Solve equations with decimals

Learning Objectives Identify one-variable equations that include decimal numbers. Understand and apply the concept of balancing equations using inverse operations. Solve one-step addition and subtraction equations involving decimals. Solve one-step multiplication and division equations involving decimals. Check their solutions by substituting the answer back into the original equation. Translate simple real-world scenarios into one-variable equations with decimals and solve them. Ever wonder how stores calculate your change when you buy multiple items? 💰 Or how a recipe scales up if you need to make 1.5 times the amount? Equations with decimals help us figure these things out! In this lesson, you'll learn how to solve equations where numbers have decimal points. This...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, connected by an equals sign (=).$x + 3.5 = 7.0$ VariableA symbol, usually a letter (like x, y, or a), that represents an unknown number in an equation.In the equation $y - 1.2 = 5.8$, 'y' is the variable. DecimalA number that includes a decimal point, representing a fractional part of a whole number.$0.5$, $2.75$, $10.0$ Inverse OperationsOperations that undo each other. Addition is the inverse of subtraction, and multiplication is the inverse of division.To undo adding 2.5, you subtract 2.5. To undo multiplying by 4, you divide by 4. Balancing EquationsThe principle that whatever operation you perform on one side of an equation, you must perform the exact same operation on the other sid...

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. This keeps the equation 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. This keeps the equation balanced. Multiplication Property of Equality If $a = b$, then $a \times c = b \times c \quad (c \neq 0)$ To undo division in an equation, multiply both sides of the equation by the same non-zero number. This keeps the equation balanced. Division Property of Equality If $a = b$, then $a / c = b / c \quad (c \neq 0)$ To undo multiplication in an equation, divide both sides of the equation by the same n...