How to Translate Phrases into an Algebraic Statement?
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What are Algebraic Statements?
An algebraic statement, or algebraic expression, uses numbers, variables, and operations to describe a quantity. A phrase such as "a number increased by 5" can be translated into \(x + 5\). If a statement includes an equals sign, it becomes an equation.
Operation Words
The key is to decide what operation each phrase describes and in what order the parts should appear.
- Addition words: plus, increased by, more than, sum.
- Subtraction words: minus, decreased by, less than, difference.
- Multiplication words: times, product, twice, double.
- Division words: quotient, divided by, ratio, per.
Watch the Order
Order matters for subtraction and division. "A number decreased by \(8\)" is \(x - 8\), but "\(8\) decreased by a number" is \(8 - x\). "The quotient of a number and \(5\)" is \(\frac{x}{5}\), while "the quotient of \(5\) and a number" is \(\frac{5}{x}\).
Translate Phrases into an Algebraic Statement
Think of this lesson as more than a rule to memorize. Translate Phrases into an Algebraic Statement is about translating words into expressions and simplifying structure. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.
The most important move is to name what is given, identify what is being asked, and choose the rule that connects those two pieces.
Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.
- Read what is given and what is being asked.
- Choose the rule that connects them.
- Substitute carefully and simplify in small steps.
- Check the final answer against the original question.
A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.
Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.
When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.
On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.
Free printable Worksheets
Exercises for Translate Phrases into an Algebraic Statement
1) Write an expression for a number plus \(6\).
2) Write an expression for \(11\) less than a number.
3) Write an expression for \(5\) times a number.
4) Write an expression for the quotient of a number and \(9\).
5) Write an expression for the sum of twice a number and \(7\).
6) Write an expression for \(4\) more than \(3\) times a number.
7) Write an expression for \(12\) decreased by a number.
8) Write an expression for a number decreased by \(12\).
9) Write an expression for the product of \(6\) and the sum of a number and \(2\).
10) Write an expression for half of a number minus \(5\).
11) Write an expression for \(3\) less than twice a number.
12) Write an expression for the difference of \(4\) times a number and \(9\).
13) Write an expression for \(9\) less than the product of \(5\) and a number.
14) Write an expression for the quotient of a number increased by \(8\) and \(3\).
15) Write an expression for the quotient of \(8\) and a number, increased by \(3\).
16) Write an expression for the square of a number decreased by \(4\).
17) Write an expression for the product of a number and \(1\) less than the number.
18) Write an expression for the sum of the square of a number and \(5\).
19) Write an expression for \(2\) more than \(3\) times the quantity \(x - 7\).
20) Write an expression for the quotient of the difference between twice a number and \(5\), and the sum of the number and \(1\).
1) \(x + 6\). Step 1: Let the number be \(x\). Step 2: "plus \(6\)" means add \(6\).
2) \(x - 11\). Step 1: Let the number be \(x\). Step 2: "\(11\) less than a number" means subtract \(11\) from the number.
3) \(5x\). Step 1: Let the number be \(x\). Step 2: "\(5\) times" means multiply by \(5\).
4) \(\frac{x}{9}\). Step 1: Let the number be \(x\). Step 2: "quotient of a number and \(9\)" means \(x\) divided by \(9\).
5) \(2x + 7\). Step 1: Twice a number is \(2x\). Step 2: The sum with \(7\) is \(2x + 7\).
6) \(3x + 4\). Step 1: \(3\) times a number is \(3x\). Step 2: \(4\) more means add \(4\).
7) \(12 - x\). Step 1: Let the number be \(x\). Step 2: "\(12\) decreased by a number" means subtract the number from \(12\).
8) \(x - 12\). Step 1: Let the number be \(x\). Step 2: "a number decreased by \(12\)" means subtract \(12\) from the number.
9) \(6(x + 2)\). Step 1: The sum of a number and \(2\) is \(x + 2\). Step 2: The product with \(6\) is \(6(x + 2)\).
10) \(\frac{x}{2} - 5\). Step 1: Half of a number is \(\frac{x}{2}\). Step 2: "minus \(5\)" means subtract \(5\).
11) \(2x - 3\). Step 1: Twice a number is \(2x\). Step 2: "\(3\) less than" means subtract \(3\).
12) \(4x - 9\). Step 1: \(4\) times a number is \(4x\). Step 2: The difference of that and \(9\) is \(4x - 9\).
13) \(5x - 9\). Step 1: The product of \(5\) and a number is \(5x\). Step 2: "\(9\) less than" means subtract \(9\).
14) \(\frac{x + 8}{3}\). Step 1: A number increased by \(8\) is \(x + 8\). Step 2: The quotient with \(3\) is \(\frac{x + 8}{3}\).
15) \(\frac{8}{x} + 3\). Step 1: The quotient of \(8\) and a number is \(\frac{8}{x}\). Step 2: "increased by \(3\)" means add \(3\) after the quotient.
16) \(x^2 - 4\). Step 1: The square of a number is \(x^2\). Step 2: "decreased by \(4\)" means subtract \(4\).
17) \(x(x - 1)\). Step 1: \(1\) less than the number is \(x - 1\). Step 2: The product with the number is \(x(x - 1)\).
18) \(x^2 + 5\). Step 1: The square of a number is \(x^2\). Step 2: The sum with \(5\) is \(x^2 + 5\).
19) \(3(x - 7) + 2\). Step 1: The quantity \(x - 7\) stays in parentheses. Step 2: \(3\) times that quantity is \(3(x - 7)\), and \(2\) more gives \(3(x - 7) + 2\).
20) \(\frac{2x - 5}{x + 1}\). Step 1: The difference between twice a number and \(5\) is \(2x - 5\). Step 2: The sum of the number and \(1\) is \(x + 1\). Step 3: The quotient is \(\frac{2x - 5}{x + 1}\).
Translate Phrases into an Algebraic Statement Practice Quiz
