Mathematics
Grade 9
15 min
Writing subtraction sentences - up to 10
Writing subtraction sentences - up to 10
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Introduction & Learning Objectives
Learning Objectives
Translate verbal phrases involving subtraction into algebraic expressions with variables.
Construct algebraic equations (sentences) from word problems that model a subtraction scenario.
Define variables to represent unknown quantities within a subtraction context.
Incorporate constraints, such as a maximum value of 10, into algebraic sentences using inequalities.
Differentiate between a subtraction expression and a subtraction equation.
Evaluate subtraction expressions for given variable values and verify if they satisfy specified constraints.
You have a $10 budget for a project. How can you create a single mathematical sentence to find your remaining funds for *any* possible expense? 💸 Let's build the algebraic model!
This tutorial elevates the si...
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Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, typically a letter (like x, y, or t), used to represent a quantity that can change or is unknown.In the expression `10 - c`, 'c' is a variable representing the cost of an item.
Algebraic ExpressionA mathematical phrase that contains numbers, variables, and operation symbols. It does not have an equals sign.`10 - x` represents 'the quantity remaining after x is subtracted from 10'.
Equation (or Sentence)A mathematical statement that asserts the equality of two expressions. It contains an equals sign (=).`10 - x = 3` is an equation stating that the result of subtracting x from 10 is 3.
MinuendThe initial quantity or the number from which another number (the subtrahend) is to be subtracted.In `10 - x`, the number 10 is the minuend....
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Core Formulas
General Subtraction Expression
a - b
Used to represent the difference between an initial amount (minuend, `a`) and an amount that is removed, lost, or used (subtrahend, `b`). This is the foundation for building any subtraction sentence.
General Subtraction Equation
a - b = c
Used when the final result (difference, `c`) is known. This creates a complete mathematical 'sentence' that can often be solved for an unknown variable.
Constraint for 'Up To 10'
expression \leq 10
When a problem states a value is 'at most 10', 'no more than 10', or 'up to 10', this inequality is used. The symbol `\leq` means 'less than or equal to'.
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Challenging
A system's memory starts at 10 MB. A process uses `x` MB. The remaining memory, `R = 10 - x`, must be at least 4 MB. Additionally, the memory used, `x`, must be an integer greater than 2. What is the sum of all possible integer values for `x`?
A.15
B.18
C.21
D.9
Challenging
Situation 1 is modeled by `10 - a = 5`. Situation 2 is modeled by `10 - b < 5`. Assuming `a` and `b` are positive numbers, what is the relationship between `a` and `b`?
A.a < b
B.a > b
C.a = b
D.a ≤ b
Challenging
A company's profit in the first quarter was `10 - x` million dollars. In the second quarter, its profit was `10 - y` million dollars. The profit decreased from the first quarter to the second. Which inequality represents this?
A.10 - x < 10 - y
B.x - y < 10
C.10 - x > 10 - y
D.y - x > 10
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