Mathematics
Grade 6
15 min
Solve one-step equations: word problems
Solve one-step equations: word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the unknown quantity in a word problem and represent it with a variable.
Translate word problems into one-step algebraic equations involving addition, subtraction, multiplication, or division.
Determine the correct inverse operation needed to solve a one-step equation.
Apply inverse operations to isolate the variable and solve one-step equations.
Check their solution to a one-step equation within the context of the original word problem.
Solve real-world problems by setting up and solving one-step equations.
Ever wonder how math helps you figure out how many cookies are left after your friends visit? 🍪 Let's unlock the power of equations to solve everyday mysteries!
In this lesson, you'll learn how to turn everyday stories into simple...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA letter or symbol (like 'x' or 'n') used to represent an unknown number or quantity in a mathematical expression or equation.In the problem 'x + 5 = 10', 'x' is the variable representing the unknown number.
EquationA mathematical statement that shows two expressions are equal, usually containing an equals sign (=).2 + 3 = 5 is an equation. x - 7 = 12 is also an equation.
One-Step EquationAn equation that can be solved by performing only one mathematical operation (addition, subtraction, multiplication, or division) to both sides.x + 8 = 20 is a one-step equation because you only need to subtract 8 from both sides to solve it.
Word ProblemA math problem presented in a story or sentence format, requiring you to read, und...
3
Core Formulas
Addition Property of Equality
If $a = b$, then $a + c = b + c$.
To undo subtraction in an equation, add the same number to both sides of the equation to keep it balanced.
Subtraction Property of Equality
If $a = b$, then $a - c = b - c$.
To undo addition in an equation, subtract the same number from both sides of the equation to keep it balanced.
Multiplication Property of Equality
If $a = b$, then $a \cdot c = b \cdot c$ (where $c \neq 0$).
To undo division in an equation, multiply both sides of the equation by the same non-zero number to keep it balanced.
Division Property of Equality
If $a = b$, then $a / c = b / c$ (where $c \neq 0$).
To undo multiplication in an equation, divide both sides of the equation by the same non-zero number to keep it balanced....
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A student solves the problem: 'A recipe needs 4 cups of sugar. You have 1.5 cups. How much more do you need?' They set up `s + 1.5 = 4` and solve it, getting `s = 2.5`. They then say, 'The answer is 2.5'. What is missing from their final answer?
A.The units (cups)
B.The variable 's'
C.The inverse operation
D.The original equation
Challenging
The equation `k / 4 = 8` is solved correctly to find `k = 32`. Which of the following word problems could this equation and solution represent?
A.pizza is cut into 8 slices. After 4 slices are eaten, how many are left? Answer: 32 slices.
B.group of 4 friends share a box of crayons. Each friend gets 8 crayons. How many crayons were in the box? Answer: 32 crayons.
C.There are 32 students in a class. They are put into 4 groups. How many students are in each group? Answer: 8 students.
D.plant grows 4 inches every week. How many weeks will it take to be 8 inches tall? Answer: 32 weeks.
Challenging
A student is told that a number 'n' decreased by 19 is 5. The student incorrectly sets up the equation as `19 - n = 5`. Why is this setup conceptually wrong for the given phrase?
A.The student should have used addition.
B.The student should have used multiplication.
C.The phrase 'n decreased by 19' means you start with 'n' and subtract 19 from it, not the other way around.
D.The variable 'n' should be on the right side of the equals sign.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free