Mathematics
Grade 10
15 min
Inequalities with addition and subtraction of fractions
Inequalities with addition and subtraction of fractions
What you'll learn
- Identify whether a given fraction inequality with addition or subtraction is true or false by finding a common denominator and comparing the resulting fractions.
- Solve for an unknown fraction in an inequality involving addition or subtraction of fractions by using inverse operations and maintaining the inequality's truth.
- Explain, using visual models (e.g., fraction bars or number lines), why adding or subtracting the same fraction to both sides of an inequality maintains the inequality's truth.
- Apply their understanding of fraction inequalities to solve word problems involving real-world scenarios with addition and subtraction of fractions, demonstrating their reasoning with written explanations.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Solve one-step inequalities involving the addition of fractions.
Solve one-step inequalities involving the subtraction of fractions.
Isolate a variable in an inequality by applying the correct inverse operation with fractions.
Find the least common denominator to combine fractions within an inequality.
Represent the solution set of a fractional inequality on a number line.
Verify the solution to an inequality by substituting a valid test value from the solution set.
Translate a real-world scenario into a one-step inequality with fractions and solve it.
A structural beam's length can be at most 15 and 1/2 meters. After cutting off a piece, it is now 14 and 3/4 meters. What is the maximum possible length of the piece that was removed? 📐
This tutori...
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Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two expressions using an inequality symbol, indicating that one expression is less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥) another.x + 1/2 > 3/4
Solution SetThe set of all values for a variable that make an inequality true. Unlike an equation which often has one solution, an inequality typically has an infinite number of solutions.For x > 2, the solution set includes 3, 5, 2.1, and 100, but not 2 or 1.
Inverse OperationAn operation that reverses the effect of another operation. Addition and subtraction are inverse operations, used to isolate a variable.To undo adding 1/4 to a variable, you subtract 1/4 from both sides of the inequality.
Least Common Denominator...
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Core Formulas
Addition Property of Inequality
If a < b, then a + c < b + c. The same property holds true for >, ≤, and ≥.
You can add the same number (including a fraction) to both sides of an inequality without changing the direction of the inequality symbol. This is used to cancel out a subtracted term.
Subtraction Property of Inequality
If a < b, then a - c < b - c. The same property holds true for >, ≤, and ≥.
You can subtract the same number (including a fraction) from both sides of an inequality without changing the direction of the inequality symbol. This is used to cancel out an added term.
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Challenging
The solution set for the inequality x - C > 1/5 is x > 1/2. What is the value of the constant C?
A.3/10
B.7/10
C.-3/10
D.1/7
Challenging
Given the inequality x - a/b ≤ c/d, where a, b, c, and d are all positive integers, which of the following represents the general solution for x?
A.x ≤ (c-a)/(d-b)
B.x ≤ (bc + ad)/bd
C.x ≤ (c+a)/(d+b)
D.x ≥ (bc + ad)/bd
Challenging
A chemical reaction requires the final mass, M, to be greater than 20 and 1/3 grams. The reaction starts with an initial mass, M_initial, and gains 4 and 5/6 grams. Which inequality correctly represents the possible initial mass?
A.M_initial < 15 and 1/2 grams
B.M_initial > 25 and 1/6 grams
C.M_initial < 25 and 1/6 grams
D.M_initial > 15 and 1/2 grams
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Frequently asked questions
What grade level is "Inequalities with addition and subtraction of fractions"?
Inequalities with addition and subtraction of fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Inequalities with addition and subtraction of fractions?
You'll be able to: Identify whether a given fraction inequality with addition or subtraction is true or false by finding a common denominator and comparing the resulting fractions; Solve for an unknown fraction in an inequality involving addition….
Is "Inequalities with addition and subtraction of fractions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Inequalities with addition and subtraction of fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.