Mathematics
Grade 10
15 min
Inequalities with addition and subtraction of mixed numbers
Inequalities with addition and subtraction of mixed numbers
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1
Introduction & Learning Objectives
Learning Objectives
Convert mixed numbers to improper fractions to facilitate calculations in inequalities.
Apply the Addition Property of Inequality to solve for a variable when mixed numbers are involved.
Apply the Subtraction Property of Inequality to solve for a variable when mixed numbers are involved.
Find a common denominator to accurately add or subtract fractional components within an inequality.
Express the solution set of an inequality as a simplified mixed number or improper fraction.
Represent the solution set of a mixed number inequality on a number line.
Imagine you're designing a bookshelf and a specific shelf must be at least 3 ½ inches taller than a 10 ¾ inch book. How do you calculate the minimum required height? 📏
This tutorial revisits the fundame...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number composed of a whole number and a proper fraction.4 ½ (four and one-half)
Improper FractionA fraction in which the numerator is greater than or equal to the denominator, representing a value of one or greater.9/2 (which is equivalent to 4 ½)
InequalityA mathematical statement that asserts that two quantities are not equal. It uses symbols like > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).x + 2 > 5
Addition Property of InequalityAdding the same number to both sides of an inequality does not change the truth of the inequality.If x - 3 > 7, then adding 3 to both sides gives x > 10.
Subtraction Property of InequalitySubtracting the same number from both sides of an inequality does not chan...
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Core Formulas
Conversion: Mixed Number to Improper Fraction
a \frac{b}{c} = \frac{(a \times c) + b}{c}
To perform arithmetic operations like addition or subtraction, it is almost always easier to first convert all mixed numbers into improper fractions.
Addition Property of Inequality
If A < B, then A + C < B + C
Use this property to isolate a variable when a number is being subtracted from it. Add the same value to both sides of the inequality.
Subtraction Property of Inequality
If A > B, then A - C > B - C
Use this property to isolate a variable when a number is being added to it. Subtract the same value from both sides of the inequality.
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Challenging
Find the solution for the inequality: x + 4 \frac{1}{2} - 2 \frac{1}{3} ≤ 7 \frac{5}{6}
A.x ≤ 5 \frac{2}{3}
B.x ≥ 5 \frac{2}{3}
C.x ≤ 6 \frac{1}{6}
D.x ≤ 5 \frac{1}{2}
Challenging
Solve for y: 20 \frac{1}{4} - y > 14 \frac{2}{3}
A.y > 5 \frac{7}{12}
B.y < 5 \frac{7}{12}
C.y < 34 \frac{11}{12}
D.y > 34 \frac{11}{12}
Challenging
Given a - 3 \frac{1}{2} > 1 \frac{1}{3} and b + 2 \frac{1}{4} < 8 \frac{1}{2}. What is the difference between the smallest possible integer value of 'a' and the largest possible integer value of 'b'?
A.1
B.0
C.-1
D.2
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