Mathematics
Grade 7
15 min
Solve equations with whole numbers
Solve equations with whole numbers
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1
Introduction & Learning Objectives
Learning Objectives
Define an equation and identify its components (variables, constants, operations).
Identify the inverse operation needed to isolate a variable in a one-step equation.
Apply the properties of equality (addition, subtraction, multiplication, division) to solve one-step equations with whole numbers.
Solve one-step equations involving addition, subtraction, multiplication, and division where the solution is a whole number.
Check their solutions by substituting the value of the variable back into the original equation.
Understand the concept of maintaining balance in an equation.
Ever wonder how detectives solve mysteries? 🕵️♀️ Just like them, we use clues to find missing pieces! In math, we'll learn to find missing numbers in equations.
This lesson wil...
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Key Concepts & Vocabulary
TermDefinitionExample
EquationA mathematical statement that shows two expressions are equal, using an equals sign (=). It's like a balanced scale.x + 5 = 12
VariableA symbol, usually a letter (like x, y, or a), that represents an unknown number in an equation.In the equation 3y = 21, 'y' is the variable.
Whole NumbersThe set of non-negative integers (0, 1, 2, 3, ...). These are the numbers we use for counting and zero.7, 0, 15, 100 are whole numbers; -3 and 0.5 are not.
Inverse OperationsOperations that undo each other. Addition is the inverse of subtraction, and multiplication is the inverse of division.To undo adding 8, you subtract 8. To undo multiplying by 4, you divide by 4.
SolutionThe value of the variable that makes the equation a true statement.For x + 5 = 12, the...
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Core Formulas
Addition Property of Equality
If \(a = b\), then \(a + c = b + c\)
You can add the same whole number to both sides of an equation, and the equation will remain balanced and true.
Subtraction Property of Equality
If \(a = b\), then \(a - c = b - c\)
You can subtract the same whole number from both sides of an equation, and the equation will remain balanced and true.
Multiplication Property of Equality
If \(a = b\), then \(a \cdot c = b \cdot c\) (where \(c \neq 0\))
You can multiply both sides of an equation by the same non-zero whole number, and the equation will remain balanced and true.
Division Property of Equality
If \(a = b\), then \(\frac{a}{c} = \frac{b}{c}\) (where \(c \neq 0\))
You can divide both sides of an equation by the same non-zero whole numbe...
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Challenging
Which of the following equations has a solution of n = 14?
A.n + 14 = 0
B.14n = 14
C.n / 2 = 7
D.28 - n = 12
Challenging
When solving the equation x + 8 = 20, we use the Subtraction Property of Equality to subtract 8 from both sides. Why does this specific step help us find the solution?
A.It isolates the variable 'x' by creating 'x + 0' on one side.
B.It makes the numbers in the equation smaller and easier to work with.
C.It moves all the numbers to the right side of the equation.
D.It is the only operation allowed on an addition problem.
Challenging
A student claims the whole number solution to 15x = 220 is x = 14. Which statement below is the most accurate evaluation of this claim?
A.The claim is correct because 220 is close to 15 times 14.
B.The claim is incorrect; the student should have subtracted 15 from 220.
C.The claim is correct because the student used the Division Property of Equality.
D.The claim is incorrect; checking the solution shows 15 * 14 = 210, not 220.
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