Mathematics
Grade 4
15 min
Solve for the variable: multiplication and division
Solve for the variable: multiplication and division
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the variable in a one-step equation.
Explain that multiplication and division are inverse operations.
Solve for a variable in a multiplication equation (e.g., 5 * n = 20).
Solve for a variable in a division equation (e.g., x / 3 = 6).
Check their solution by substituting the value back into the original equation.
Write a simple multiplication or division equation from a word problem.
If you have 24 cookies to share equally among your friends, but you don't know how many friends are coming, how can you figure it out? 🍪 Let's learn how to solve these kinds of mysteries!
In this lesson, we will learn how to find a missing number in an equation when it involves multiplication or division. This skill is like being a math detective, using c...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA letter or symbol that stands for a number we don't know yet. It's a placeholder for a mystery number.In the equation 3 * p = 12, the letter 'p' is the variable.
EquationA math sentence that says two things are equal. It always has an equals sign (=).7 * 4 = 28 is an equation.
MultiplicationAn operation that combines equal groups to find a total. It's like repeated addition.4 * 6 means 4 groups of 6, which equals 24.
DivisionAn operation that splits a total into equal groups. It's the opposite of multiplication.30 / 5 means splitting 30 into 5 equal groups of 6.
Inverse OperationsOperations that 'undo' each other. Multiplication and division are inverse operations.If you multiply by 5 (4 * 5 = 20), you can undo it by d...
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Core Formulas
The Rule for Solving Multiplication Equations
If a * n = b, then n = b / a
To find the missing number in a multiplication problem, you use the inverse operation, which is division. You divide the total (the product) by the number you know (the factor).
The Rule for Solving Division Equations
If n / a = b, then n = a * b
To find the missing starting number in a division problem, you use the inverse operation, which is multiplication. You multiply the number you divided by and the answer.
4 more steps in this tutorial
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Challenging
A librarian took a total of 'b' books and sorted them onto 9 empty shelves. She put exactly 12 books on each shelf. Which equation correctly finds the total number of books, and what is the value of 'b'?
A.9 * b = 12; b = 1.33
B.b / 9 = 12; b = 108
C.12 / b = 9; b = 1.33
D.b * 12 = 9; b = 0.75
Challenging
A factory produced 120 toy cars. They were packaged into 'p' packages, with 10 cars in each package. Which equation finds the number of packages, and what is the value of 'p'?
A.10 * p = 120; p = 12
B.p / 10 = 120; p = 1200
C.120 * p = 10; p = 12
D.120 / 10 = p; p = 10
Challenging
If 6 * x = 48 and y / 4 = x, what is the value of y?
A.y = 2
B.y = 8
C.y = 12
D.y = 32
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